plastics testing and characterization - industrial applications

Alberto NaranjoMaría del Pilar Noriega E.Tim A. OsswaldAlejandro Roldán-AlzateJuan Diego Sierra

Plastics Testingand Characterization

Industrial Applications

Hanser Publishers, Munich • Hanser Gardner Publications, Cincinnati

The Authors:Prof. Dr. Tim A. Osswald, Alejandro Roldán-Alzate,Polymer Engineering Center, Department of Mechanical Engineering University of Wisconsin-Madison. Madison,WI, USA.Dr. Alberto Naranjo, María del Pilar Noriega Ph. D., Dr. Juan Diego Sierra,ICIPC – Plastic and Rubber Institute for Training and Research. Medellín, Colombia

Distributed in the USA and in Canada by Hanser Gardner Publications, Inc. 6915 Valley Avenue, Cincinnati, Ohio 45244-3029, USA Fax: (513) 527-8801 Phone: (513) 527-8977 or 1-800-950-8977 www.hansergardner.com

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Library of Congress Cataloging-in-Publication Data

Plastics Testing and Characterization / Alberto Naranjo ... [et al.]. p. cm. Includes bibliographical references and index. ISBN 978-1-56990-425-1 (hardcover) 1. Plastics--Testing--Dictionaries. I. Naranjo, Alberto. TA455.P5T455 2008 620.1‘923--dc22 2008003495

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ISBN 978-3-446-41315-3

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PREFACE vii

PREFACE

Designed to provide a polymer materials testing and characterization background to bothengineering students and practicing engineers, this book is written at an intermediate levelwith the technical information and industrial applications needed for an engineer to makethe right decisions regarding testing methods, as well as troubleshoot problems encounteredin polymer characterization and processing.Testing and Characterization of Plastics is based on lecture notes from the graduate

programProcessing of Plastics andRubber at EAFITUniversity and the polymer engineeringcourses at the University of Wisconsin-Madison, as well as the consulting and research anddevelopment activities at the Rubber and Plastic Institute for Training and Research (ICIPC)done for the plastics and rubber industry.The organization of the book, the clear presentation of data, and the industrial case studies

in polymer characterization and testing make it an ideal reference book for engineeringstudents and practicing engineers. The information is particularly valuable to part designers,processors, and raw materials suppliers.The authors would like to acknowledge the persons who helped in the preparation of

this manuscript: The colleagues at ICIPC are acknowledged, especially the chemist SilvioOspina, for the measurements done at the instrumental analysis laboratory using DSC, TGA,FTIR, GC/MSD, among others; the engineers Juan Carlos Gallego and Juan Carlos Posadafor the micrograph pictures and the rheological measurements; and the technician DianaAngel for the excellent job in drawing and preparing most of the figures. Furthermore, thenumerous students who have attended the authors’ lectures and have served as sounding

viii PREFACE

boards during past few years are also acknowledged. The authors would like to thank Ms.Shannon Proulx for her efforts in copyediting the manuscript. Thanks are also due to Dr.Christine Strohm, Oswald Immel and Steffen Jorg of Carl Hanser Verlag for their supportthroughout the development of this book.Above all, the authors would like to thank their families for their valuable and uncondi-

tional support during their academic careers.

Tim A. OsswaldAlejandro Roldan-Alzate

Madison, Wisconsin, U.S.A.

Alberto NaranjoMarıa del Pilar NoriegaJuan Diego Sierra

Medellın, Colombia

December 2007

ix

TABLE OF CONTENTS

Preface vii

1 Introduction 1

1.1 Testing Techniques 1

1.2 Steps for Successful Polymer Characterization 4

1.3 Preparation and Separation Techniques 4

References 6

2 Spectroscopy 7

2.1 FTIR Spectroscopy 8

2.1.1 FTIR Spectrophotometer 9

2.1.2 FTIR Techniques 11

2.1.3 Correlation of Polymer and Additives Structure and FTIR Spectra 14

2.1.4 Useful FTIR Standard Measuring Techniques 20

2.2 Raman Spectroscopy 45

2.3 Energy Dispersive X-Ray Spectroscopy 51

References 53

3 Gas Chromatography and Selective Mass Detection 55

3.1 Gas Chromatography Instrumentation 55

x TABLE OF CONTENTS

3.2 Correlation of Additive Structure and Mass Spectra 59

3.3 Selected Standards for Gas Chromatography Testing 62

References 73

4 Thermal Properties 75

4.1 Thermal Conductivity 75

4.2 Specific Heat and Specific Enthalpy 80

4.3 Density 84

4.4 Thermal Diffusivity 84

4.4.1 New Developments in Thermal Diffusivity Measurement 88

4.5 Linear Coefficient of Thermal Expansion 91

4.6 Curing Behavior 97

4.7 Thermal Analysis and Measuring Devices 100

4.7.1 Differential Scanning Calorimetry (DSC) 102

4.7.2 Thermogravimetry (TGA) 120

References 126

5 Melt Rheology 127

5.1 Basic Concepts and Terminology 128

5.2 Constitutive Models 142

5.2.1 Newtonian Model 143

5.2.2 Power Law Model 143

5.2.3 Bird-Carreau-Yasuda Model 144

5.2.4 Pressure Dependence of Viscosity 145

5.2.5 Phan-Thien and Tanner Multimode Model 146

5.3 Rheometry 147

5.3.1 The Melt Flow Indexer 147

5.3.2 Capillary Viscometer 150

5.3.3 Rotational Rheometry 157

5.3.4 Extensional or Elongational Rheometry 165

References 183

6 Mechanical Properties 185

6.1 Mechanical Properties 185

6.1.1 The Short-Term Tensile Test 185

6.1.2 Impact Strength 200

6.1.3 Creep Behavior 225

6.1.4 Dynamic Mechanical Tests 241

6.1.5 Fatigue Tests 246

TABLE OF CONTENTS xi

6.1.6 Strength Stability Under Heat 253

References 260

7 Permeability Properties 263

7.1 Sorption 264

7.2 Diffusion and Permeation 265

7.3 Measuring S,D, and P 275

7.4 Diffusion of Polymer Molecules and Self-Diffusion 281

References 285

8 Environmental Effects and Aging 287

8.1 Water Absorption 287

8.2 Weathering 291

8.3 Chemical Degradation 301

8.4 Thermal Degradation of Polymers 308

References 314

9 Electrical, Optical, and Acoustic Properties 315

9.1 Electrical Properties 315

9.1.1 Dielectric Behavior 315

9.1.2 Electric Conductivity 321

9.1.3 Application Problems 326

9.1.4 Magnetic Properties 338

9.2 Optical Properties 339

9.2.1 Index of Refraction 340

9.2.2 Photoelasticity and Birefringence 342

9.2.3 Transparency, Reflection, Absorption, and Transmittance 344

9.2.4 Gloss 349

9.2.5 Color 351

9.3 Acoustic Properties 353

9.3.1 Speed of Sound 354

9.3.2 Sound Reflection 354

9.3.3 Sound Absorption 355

References 357

INDEX 359

1

CHAPTER 1

INTRODUCTION

This book is designed to provide a background in polymer properties and testing in the areasof characterization and processing to engineering students and practicing engineers. Thebasic properties of interest and the testing and characterization techniques used to measurethem are presented.Combined with a solid engineering background, this book has the information and in-

dustrial case studies an engineer needs to both make informed decisions about selectingappropriate testing techniques and effectively troubleshoot problems in the field of plasticstechnology. The scope of this book also includes relevant and concise information for datainterpretation using the most important characterization techniques.

1.1 TESTING TECHNIQUES

Polymer testing and characterization involves several analytical techniques that evaluate thephysical and chemical structure of polymers and their additives. This field is important inseveral industrial and scientific areas, including quality assurance of polymers and additives,research and development of new materials, design of polymeric formulations, analysis ofunknown samples, reformulations, and troubleshooting.

2 1 Introduction

Today, the different instrumental analysis techniques have rapidly changed because of theadvances in electronics and computers that allowed the introduction of new characterizationequipment and methods for improving existing techniques. The main technological trendsin polymer testing and characterization are:

• Easier sample preparation• On-line measuring and data acquisition• Automation by means of microprocessors and computers• Sensitivity enhancement (better signal/noise ratio)• Lower detection limits• Accuracy and precision improvement• Miniaturization• Instruments that are easier to operate• Databases and specialized software that facilitate result analyses• Remote diagnosis and configuration (via Internet)• Modular and flexible equipment, "Plug and Play" setup• Important reduction of instrument cost

This book is broken down into the following categories of techniques and properties:

• Fourier transform infrared spectroscopy (FTIR)• Raman spectroscopy• Energy dispersive X-ray spectroscopy• Gas chromatography and selective mass detection (GC/MSD)• Thermal properties

– Thermal conductivity

– Specific heat

– Density

– Thermal diffusivity

– Linear coefficient of thermal expansion

– Curing behavior of thermosets and elastomers

– Differential scanning calorimetry (DSC)

– Thermogravimetrical analysis (TGA)

• Melt rheology• Mechanical properties• Permeability properties• Aging• Electrical properties• Optical properties

– Imaging techniques (Introduced in various examples throughout the book)

1.1 Testing Techniques 3

• Acoustic properties

However, according to the authors’ experience, polymer testing and characterization in-volves other complementary techniques to gain detailed information about the physical andchemical structure of polymers and their additives; These are not going to be treated in thisbook; however, some of these techniques are:

• Visible and ultraviolet spectroscopy (UV/VIS)• Nuclear magnetic resonance (NMR)• Atomic absorption spectroscopy (AA)• High-performance liquid chromatography (HPLC)• Gel permeation chromatography (GPC)• Ionic chromatography (IC)• Thin layer mass chromatography• Transmission electron microscopy (TEM)• Atomic force microscopy• Thermomechanical analysis (TMA)• Differential thermal analysis (DTA)• Dynamic mechanical analysis. (DMA)• Dynamic electrical analysis (DEA)• Dilatometry• Diffraction

– X-ray diffraction

- WAXS: wide-angle X-ray scattering

- SAXD: small-angle X-ray scattering

– Electron diffraction

– Neutron diffraction

• Polarography• X-ray compositional microanalysis• Wavelength dispersive spectrometer (WDS)

Finally, this book presents each set of properties with sets of graphs that illustrate howvarious conditions affect it. Additionally, the graphs compare the most important plastics toeach other, and often to other materials.

4 1 Introduction

1.2 STEPS FOR SUCCESSFUL POLYMER CHARACTERIZATION

For successful polymer testing and characterization, there are several techniques and tricksthat must be followed, beginning with a clear problem statement. Although measurementsmay take a short time, the characterization aspects, such as sampling, sample preparation,and data analysis, can be very involved and may take several hours or even days. Based onthe authors’ experience, the following steps can be followed:

• Problem statement –Every characterization should start with a clear problemstatementto avoid unnecessary measurements. The problem statement is typically presented asthe questions to be answered after the characterization work. Usually, a detailedanalysis of the problem requires accuracy in meeting the expectations of the end userof the sought information.

• Sampling – Because most of the techniques use very small samples (in the order ofmilligrams), a representative sample should be collected and homogenized.

• Sample preparation – This activity usually includes operations such as size reduction,dissolution, isolation of substance of interest, and interference elimination. Some-times, the addition of internal standards is required to allow an easier quantificationand recovery estimate1.

• Measuring – In order to estimate the precision of the method, repeated analysis andsample preparations are usually done.

• Data processing – Includes data validation, statistical processing of results, and thewriting of a final report.

• Problem solving – At the end of the procedure, check to see if the questions of theproblem statement were solved before delivering the final report.

1.3 PREPARATION AND SEPARATION TECHNIQUES

The sample preparation depends on the particular technique used and the purpose of theanalysis. Some techniques of FTIR (such as transmission, ATR, and photoacoustic) andDSC do not require any sample preparation. Other techniques need preparation procedures,including extraction, dissolving, pressing, microtoming, or acid digestion. A review of themain preparation techniques and their recommended use is presented in Table 1.1. Forselective extraction of some additives used in PVC compounds, as well as in other polymers,some specific solvents are recommended (see Table 1.2)

1This factor accounts for the amount of sample that was not effectively extracted and that could be lost during thepreparation procedure.

1.3 Preparation and Separation Techniques 5

Table 1.1: Preparation techniques and their recommended use

Preparation technique Recommended use

Size reduction (also calledcomminution)

Usually the first step in any sample preparation. It is used to reducethe inhomogeneities and maximize the superficial area to enhancelater extraction and dissolution. Size reduction can be done in dif-ferent equipment, being the most recommended the refrigerated millusing high speed knives.

Solvent extraction Used to selective extract additives, ingredients and substances thatinterfere with the analysis. The solvent has to be carefully selectedaccording to the matrix (polymer substrate) and the particular sub-stance to extract. Several techniques are used, such as Soxhlet ex-traction, supercritical fluid extraction, ultrasonic extraction, and mi-crowaves extraction.

Dissolution It is possible for some polymers to use the selective dissolution andseparation from other additives and ingredients. One of the mostused solvents is the tetrahydrofuran (THF).

Incineration Used to separate the inorganic filler from the polymer and otherorganic ingredients. After the incineration, FTIR analysis and aciddigestion to analyze metals are normally done.

Acid digestion The ashes of the sample are dissolved and reduced to compounds thatare more easily analyzed by using polarography, atomic absorptionspectroscopy, and visible and ultraviolet spectroscopy.

Chemical derivatization Some ingredients that are difficult to analyze should be converted inother products that are more easily analyzed. The detection of thechemical derivatives offers important information of the chemicalstructure of the sample. For example, this technique is useful toidentify plasticizers in several polymers.

Complex formation The interest substance reacts with a special chemical substance toform a complex that is easily separated and analyzed. This techniqueis used, for example, in metal and pesticide analysis, where thedetection limit could be significantly enhanced.

6 1 Introduction

Table 1.2: Recommended solvent for additives extraction [1]

Additives Recommended solvent

Phthalate plasticizers Ethyl ether, diethyl ether or carbon disulfide

Phosphate plasticizers Ammonium molybdate, perchloric acid 40%, and hy-drochloric acid; subsequently saturated hydrazine sulfate so-lution

Citrates plasticizers Ethanol vanillin solution; subsequently sulfuric acid

Nitrogenated stabilizers Methanol or diethyl ether

Tin organic stabilizers Acetic acid/n-heptane 1:1

Antioxidants Chloroform

Benzotriazole UV absorbers Benzene/petroleum ether 7:3

Benzophenone UV absorbers Ethanol/water 7:3

References

1. N. P. Cheremisinoff. Polymer Characterization - Laboratory Techniques and Analysis. WilliamAndrew Publishing/Noyes, 1996.

7

CHAPTER 2

SPECTROSCOPY

In polymer technology and processing, there are many analytical spectroscopic systems thatcan aid in identifying polymers and monitoring reactions during a process, or even the lifeof a product. Spectroscopy typically measures interactions between a type of radiation andelements within a material. (electromagnetic, light, infrared, particle, and X-ray, to name afew). A spectrometer measures these interactions and delivers what is called a spectrogramor spectrum.Some of the most commonly used spectroscopy systems are:

• Energy dispersive X-ray• Flame• Infrared• Mossbauer• Nuclear magnetic resonance• Photoemission• Raman• Thermal infrared• Ultraviolet• Visible

8 2 Spectroscopy

Of these many techniques, we will present infrared spectroscopy and introduce Ramanspectroscopy, as well as energy-dispersive X-ray spectroscopy.

2.1 FTIR SPECTROSCOPY

Fourier transform infrared spectroscopy (FTIR),more commonly referred to as infrared spec-troscopy, has evolved into one of the most important techniques used to identify polymericmaterials. It is based on the interaction between matter and electromagnetic radiation ofwavelengths in the infrared region (13300 to 20 cm -1). The infrared electromagnetic radia-tion produces vibrational and rotational changes in the molecule distinctive of the analyzedsubstance’s chemical structure. It can be concluded that the infrared spectrum of any sub-stance is like the fingerprint of humans: every chemical group of the polymer (or additive)has a characteristic IR absorption pattern that can be correlatedwith its molecular structure.Table 2.1 is a review of the different types of interactions of matter with electromagneticradiation.

Table 2.1: Interactions of matter with electromagnetic radiation

Electromagnetic Radiation Types of interactions

Gamma rays (0.01 – 0.1 nm) Nuclear reactionsX-rays (0.1 – 1.0 nm) Internal electron transitions bond breaking

Far UV (10 – 200) External electron transitionsUV (200 – 400 nm)

Visible (400 – 700 nm) Molecular vibrationsNear IR (0.7 – 2 μm or 13300 – 4 000 cm-1)

Mid IR (2 – 25 μm or 4000 – 400 cm-1) Molecular rotationsFar IR (25 – 1000 μm or 400 – 20 cm-1)

Microwaves (1 – 300 mm) Nuclear and electronic spin changesRadio waves (>10 m)

This technique offers almost unlimited opportunities for polymer and additive characteri-zation because it offers the following advantages: very fast, easy qualitative and quantitativeanalysis, and relatively low instrumentation cost.The first IR spectroscopy instrument, a dispersive infrared spectrophotometer, was intro-

duced at the beginning of the 1950s [1]. At the end of the 1960s, the first Fourier transforminfrared spectrophotometer was introduced, overcoming some limitations of the dispersiveinfrared instruments but with a considerably higher cost. In the mid 1980s, a new generationof FTIR spectrophotometer was introduced with a more competitive price and many advan-tages over the dispersive instruments [1].


Figure 2.1: Schematic diagram of an infrared spectrometer

Some of these improvements are:

• Reduction in the time for acquisition of spectrum• Improvement in the energy throughput that make possible the development of newpowerful techniques such as attenuated total reflectance (ATR), diffused reflectanceinfrared fourier transform spectroscopy (DRIFTS), and photoacoustic spectroscopy(PAS)

• Improvement in sensitivity and resolution (higher signal/noise ratio and better peakresolution)

2.1.1 FTIR Spectrophotometer

An infrared spectrophotometer, or infrared spectrometer, that measures a material’s ab-sorption spectrum is schematically represented in Fig. 2.1. The FTIR spectrophotometercomprises the following main components: IR source, beam splitter, sample compartment,detector, and signal process unit. The IR source, beam splitter, and detector will be studiedin some detail in the following sections.

IR sources: The source is the component of the FTIR spectrophotometer that produceswide spectra of IR radiation to interact with the sample. Typically, the IR source is arefractory material heated at a high temperature by means of a metallic filament (usuallya nickel chromium filament). The IR radiation emitted by the source is a function of thetemperature; the emitted IR energy decays dramatically by decreasing the temperature ofthe source. As a consequence, for a high stability of the source the temperature has to becarefully controlled, and a background correction of the sample spectrummust be done. Themain refractory materials used are:

• GLOBAR –A sintered silicon carbide bar heated at temperatures in the range of 750 to1200 ◦C. Thismaterial has a high vulnerability to oxidation, so the heating temperatureis lower than other IR sources and the emitted IR intensity is decreased. A GLOBARsource has a typical IR spectrum in the range of 9000 to 50 cm -1.

IR source

10 2 Spectroscopy

• NERNST – A tube of zirconium and yttrium heated at temperatures around 1750 ◦C.Because of the high temperature, the emitted IR intensity is increased but the life isdecreased.

• EVER GLO – This source uses the IR radiation produced by a black body and has atypical IR spectrum in the range of 9600 to 50 cm-1.

• Tungsten filament – This type of source is used primarily in the near infrared. Thissource has a typical IR spectrum in the range of 15000 to 8000 cm -1.

Beam splitters: The beam splitter is a moving semitransparent mirror where the in-terference phenomenon occurs, and all the wavelength of the IR radiation is encoded inan interferogram by using a Fourier transform. After the interaction with the sample, theinterferogram can be decoded into the IR absorption spectrum by means of a Fourier de-convolution. A laser signal (typically a He/Ne laser) is used for the internal calibration ofthe interferometer, leading to a precision of around ±0.01 cm -1. The most important beamsplitters used in the FTIR instruments are:

• Quartz – Spectral range 15000 to 5500 cm-1, used in near IR spectroscopy

• CaF2 – Spectral range 11500 to 1800 cm-1, used in near and mid IR spectroscopy

• KBr – Spectral range 7400 to 550 cm-1, used in mid IR spectroscopy

• Ge on KBr – Spectral range 8000 to 500 cm-1, used in mid IR spectroscopy

• Ge on CsI – Spectral range 6500 to 200 cm-1, used in mid and far IR spectroscopy

• MYLAR� – Spectral range 500 to 25 cm-1, used in far IR spectroscopy

Detectors: The detector is the component of the FTIR spectrophotometer that registersthe absorption IR spectra of the sample. The most important detectors used in the FTIRinstruments are:

• DTGS/KBr – Deuterated triglycine sulfate in a KBr support. It can operate at roomtemperature, and its linearity decreases significantly at high absorbance (usually over1.5 units of absorbance). The signal/noise ratio decreases appreciably at high beamsplitter velocity. Recommended velocity is 0.6329 cm/s or lower, best at 0.3165 cm/s.This detector has a typical spectral range of 6000 to 400 cm-1.

• DTGS/CsI – Deuterated triglycine sulfate in a CsI support. Same as DTGS/KBr butwith a spectral range of 6000 to 250 cm-1.

• DTGS/Polyethylene – Deuterated triglycine sulfate in a polyethylene support. It isused in far IR spectroscopy and has a spectral range of 700 to 30 cm -1.

• MCT –Mercury cadmium telluride. To operate, it must be cooledwith liquid nitrogen,and the sensitivity is considerably higher than the DTGS detector. Because of itshigh sensitivity is used in IR microscopy. Its linearity decreases significantly at highabsorbance (usually over 1.0 units of absorbance). The signal/noise ratio is practicallyindependent of the beam splitter velocity. This detector has a typical spectral range of8000 to 400 cm-1.


2.1.2 FTIR Techniques

Today a wide range of techniques for FTIR analysis are available, and the selection of theproper technique depends on various criteria. These are:

• Sample type – The proper technique depends on the physical state, reactivity, corro-siveness, and dilution of the sample.

• Information sought – The type of information required could determine the techniqueselection. Some of the typical factors include: qualitative or quantitative, surface orbulk analysis, and intensity of the peaks of interest.

• Sample size – Very small samples require special techniques, such as IR microscopyand photoacoustic.

• Destructive or non-destructive analysis – The possibility of preparing the sample bydividing, dissolving, pressing, changing the form, and sometimes destroying it, couldinfluence the selection of the measurement technique.

• Time –This includes the time in sample preparation and the time to obtain a satisfactoryIR spectrum. In particular the photoacoustic is a very time consuming techniquebecause several scans are required to obtain good spectra.

• Cost – The use of expensive chemicals and highly qualified personnel during prepa-ration and repetitive analysis could influence the choice of technique.

Transmission: Transmission is a very simple FTIR technique. The sample is placed inthe IR beam emitted by the source, and the transmitted radiation is directed to the detector.The sample could be placed directly in the IR beam in the case of films and sheets. In caseof a powder sample, it could be supported in an IR transparent powder or in a liquid sample.It could be also supported in a transparent window.

Table 2.2: IR transparent powders for transmission technique [2]

Material IR spectral Refractive index Relative costrange (cm-1) (at 2000 cm-1) (Relative to KBr)

KBr 40000 to 400 1.52 1.0

KCl 40000 to 500 1.46 N/A

CsI 40000 to 200 1.74 3.0

KRS-5 20000 to 250 2.45 2.0

Polyethylene 625 to 33 N/A 0.6

Solid Samples: Solid samples are finely groundwith a transparent powder using,for example,a mortar. The concentration of sample in the transparent powder is typically 0.1 to 2.0%by weight and has to be adjusted according to the signal observed in the FTIR instrumentfor the peak of interest. The main characteristics of commercially available IR transparentpowders are presented in Table 2.2. For best spectra, a finely ground IR transparent powder

12 2 Spectroscopy

with a refractive index similar to the sample is recommended. For most of organic materialsanalyzed, KBr is normally used.Alternative transmission techniques for solids include:

• Mull – This is a technique where the solid sample is ground to a paste in an oil.As a result, the solid sample is suspended in the IR transparent oil such as Nujol� orFluorolube�. Nujol� is chemically inert paraffinwith a relatively simple IR spectrumwith absorption bands at 3000, 2800, 1500, 1350, and 720 cm -1. Fluorolube� has noabsorption bands at wavenumbers higher than 1400 cm -1.

• Cast film – The solid is dissolved in a proper solvent. Once the solvent is evaporated,a film can be analyzed directly by transmission. The principal limitation of thistechnique is that most of polymers and inorganic additives are difficult to dissolve atroom temperature using available solvents.

• Pressed film – Most thermoplastics and several additives can be pressed into a filmby using the proper temperature and pressure. This film can be analyzed directly bytransmission.

• Free-standing film – In most cases, the films can be analyzed without any preparation;however for coextrudedfilms, laminations, or non-transparent films, the ATR and PAStechniques are also recommended.

Liquid Samples: Liquid samples can bemeasured directly by transmission using IR transpar-ent windows. Selection criteria for choosing the proper IR transparent windows includes IRspectral range, cost, chemical compatibility with sample, refractive index, and mechanicaland thermal properties. Several IR transparent materials can be used as a window for liquidanalysis. Some of the most used materials are:

• KBr, KCl, or NaCl – Traditionally used because of the wide IR spectral range andrelative low cost. It is not recommended for aqueous solutions, alcohol, and glycerin.Cleaning solvents are acetone, toluene, cyclohexane, hexane, or methylene chloride.Spectral range for KBR is from 40000 to 400 cm-1, KCl from 30000 to 500 cm-1, andNaCl from 40000 to 490 cm-1.

• AgCl – Used when aqueous solution resistance is required. Main drawbacks are lightsensitivity, corrosiveness, higher cost, and lower mechanical and thermal resistance.Cleaning solvents are acetone or water. Spectral range is from 25000 to 450 cm -1.

• BAF2 or CaF2 – Although the IR spectral range is narrower compared with bromidesand chlorides and the cost is higher, thesematerials are selectedwhen aqueous solutionresistance and a high resistance to pressure and temperature are required. Cleaningsolvents are acetone or water. Spectral range for BaF2 is from 50000 to 850 cm -1 andfor CaF2 from 50000 to 1140 cm-1.

• ZnS or ZnSe – Although they have a higher cost, these materials are selected whenaqueous solution resistance and higher refractive index are required. The hardness ishigher than normal bromide and chloride windows. Cleaning solvents are acetone orwater. Spectral range for ZnS from 17000 to 833 cm -1 and for ZnSe is from 20000 to500 cm-1.

• Polyethylene – Very inexpensive and chemically resistant to most of solvents. Pri-marely used in the far IR region. Spectral range is from 650 to 33 cm -1.


Attenuated total reflectance (ATR): In the ATR technique, the IR radiation emitted bythe source is internally reflected in a high refractive index crystal. Some of the IR radiation(evanescent waves) interacts with the sample in direct contact with the crystal. Therefore,a surface IR spectrum of the sample is obtained. The penetration depth as a function of thewavelength of incident radiation, the angle of incidence, and the refractive index of crystaland sample can be expressed using Eq. 2.1. The higher the wavelength and the refractiveindex of the crystal, the lower the penetration depth. For a typical refractive index of an ATRcrystal at the mid-IR wavelength, the penetration depth is less than 1 micrometer.

Table 2.3: Commercially available ATR crystals [2]

ATR crystal IR spectral Refractive index Commentsrange (cm-1) at 2000 (cm-1)

ZnSe IRTRAN4� Orangecolor

20000 to 454 2.43 Ideal for aqueous solutions.Scratches easily. Brittle. Sensi-tive to acids and strong alkalis.Cleaning agents are acetone orwater.

Germanium Mirror-like 5500 to 600 4.01 High chemical resistance onlyattacked by hot sulfuric acidand aqua regia. Very brittle.Scratches easily. Due to thehigh refractive index is use-ful for low penetration analysis.Cleaning agents are toluene orwater.

KRS-5� Red color 20000 to 250 2.38 Mixed crystal (thallium bro-mide and iodide). Highly toxic.Ideal for wide spectral rangestudies. Scratches very easily.Sensitive to aqueous solutions,acids and alkalis. Cleaningagents are xylene or methanol.

ZnS CLEARTRAN� andIRTRAN 2�

17000 to 838 2.25 Ideal for aqueous solutions.High mechanical and thermalstrength. Sensitive to strong ox-idizing agents. Cleaning agentsare acetone or alcohol.

14 2 Spectroscopy

dp =λ

2πn1

√(sin2θ − n2

n1)

(2.1)

Where dp is the penetration depth, λ is the wavelength of incident radiation, n 1 is therefractive index of the crystal, n2 is the refractive index of the sample, and θ the angle ofincidence.The ATR technique is very useful for the analysis of liquids, coextruded films, lamina-

tions, coatings, diagnose of blooming problems, metallic depositions, and surface chemicalanalysis. Some of the surface chemical analyses include surface chemical reaction studies,demolding aids analysis, slip additives migration, corona, and flame and plasma treatment.Some of the commercially available crystals are presented in the Table 2.3.

Photoacoustic spectroscopy (PAS): In the PAS technique, the infrared radiation isdirected to the sample, and the modulated heating at the surface causes pressure variationsof a gas within the sample compartment. A very sensitive microphone detects this acousticsignal. This microphone generates a signal similar to the interferogram of the absorbed IRspectrum. An IR non-absorbing gas with high thermal conductivity is required, typicallyhelium. Additionally, a background with a non-absorbing carbon black powder is required.The PAS technique is an advantageous technique because it is not necessary to prepare thesample and it is non-destructive.The penetration depth as a function of the wavenumbers of incident radiation and the

beam splitter speed can be expressed by Eq. 2.2. For a good signal/noise ratio a low beamsplitter is recommended, typically 0.15 cm/s.

dp = (k

2ρπCpπV ω)

12 (2.2)

Where dp is the penetration depth, ω represents the wavenumbers of incident radiation,k is the thermal conductivity of the gas, Cp the heat capacity of the gas, ρ the density of thegas, and V the speed of the beam splitter.

Diffused reflectance infrared Fourier transform spectroscopy (DRIFTS): Thisis a very useful technique for powders because preparation is not required. It is also appro-priate for matte or rough surfaces. The IR radiation is directed to the sample cup, wherepowdered sample diluted with KBr is located. The scattered IR radiation is collected anddirected to the detector by means of a curvedmirror assembly. For optimal results and betterIR spectra, the sample has to be diluted in KBr or KCl to 5% or less. The particle size ofdiluted sample has to be fine (between 75 to 90 microns) and very uniform in size.

2.1.3 Correlation of Polymer and Additives Structure and FTIR Spectra

Correlation of polymers and additives structure and FTIR spectra is necessary when inter-preting data resulting from an IR test. This is the most difficult task in infrared spectroscopy.A review of the correlation of the chemical structure with IR absorption bands is presentedin Table 2.4. Additionally in Table 2.5, the characteristic IR absorption bands for a selectedgroup of polymers are summarized. Table 2.6 presents the characteristic IR absorption bandsfor a selected group of additives.


Table 2.4: Correlation of chemical structure and FTIR spectra [2, 3, 4]

Chemical group Frequency, cm-1 Comments

Aliphatic

–CH3 2952 to 2972 Asymmetric extension of C–H2862 to 2882 Symmetric extension of C–H1430 to 1480 Asymmetric flexion of C–H1370 to 1380 Symmetric flexion of C–H

–CH2- 2920 to 2930 Asymmetric extension of C–H2848 to 2858 Symmetric extension of C–H1450 to 1480 Flexion of C–H1150 to 1350 Torsion of C–H700 to 1100 Balancing of C–H

–CH< 2880 to 2900 Extension of C–H

–(CH2)n– 720 to 740 For n≥4, vibration of –CH2– skeleton

–CH(CH3)– 1110 to 1140 Vibration of –CH2– skeleton

–CH=CH– 967 Vinylidene unsaturation

Aromatic

–CH 3000 to 3125 Extension of C–H of aromatic ring1650 to 2000 Flexion out of plane of CH – (Harmonics)1575 to 1625 Aromatic ring vibration1520 to 1480700 to 800 Flexion of aromatic ring

Aliphatic C=C

–C=CH2 3070 to 3090 Asymmetric extension of C–H2985 to 3005 Symmetric extension of C–H

–CH=CH–(trans) 3010 to 3040 Extension of C–H960 to 970 Deformation out of plane of C–H

>C=C< 1615 to 1670 Extension of C=C non conjugated1600 to 1590 Extension of C=C conjugated

–CH2–CH=CH2 955 Allylic unsaturation

–CH=CH2 990 and 908 Vinyl unsaturation

>C=CH2 888 Vinylidene unsaturation

Triple bond

–C≡CH 3310 to 3200 Extension of C–H

–C≡C– 2150 to 2250 Extension of C≡CR–C≡N 2260 to 2240 Extension of C≡N

Continued on next page

16 2 Spectroscopy


Alcohol O–H

–OH 3200 to 3400 Extension O–H (wide and strong)

–CO 1050 to 1150 Extension C–O (strong)

–OH 1310 to 1410 Flexion OH

Amides

R(CO)NH2 3420 to 3550 Asymmetric extension of C–H3450 to 3320 Symmetric extension of C–H1650 to 1690 Carbonyl extension (–C=O)1600 to 1640 Flexion of NH2

1405 to 1420 Extension of N–H

R(CO)NHR 3440 Extension of C–N1640 to 1680 Carbonyl extension (–C=O)1530 to 1570 Flexion of NH2

1300 to 1260 Extension of N–H

R(CO)NR2 1650 Absence of band of NH

Esters

–C=O 1735 Carbonyl extension (–C=O)

–COC– 1185 to 1275 Asymmetric extension C–O–C (strong)

–COC– 1050 to 1160 Symmetric extension C–O–C

Acids, Peroxides and Anhydrides

–C=O 1750 to 1765 Carbonyl extension (–C=O)

–OH 3550 Extension O–H (wide and strong)

–OH 1420 Flexion OH

–CO 1250 Extension C–O

–OH 860 to 900 Flexion out of plane of –OH

Peroxides 1780 to 1820 Asymmetric –C=O extension –(CO)OO(CO)–1750 to 1770 Symmetric –C=O extension –(CO)OO(CO)–820 to 890 Very weak (–COOC–)

Anhydrides 1810 to 1830 Asymmetric –C=O extension of –(CO)O(CO)–

1750 to 1770 Symmetric –C=O extension –(CO)O(CO)–

Aldehydes

–C=O aliphatic 1715 to 1725 Carbonyl extension (–C=O)

–C=O aromatic 1700 Carbonyl extension (–C=O)Continued on next page



Ketones

–C=O aliphatic 1710 to 1720 Carbonyl extension (–C=O)

–C=O aromatic 1690 Carbonyl extension (–C=O)

–C(CO)C– 1100 Flexion of –C(CO)C–

Ethers and Epoxides

–COC– aliphatic 1070 to 1150 Asymmetric extension –COC–

–COC– aromatic 1200 to 1275 Asymmetric extension –COC– (strong)1020 to 1075 Symmetric extension –COC– (weak)

Acetals 1116 to 1103 Characteristic of acetals (–COCOC–)

Amines

RNH2 3420 to 3550 Asymmetric extension of C–H3450 to 3320 Symmetric extension of C–H1560 to 1640 Flexion in the plane of NH–1030 to 1230 Extension of C–N650 to 900 Flexion out of the plane of NH– (weak)

R2NH 3310 to 3450 Asymmetric extension of C–H1490 to 1580 Flexion in the plane of NH– (weak)1100 to 1150 Extension of C–N

R3N 1030 to 1230 Extension of C–N (doublet)

Table 2.5: Characteristic IR absorption bands for a group of polymers [5, 6, 7]

Polymer Characteristic IR absorption bands, cm-1

PE 2920, 1470, 1380, 730-720 (doublet)

Isotactic PP 2950, 2920, 1470, 1380, 1160, 970

EVA 1430, 1235, 1025 (0 to 8%VA), 609 (5 to 20%VA)

POM 1240, 1110, 935, 910 (broad)

PMMA 1265, 1240, 1190-1150

PS 760, 700

HIPS 970, 760, 700

ABS 2260, 970, 760, 700

PVC 1430, 1325, 690

PVdC 1400, 1050 (doublet)

PVdF 1400, 1300-1000, 880, 840


18 2 Spectroscopy

Polymer Characteristic IR absorption bands, cm-1

PTFE 1220-1150 (doublet)

Methyl siloxane 1265, 1110-1000, 800

Phenyl siloxane 1430, 1110-1000

1,4 trans butadiene 2940, 1450, 970

1,4 cis butadiene 3010, 2940, 1450, 740

1,2 Polybutadiene 3070, 2920, 11640, 990, 910

Polyvinyl alcohol 3330, 1430, 1100 (broad)

Polyethylene oxide 2880, 1470, 1110 (broad)

Polypropylene oxide 2980, 2880, 1470, 1370, 1110 (broad)

PPO 1190, 855

PPS 1095, 1075, 1010, 820, 700, 500

PSU (Bisphenol A) 1320, 1250, 1165, 833

Polyethylene acrylate 1630, 1250, 1190-1150

PC 1775, 1235, 830

PET 1740, 1333-1212 (broad), 1120, 830, 720

PI 1780, 1718

Styrene/maleic anhydride 1860, 1790, 1225, 1080, 760, 700

Polyether urethane 3330, 1695, 1540, 1220, 1110

Polyester urethane 3330, 1735, 1695, 1540, 1220

Cellulose acetate 1230, 1110-1050 (broad)

Table 2.6: Characteristic IR absorption bands for a group of additives [5]

Additive Characteristic IR absorption bands, cm-1

Phthalate ester plasticizer Carbonyl group (C=O): 1725 cm-1, 1598 and 1580 cm-1

(doublet), 1270 cm-1, 1121 cm-1

Phosphate plasticizer 1121 cm-1, 1035 cm-1, 965 cm-1

Lead stabilizers Lead basic carbonate: 1410 cm-1

Lead basic sulfate: 1130 cm-1

Lead dibasic phthalate: 1535 cm-1

Tin stabilizers (Tin thioglycolates) Carbonyl group (C=O): 1739 cm-1 and 1147 cm-1

Second carbonyl group: 1660 to 1710 cm-1

Inorganic fillers Calcium carbonate: 877 cm-1

Kaolin: 1075 cm-1

Antimonium oxide: 1130 cm-1

Trihydrated alumina: 3521 cm-1


Tables 2.7 and 2.8 present the characteristic IR absorption bands for the two most thor-oughly studied polymers – polyethylene and polypropylene. The assignations for the bandsin 1471, 954, 859, 839, 802, and 784 cm -1 are tentative and have not beenwell correlated for aspecific vibration. Bands markedwith asterisk (*) correspond to the helicoidal conformationof polypropylene associated with an isotactic structure.

Table 2.7: Characteristic IR absorption of polyethylenes: Wavenumbers between 1500and 700 cm-1[6]

ω (cm-1) Assignation ω (cm-1) Assignation

1471 Symmetric bending of methylene.(tentative)

910 Terminal vinyl groups along with990

1463 Asymmetric bending ofmethylene 908 Also associated with terminalvinyl groups

1378 Symmetric bending of methyl 903 With the one on 889 it is assignedto terminal methyl groups fromalquidic chains longer than ethyl

1367 Scissoring bending of methylene 889 Bending vibration of methylgroups from n-hexyl; if there isan overtone in 745 corresponds ton-butyl

1353 Torsion bending of methylene 888 Vinylidene type unsaturations

1346 Bending ofmethylene for a regularpack structure

849 Vibration of CH2 related witha crystalline conformation of thechain

1304 Bending of methylene associatedto the amorphous part

839 Possibly due to 3 substitutedalkenes, such as a diallyl group(tentative)

1176 Wagging of C-C from methylene 802 Like the one in 839 (tentative)

1151 Vibration of C-C from methyl 784 Vibration of methylene longerthan ethyl (tentative)

990 Vibration CH of terminal vinylgroups

762-770 Vibrations of CH from ethylgroup, (two consecutive CH2

groups)

967 Vibration CHof vinylidene groups(refer to as internal trans unsatura-tion)

745 This band along with the onein 890 can be related to n-butylbranches

954 Vibrations of the allyl type (tenta-tive)

730 Indicative of long aliphaticsemicrystalline chains of carbonbonds, attributed to the rockingof methylene in the crystal ofpolyethylene

937 Out of plane tension of terminalmethyl groups

720 Rocking vibration of a minimum 4consecutive CH2 groups

20 2 Spectroscopy

Table 2.8: Characteristic IR absorption of polypropylenes: Wavenumbers between1500and 700 cm-1 [7]

ω (cm-1) Assignation ω (cm-1) Assignation

1467 Scissoring bending of methylene 972 * Assigned to two or more head totail units of following PP

1456 Asymmetric bending of methyl 960 Sequence of two contiguous unitsof polypropylene

1379 Symmetric bending of methyl 940 Rocking of methyl group

1359 Scissoring bending of methylene 899 * Assigned to a helicoidal confor-mation of polypropylene

1304 Torsion and wagging stretching ofmethylene

840 * Helicoidal conformation. It isalso attributable to a length of iso-tactic sequences of 13 to 15 units

1255 Vibrations of carbon backbone forC–CH3 bonding

809 * Related also with the helicoidalconformation bands of: 1219,1167, 972, 899, and 840

1219 * Attributed to the helicoidal con-formation of polypropylene

732 Only presented in random copoly-mer, due to a sequence of 3 con-tiguous CH2 groups

1167 * As the band in 1219 728 Sequence of four contiguousmethylene groups

1153 Stretching wagging of methyl as-signed to solely polypropyleneunits, presented only in copoly-mers

720 Only presented in block copoly-mer. Assigned to a sequence offive ormore contiguous methylenegroups

997 * Helicoidal conformation; it alsocan be due to a length of isotacticsequences from 11 to 12 units.

2.1.4 Useful FTIR Standard Measuring Techniques

This section presents some commonly used FTIR standard measuring techniques used toevaluate various polymeric materials. The standards presented in this section are all basedon ASTM Standards.


Table 2.9: Standard test methods for absorbance of polyethylene due to methyl groups 1at 1378 cm-1

Standard ASTM D 2238 - 92 (Reapproved 2004)

Scope These are infrared absorption spectrophotometry measurements of the1378.4 cm-1 (7.255 μm) band in polyethylene due to methyl groups. Two testmethods are included:Test Method A uses compensation with a standard sample film of known methylcontent.TestMethodBuses compensationwith a filmof polymethylene or a polyethyleneof known low methyl content.These test methods are applicable to polyethylenes of Type I (density 910 to925 kg/m3), Type II (density 926 to 940 kg/m3), and Type III (density 941 to965 kg/m3).It should be noted that in cases of Type III polyethylene with densities greaterthan 950 kg/m3, different results are obtained with the two test methods.

Specimen Quenched polyethylene films with a thickness about 0.3 mm.

Apparatus A double beam dispersive Infrared Spectrophotometer or a Fourier TransformInstrument, capable of a spectral resolution of at least 2.0 cm-1. A smallcompression-molding press with platens that can be heated to 170◦C. Smoothmetal plates, approximately 150 mm X 150 mm X 0.5 mm. Brass shims, ap-proximately 75 mmX 75 mm or larger with a center hole at least 25 by 38 mm ina series of at least five thicknesses from 0.1 mm to 0.5 mm. Micrometer calipers,with 0.001 mm resolution. Mounts, for film specimens with aperture at least6 mm X 27 mm.

Test procedures A calibration is done with an annealed HDPEwith a methyl group content lowerthan 0.3 for 1000 carbon atoms and with thickness between 0.1 to 0.5 mm.A calibration curve of methyl absorbance at 1378 cm-1 related with the ab-sorbance at 1304 cm-1 is obtained. In the calibration curve, the absorbancevalues are corrected with the thickness and the density. The infrared spectrumof the sample is measured between the range of 1430 to 1250 cm-1. The ratioof the 1378/1304 cm-1 is measured and used to calculate the methyl content for1000 carbon atoms with a factor of calibration previously stated with a cetanestandard. Alternative the method B uses an special wedge for calibration andcompensation of the sample.

Values and Units Absorbance values at 1378.4 cm-1 (7.255 μm). Total methyl groups (calculatedas methyl in alkyl groups greater than C3)

22 2 Spectroscopy

Table 2.10: Standard methods for rubber–identification by infrared spectrophotometry

Standard ASTM D3677-00 (2004)

Scope This technique is intended for rubber identification and is based on infraredexamination of pyrolyzates products and films. The test methods are applicableto rubbers in the raw state as well as cured and uncured compounds.This method comprises 2 test methods:TestMethod1: based on infrared examination of pyrolyzates products andfilms,occurring alone or in binary blends in the range from 80 % major component to20 % minor component.Test Method 2: These test methods describe the semiquantitative detection ofcertain rubbers in blends, for example: Polyisoprene (IR and NR), BR, and SBRin binary and ternary blends with an accuracy of approximately ±5 % of the totalrubber content. Saturated rubbers (IIR, CIIR and BIIR or EPDM) are detected inthe presence of unsaturated rubbers (NR, IR, BR, SBR, andCR)with an accuracyof approximately 3 to 6 % of EPDM or IIR alone. When both EPDM and IIRare present, the minimum detection limit is approximately 12 % of either rubber.

Specimen Test Method 1:From pyrolyzates: A small quantity of extracted and dried rubber.Fromfilms: Film of extracted and dried rubber, dissolved in 1,2-dichlorobenzeneand filtered. The film is cast on a salt plate.Test Method 2:A film obtained from milled samples, digested in hot 1,2-dichlorobenzene andfiltered to remove carbon black.A milled vulcanizate, digested with a hot solution of sulfuric and chromic acid.A film of the residue is dissolved in boiling dichloromethane is cast on salt plate.

Apparatus Test Method 1:Extraction Apparatus: Test tubesPyrolysis Apparatus: Salt plates, polished (sodium chloride or potassium bro-mide), 4 mm X 25 mm (windows for the spectrophotometer). High-resolutioninfrared spectrophotometer, double beam, capable of recording a spectrum overthe 2.5 to 15 μm (4000 to 667 cm-1) region.Test Method 2:In addition to the ones of the test method 1:- Grinding mill capable of grinding vulcanized rubber to 420 μm (40 mesh)- Magnetic stirring hot plate, with controlled stirring rates, capable of holdingseveral 50 cm3 conical flasks. Magnetic stirring bars, covered with a chemical-resistant coating, approximately 25 mm long.- Buchner funnel, for use with 5.5 cm filters.- Glass fiber filters, 5.5 cm in diameter.- Vacuum filtering device and vacuum oven.- Heat resistance conical flasks, 50 cm3 and 250 cm3 capacity



Standard ASTM D3677-00 (2004)

Test procedures Test Method 1: Few drops of the pyrolyzate are placed in the salt plate andthe infrared spectrum is recorded in the 4000 to 667 cm-1 region. The rubbershould be identified by comparison with standard spectra and by reference tocharacteristic infrared absorption.Test Method 2: The approximate composition of blend is obtained from ab-sorbance ratio of certain characteristic bands with the 1450 cm-1 reference band.A previous calibration with reference blends is necessary.

Values and Units Type o f rubber identified in the compound. Approximate composition in accor-dance with the scope of test method.

Table 2.11: Standard test method for copolymerized ethyl acrylate In ethylene-ethylacrylate copolymers

Standard ASTM D3594-93(2000)

Scope Intended for determining content of ethyl acrylate comonomer, between therange of 1 to 25 % weight, in ethylene-ethyl acrylate copolymers.

Specimen Thick films, in the range of 0.18 to 0.50 mm (depending of the comonomercontent).

Apparatus Infrared Spectrophotometer capable of spectral resolution equivalent to that de-fined by Practice E 275. It should be capable of scale expansion along thewavelength (or wave number) axis, or a Fourier Transform Infrared Spectropho-tometer (FT-IR), with nominal 4 cm-1 resolution. A small compression-moldingpress, that can be heated to 150◦C. Two smooth 0.5 mm X 150 mm X 150 mmor larger metal plates (chromium plated). Three 75 mm X 75 mm brass shimswith 0.50 mm, 0.25 mm, and 0.18 mm thickness, respectively, and a center holeof at least 25 mm X 38 mm. Micrometer calipers, with thimble graduations of0.001 mm. Film Mounts, with holes of at least 6 mm X 27 mm to hold thespecimens in the spectrophotometer

Test procedures The ratio of the absorbance at 11.6 μm and thickness in mm, is used to determinethe ethyl acrylate comonomer content. A calibration curve with ethylene-ethylacrylate copolymers of known composition, is used.

Values and Units Weight percent ethyl acrylate comonomer.

24 2 Spectroscopy

Table 2.12: Determination of ethylene units in EPM (ethylene-propylene copolymers)and EPDM (ethylene-propylene-diene terpolymers)


Scope These infrared test methods are used to determine the proportion of ethyleneand propylene units in ethylene-propylene copolymers (EPM) and ethylene-propylenediene terpolymers (EPDM) over the range from 35 to 85 mass %ethylene. Four test methods are needed to cover the variety of commercialpolymers that contain additives or polymerized diene units that interfere withthe various infrared peaks. Except when interferences are present, all four testmethods should give similar results.Test Method A - For EPM and EPDM between 35 and 65 mass % ethyleneTest Method B - For EPM and EPDM between 60 and 85 mass % ethylene,except for ethylene/propylene/1,4-hexadiene terpolymersTest Method C - For all EPM and EPDM polymers between 35 and 85 mass %ethylene, using near infrared.Test Method D - For all EPM and EPDM polymers between 35 and 85 mass %ethylene, except for ethylene/propylene/1,4-hexadiene terpolymers. These testmethods are not applicable to oil-extended EPDM unless the oil is first removedin accordance with Test Method D.

Specimen Pressed or cast films.

Apparatus Hydraulic press, capable of 200 MPa (29 000 psi) and 150◦C. Infrared spec-trophotometer. Fourier transform infrared (FT-IR) may be used.

Test procedures Test MethodA - Pressed films are measured for their infrared absorbance ratiosat 8.65/13.85 μm (1156/722 cm-1), and mass percent ethylene is read from acalibration obtained from standard polymers.Test Method B -Thin pressed films are measured for their infrared absorbanceratios at 7.25/13.85 μm (1379/722 cm-1), and mass percent ethylene is read froma calibration obtained from standard polymers.Test MethodC - Pressed films are measured for their infrared absorbance ratiosat 8.65/2.35μm(1156/4255 cm-1) using near infrared, andmass percent ethyleneis read from a calibration obtained from standard polymers.Test Method D - Ultra-thin cast films on a salt plate are measured for theirinfrared absorbance ratios at 7.25/6.85 μm (1379/1460 cm-1), and mass percentethylene is read from a calibration obtained from standard polymers.

Values and Units Weight percent of ethylene comonomer.


Table 2.13: Standard practice for rubber chemicals-determination of infrared absorptioncharacteristics

Standard ASTM D2702-05

Scope Describes a simple, rapid practice to prove the identity of a rubber chemicalbefore incorporation into a rubber mix by comparison of its infrared absorptionspectrum with that of a reference specimen.This technique can also be used to detect gross contamination or large differ-ences in rubber chemicals. Thus, it can provide a basis for producer-consumeragreement.

Specimen The physical nature of the specimen will determine the specimen preparationprocedure. They can be: Liquid or solid (powder, melted films, dissolved insolvent, film cast from solution, specimen intimately mixed with KBr powderand pressed into a pellet)

Apparatus Agate mortar and pestle, small.Wig-L-bug amalgameter.Mold and press for KBr pellets: The die size will depend on the disk holderavailable with the user’s infrared spectrophotometer. The hydraulic press shouldbe capable of exerting 140 MPa (20 000-psi) pressure.Vacuum pump, operating at 250 Pa or less.Infrared spectrophotometer: The spectral region from 2.5 to 15 μm (4000 to667 cm-1 ) is the region most often used for rubber chemical identification,although inorganic chemicals may have useful bands down to 250 cm-1 .Demountable Cells - Liquid cells ranging from 0.025 to 1.0mm in specimen pathlength and KBr pellet holder should be available. On occasion, a variable-pathcell is useful.KBr or NaCl plates, of suitable size for spectrophotometer.

Test procedures The infrared spectra of the sample and the reference are compared in the regionfrom 4000 to 667 cm-1 under the same conditions.

Values and Units Comparison of infrared spectra of sample and reference.

26 2 Spectroscopy

Table 2.14: Standard testmethod for vinylidene unsaturation in polyethylene by infraredspectrophotometry

Standard ASTM D3124-98 (Reapproved 2003)

Scope This technique is intended to measure the vinylidene unsaturations in all typesof polyethylenes, those ethylene plastics consisting of ethylene and α-olefincopolymers longer than propylene, and blends of the above in any ratio.

Specimen Brominated and unbrominated pressed films of polymer

Apparatus Infrared spectrophotometer, either double beam or Fourier transform (FTIR):- Double-beam infrared spectrophotometer, capable of spectral resolution thevalues. The instrument should be capable of scale expansion along the wave-length (or wave number) axis.- Fourier transform infrared spectrometer, capable of 4 cm-1 resolution and scaleexpansion along the wavelength axis.- A small compression-molding press with platens capable of being heated to170◦C.- Two smooth 150 mm X 150 mm X 0.5 mm metal plates, preferably chromiumplated.- Brass shims, approximately 75mmX 75mmX0.5 mmwith a 25 mmX 38mmcenter hole.- Micrometer calipers, with thimble graduations of 0.001 mm.

Test procedures The absorption band at 888 cm-1 (11.26μm) is characteristic of vinylidene unsat-urations (>C=CH2) in Polyethylenes and it is characteristic of the deformationvibrations of the C - H bonds in the CH2 group. Since this band is overlappedby absorption from vibrations of terminal methyl groups on alkyl groups longerthan ethyl, the samples is brominated to destroy the unsaturation. The concen-tration of the vinylidene unsaturations could be determined by comparison withthe unbrominated sample and with a standard of 2,3-dimethyl-1,3-butadiene.

Values and Units Number of vinylidene unsaturations per 1000 carbon atoms.


Table 2.15: Standard determination of the vinyl acetate content of ethylene-vinyl acetate(EVA) copolymers by Fourier transform infrared spectroscopy (FT-IR)

Standard ASTM 5594 -94

Scope This test method determines vinyl acetate content of EVA copolymers usingpressed films (Procedure A) or molded plaques (Procedure B) and internal cor-rections for sample thickness. This test method is applicable to the analysis ofEVA copolymers containing 0.5 to 29% vinyl acetate.

Specimen Pressed polymer film. Molded plaques material sample in sandwich withpolyester sheets

Apparatus Fourier transform infrared (FT-IR) spectrophotometer, a hot plate (Procedure Aonly, a microscope slides (procedure A only), a laboratory press, backing plates,a brass shim stock (Roll), a polyester sheet, and a metal template.

Test procedures The ratio of the absorbance at 609 cm-1 and absorbance at 1465 cm-1, is usedto determine the vinyl acetate comonomer content. A calibration curve withethylene-vinyl acetate copolymers of known composition, is used.

Values and Units Weight percent of vinyl acetate comonomer

Table 2.16: Standard test methods for rubber-determination of ethylene units inethylene-propylene copolymers (EPM) and in ethylene-propylene-diene terpolymers(EPDM) by Infrared spectrometry


Scope These test methods are used for determining the proportion of ethyleneand propylene units in ethylene-propylene copolymers (EPM) and ethylene-propylenediene terpolymers (EPDM) over the range from 35 to 85 mass %ethylene. Four test methods are needed to encompass the variety of commercialpolymers that contain additives or polymerized diene units that interfere withthe various infrared peaks:Pressed Film Test Methods:Test Method A - For EPM and EPDM between 35 and 65 mass % ethyleneTest Method B - For EPM and EPDM between 60 and 85 mass % ethylene,except for ethylene/propylene/1,4- hexadiene terpolymersTest Method C - For all EPM and EPDM polymers between 35 and 85 mass %ethylene, using near infrared


28 2 Spectroscopy


Cast Film Test Methods:Test Method D - For all EPM and EPDM polymers between 35 and 85 mass %ethylene, except for ethylene/propylene/1,4- hexadiene terpolymersExcept when interferences are present, all four test methods should give similarresults. These test methods are not applicable to oil-extended EPDM unless theoil is first removed in accordance with Test Method D.

Specimen Pressed films, ultra thin cast film.

Apparatus Hydraulic Press, capable of 200 MPa (29 000 psi) and 150◦C.Infrared Spectrophotometer, double-beam, having a percent transmission spec-ification of 6 1 %, or better, at full scale, capable of recording a spectrum overthe 2.5 to 15μm (4000 to 667 cm-1) region for Test Methods A, B, and D. TestMethod C requires an instrument capable of recording a spectrum over the 2.0 to15 μm (2000 to 667 cm-1) region. For routine testing, Fourier transform infrared(FTIR) may be used in place of double beam instruments provided the baselinecalculation procedures. Sample film temperature is lower with FTIR than doublebeam instruments

Test procedures Test Method A: The test method uses the ratio of the absorbance of methylgroups from polypropylene units (at 1156 cm-1) versus the absorbance of methy-lene sequences from ethylene units (at 722 cm-1) to determine ethylene percent-age using a calibration curve.Test Method B: The test method uses the ratio of the absorbance of methylgroups from polypropylene units (at 1379 cm-1) versus the absorbance of methy-lene sequences from ethylene units (at 722 cm-1) to determine ethylene percent-age using a calibration curve.Test Method C: The test method uses the ratio of the absorbance of methylgroups from polypropylene units (at 1379 cm-1) versus the absorbance of C-Hbonds from ethylene units (at 4255 cm-1) to determine ethylene percentage usinga calibration curve.Test Method D: The test method uses the ratio of the absorbance of methylgroups from polypropylene units (at 1379 cm-1) versus the absorbance of theabsorbance of C-H bonds for internal thickness (at 1460 cm-1) to determineethylene percentage using a calibration curve.

Values and Units For EPM: mass percent ethylene to the nearest whole number.For EPDM: ethylene/propylene mass ratio, uncorrected for diene content, to thenearest whole number.


Table 2.17: Standard test method for rubber-determination of residual unsaturation inhydrogenated nitrile rubber (HNBR) by infrared spectrophotometry


Scope This test method is used to determine the percentage of residual unsaturation inhydrogenated nitrile rubber and is based on infrared examination of rubber filmscast from solution.This test method is applicable to all grades of hydrogenated nitrile rubber in theraw state.

Specimen Rubber specimen purified by precipitation, rubber specimen purified by extrac-tion, cast rubber films.

Apparatus Preparation of rubber solution:Erlenmeyer flask with ground glass stopper (50 cm3).Flask shaker.Precipitation of rubber from solution:Beaker (250 cm3).Magnetic stirrer.Dropping funnel (150 cm3).Extraction of rubber:Soxhlet extraction apparatus with flask (150 cm3).Extraction thimbles (27 mm X 100 mm).Reagents:MethanolDry compressed nitrogenMethyl ethyl ketone MEKExtraction thimbles (27 mm X 100 mm).Kofler heating bench or other heating device, with temperature control.Spectrophotometer, required resolution capability of 2 cm-1 and spectral regionof 2500 - 600 cm-1.

Test procedures The specimen is previously purified by precipitation with methanol from aMEKsolution or by soxhlet extraction withmethanol. The purified sample is dissolvedagain with MEK and cast in KBr disc. The FTIR spectra is obtained the cor-rected absorbance (from baseline) of acrylnitrile, butadiene and hydrogenatedbutadiene.

Values and Units Residual unsaturations of the HNBR specimen(s) reported to the nearest 0.1percentage point.

30 2 Spectroscopy

INDUSTRIAL APPLICATION 2.1

Multilayer film characterization

Here, a coextruded and laminated film was analyzed to determine the layer structure.Because the objective was the determination of the composition of each layer, the fol-lowing analyses were considered: a morphological study in an optical microscope, anATR analysis for each film side, a transmission FTIR, and a DSC (presented in detailin Chapter 4 of this book)

Figure 2.2: Optical microscopy photograph of the film.

Morphological Study: A morphological study of the film was done in an opticalmicroscope and a photograph of the layer structure is presented in Fig. 2.2. The sam-ples were cut and supported in an special fixture to be observed at 500 magnificationwith transmitted light, after a selective dyeing for the possible presence of polyamideor ethylene vinyl alcohol. The morphological study revealed that the film had sevenlayers, one being polyamide or ethylene vinyl alcohol.

ATRAnalysis: TheATRspectrumof sideA (external) of thefilm,aswell as the spec-trum of a polyethylene terephthalate (PET) are presented in Fig. 2.3. The spectrumfrom side A exhibited an excellent coincidence with the polyethylene terephthalatespectra from the library. The spectrum also exhibited the following characteristic ab-sorption bands typical of PET (see Tables 2.4 and 2.5):

– A strong band was observed around 1740 cm-1, characteristic of the carbonyl group(C=O bond) stretching in polyesters.– A broad and strong band was observed between 1300 and 1200 cm -1, characteristicof the asymmetric extension of ester group (C-O-C).– A broad and strong band was registered between 1200 and 1050 cm -1, characteristic


of the symmetric extension of ester group (C-O-C).– A strong and sharp band was detected around 830 cm -1, characteristic of the flexionof aromatic ring.– The comparisonwith the IR spectra library confirmed a goodmatch with a polyethy-lene terephthalate (PET).

Figure 2.3: ATR analysis of the side A (external) of the film

Figure 2.4: ATR analysis of the side B (internal) of the film

32 2 Spectroscopy

The ATR spectrum of side B (internal) of the film, as well as the spectrum of a low-density and linear low-density polyethylene are presented in Fig. 2.4. The spectrumfrom side B exhibited an excellent coincidence with the low-density and linear low-density polyethylene spectra from the library. The spectrum also exhibited the follow-ing characteristic absorption bands of polyethylenes (see Tables 2.4 and 2.5):

– Strong and sharp bands were observed between 3000 and 2800 cm -1, characteris-tic of the symmetric and asymmetric extension of aliphatic C-H bond of methyl andmethylene groups of polyethylenes.– A broad and strong band was registered around 1450 cm -1, characteristic of the flex-ion of C-H in methylene groups of polyethylenes.– A broad and low intensity band was observed around 1380 cm -1, characteristic ofthe flexion of C-H in methylene groups of polyethylenes.– The comparison with the IR spectra library confirmed a good match with a low-density and linear low-density polyethylene.

Transmission FTIR: The transmission FTIR spectrum of the film, as well as the spec-trum of polyethylene terephthalate (PET) and ethylene vinyl alcohol (EVOH), arepresented in Fig. 2.5. The transmission spectrum of the film exhibited an excellentcoincidence with both the PET and EVOH spectra from the library. The transmissionspectra exhibited the following characteristic bands of PET and EVOH (see Tables 2.4and 2.5):

– A broad band was observed between 3600 and 3000 cm -1, characteristic of the OHbond stretching in the ethylene vinyl alcohol.– A strong band was registered around 1740 cm-1, characteristic of the carbonyl group(C=O bond) stretching in polyesters.– A band at 1464 cm-1 was observed, characteristic of the symmetric bending ofmethylene group of polyethylene, and it is also overlapped with the CO stretching ofthe ethylene vinyl alcohol.– A band of the OH flexion in the ethylene vinyl alcohol was observed in the range of1310 to 1410 cm-1.– A broad and strong band was registered between 1200 and 1050 cm -1, characteristicof the symmetric extension of ester groups (C-O-C), and it is overlapped with theflexion of an OH bond in the alcohol group.– Bands at 730 and 720 cm-1 were observed, characteristic of the rocking of methy-lene in the crystal and the rocking vibration of a minimum of four consecutive –CH 2-groups of polyethylene and the ethylene vinyl alcohol, respectively. These bands areoverlapped with the flexion of an aromatic ring of PET.– The comparison with the IR spectra library confirmed a good match with polyethy-lene terephthalate (PET) and ethylene vinyl alcohol.

Conclusions: The FTIR analysis of the film revealed the presence of low-density andlineal low-density polyethylene, ethylene vinyl alcohol, and polyethylene terephtha-late. The FTIR analysis and the morphology study suggested that the film had seven


Figure 2.5: Transmission FTIR spectra of the film

Figure 2.6: Proposed multilayer structure of the film

34 2 Spectroscopy

layers, with the structure shown in Fig. 2.6. To guarantee the good adhesion of thelayers, tie layers between PET and the polyethylenes and between the EVOH and thepolyethylenes were observed. More details of the particular type of polyethylene anda confirmation of the proposed structure will be presented in detail in Chapter 4.


Analysis of an EVA-based foam

In this case study, an unknown black foamed product was analyzed to determine theformulation of this elastomeric-likematerial. The samplewasfirst dissolved in tetrahy-drofuran (THF), filtered, and precipitatedwith methanol. The precipitated sample wasdried in a KBr window and then analyzed by FTIR spectroscopy.The obtained FTIR spectrum is presented in Fig. 2.7. The spectrum of an ethylenevinyl acetate copolymer obtained from the IR library was also presented for compari-son purposes. The transmission spectrum exhibited the following characteristic bandsof the ethylene vinyl acetate copolymer (see Tables 2.4, 2.5, and 2.6):

vinyl

Figure 2.7: FTIR spectrum of black foamed product

– A strong and sharp band was observed between 3000 and 2800 cm -1, characteristicof the symmetric and asymmetric extension of aliphatic C-H bond of methane, methyl,and methylene groups present in the ethylene vinyl acetate copolymers.– A strong and sharp band was observed around 1740 cm -1, characteristic of the car-bonyl group (C=O bond) stretching in the acetate group present in the ethylene vinylacetate copolymers.– A band was registered around 1450 cm-1, characteristic of the flexion of C-H inmethylene groups present in the ethylene vinyl acetate copolymers.


–A broad and low intensity bandwas observed around 1380 cm -1, characteristic of theflexion of C-H in methylene groups present in the ethylene vinyl acetate copolymers.– A strong and sharp band was observed around 1240 cm -1, characteristic of the asym-metric extension C-O-C in the acetate group present in the ethylene vinyl acetatecopolymers.– A sharp band was observed around 1020 cm-1, characteristic of the symmetric ex-tension C-O-C in the acetate group present in the ethylene vinyl acetate copolymers.– Bands at 730 and 720 cm-1 were observed, and they are characteristic of the rockingof methylene in the crystal and the rocking vibration of a minimum of four consecu-tive –CH2- groups of the ethylene vinyl acetate copolymers. The sample presented ahigh content of vinyl acetate comonomer due to a low intensity (related with the otherbands) of these bands, which are representative of the ethylene comonomer.– The comparisonwith the IR spectra library confirmed a goodmatch with an ethylenevinyl acetate copolymer.

Conclusions: The FTIR analysis of the unknown black foamed product revealed thepresence of an ethylene vinyl rubber (EVA). A thermogravimetric analysis (TGA) ofthis sample will be presented in detail in Chapter 4 of this book.


Formulation analysis for PVC plastisol applications

A sample of car upholstery was analyzed to determine its possible composition. Aprevious identification test using flame showed that it potentially is a flexible PVCcom-pound. Before any test, it was recommended to perform a separation and interferenceelimination following the method presented in Fig. 2.8.The soluble fraction in THF, precipitated with methanol, was analyzed by FTIR.

The resulting IR spectrum is presented in Fig. 2.9. The FTIR spectrum of the solu-ble fraction in THF precipitated with methanol exhibited the characteristic absorptionbands of a polyvinyl chloride (PVC), which confirmed that the car upholstery was aflexible PVC compound. The FTIR spectrum could be detailed as follows (see Tables2.4 and 2.5):– The characteristic bands of C-H bond stretching in aliphatic compound (–CH 2–and –CH<) were observed in the regions of 2920 to 2930 and 2848 to 2858 cm -1.– The characteristic band of C-H bond flexion in aliphatic compoundwas observed inthe region of 1450 to 1480 cm-1.– The characteristic band of C-H bond flexion in CH-Cl compound was observed at1250 and 1350 cm-1.– The characteristic band of C-H bond torsion in aliphatic compoundwas observed inthe region of 1150 to 1350 cm-1.– The characteristic band of C-Cl compound was observed at 600 to 690 cm -1.– The comparisonwith the IR spectra library confirmed a goodmatch with a polyvinylchloride.

36 2 Spectroscopy

Figure 2.8: Recommended method for separation and interference elimination in PVC compounds

Figure 2.9: FTIR spectrum of the soluble fraction in THF and precipitated with methanol

First, the different layers and woven fabric were separated from the sample. Aftersize reduction, the sample was extracted with acetic acid/n-heptane, and the solventof the extract was carefully evaporated in a vacuum oven. The FTIR spectrum of thefinal extract is presented in Fig. 2.10. This FTIR spectrum exhibited a good match


Figure 2.10: FTIR spectrum of acetic acid/n-heptane extract after solvent evaporation

with the organotin stabilizers spectra in the IR spectra library. The characteristicabsorption bands of the organotin stabilizers were observed particularly at 1725, 1600,and 1100 cm-1.

Figure 2.11: FTIR spectrum of the insoluble fraction in THF

The insoluble part in THF for one of the layers was analyzed by the FTIR tech-nique, and the spectrum appears in Fig. 2.11. The characteristic band of trihydratedalumina is observed at 3521 cm-1, as well as a good match with this flame retardantspectra in the IR spectra library. Additionally, the presence of phosphate plasticizers,also a flame retardant, was confirmed within the soluble fraction in THF after the se-lective dissolution and precipitation was analyzed by the GC/MSD. The results of theGC/MSD analysis are presented in Chapter 4 of this book.Conclusions: The analyzed sample of car upholstery was a flexible PVC compoundwith the presence of an organotin thermal stabilizer, trihydrated alumina flame retar-dant, and a mixture of phosphate plasticizers (also used as flame retardant).

38 2 Spectroscopy


Characterization of a plastic hose

A plastic hose composed of an exterior layer, a central fiber reinforcement, and aninterior core was analyzed to determine the polymeric materials of each layer. Verythin specimenswere cut in themicrotome from the exterior and the core layers andwereanalyzed by FTIR spectroscopy. Fibers of the central reinforcement were manuallyremoved from the hose and analyzed by the photoacoustic technique.The transmission FTIR spectrum of the interior core, as well as the spectrum of

a nitrile rubber and DOP plasticized polyvinyl chloride, are presented in Fig. 2.12.The transmission spectrum exhibited characteristic bands of the nitrile rubber, thedioctylphthalate (DOP) plasticizer1 and polyvinyl chloride (see Tables 2.4, 2.5, and2.6).

Figure 2.12: Transmission FTIR spectrum of the interior core of a plastic hose

The characteristic bands of nitrile rubber observed was a very sharp band at 2260to 2240 cm-1, characteristic of a nitrile (-C≡ N) bond. The comparison with the IRspectra library confirmed a good match with a nitrile rubber.The characteristic bands of polyvinyl chloride observed were:

– The characteristic bands of C-H bond stretching in aliphatic compound (–CH 2–and –CH<) were observed in the regions of 2920 to 2930 and 2848 to 2858 cm -1.– The characteristic band of C-H bond flexion in aliphatic compound was observed in

1Bis(2-ethylhexyl phthalate)


the region of 1450 to 1480 cm-1.– The characteristic band of C-H bond flexion in CH-Cl compound was observed at1250 and 1350 cm-1.– The characteristic band of C-H bond torsion in aliphatic compoundwas observed inthe region of 1150 to 1350 cm-1.– The characteristic band of C-Cl compound was observed at 600 to 690 cm -1.– The comparisonwith the IR spectra library confirmed a goodmatch with a polyvinylchloride.

The characteristic bands of dioctylphthalate plasticizer (DOP) observed were:

– The characteristic bands of C-H bond stretching in aliphatic compound (–CH 2–and –CH<) were observed in the region of 2920 to 2930 and 2848 to 2858 cm -1.– A strong band was observed around 1740 cm-1, characteristic of the carbonyl group(C=O bond) stretching in polyesters.– A doublet of band with low intensity at 1598 and 1580 cm -1 was observed. This isvery characteristic of DOP plasticizers.– A broad and strong band was observed between 1300 and 1200 cm -1, characteristicof the asymmetric extension of the ester group (C-O-C).– A broad and strong band was registered between 1200 and 1050 cm -1, characteristicof the symmetric extension of the ester group (C-O-C).– The comparisonwith the IR spectra library confirmed a goodmatchwith a dioctylph-thalate (DOP) plasticizer.

Figure 2.13: Transmission FTIR spectrum of the exterior layer of a plastic hose

40 2 Spectroscopy

The transmission FTIR spectrum of the exterior layer, as well as the spectrum of adioctylphthalate (DOP) plasticizers and polyvinyl chloride, are presented in Fig. 2.13.The transmission spectrum exhibited characteristic bands found in dioctylphthalate(DOP) plasticizers and polyvinyl chloride (see Tables 2.4, 2.5, and 2.6).The characteristic bands of polyvinyl chloride observed were:

– The characteristic bands of C-H bond stretching in aliphatic compound (–CH 2–and –CH<) were observed in the regions of 2920 to 2930 and 2848 to 2858 cm -1.– The characteristic band of C-H bond flexion in aliphatic compound was observed inthe region of 1450 to 1480 cm-1.– The characteristic band of C-H bond flexion in CH-Cl compound was observed at1250 and 1350 cm-1.– The characteristic band of C-H bond torsion in aliphatic compound was observed inthe region of 1150 to 1350 cm-1.– The characteristic band of C-Cl compound was registered at 600 to 690 cm -1.– The comparisonwith the IR spectra library confirmed a goodmatch with a polyvinylchloride.

The characteristic bands of dioctylphthalate (DOP) plasticizer were:

– The characteristic bands of C-H bond stretching in aliphatic compound (–CH 2–and –CH<) were observed in the region of 2920 to 2930 and 2848 to 2858 cm -1.– A strong band was observed around 1740 cm-1, characteristic of the carbonyl group(C=O bond) stretching in polyesters.– A doublet of band with low intensity at 1598 and 1580 cm -1 was observed. This isvery characteristic of DOP plasticizers.– A broad and strong band was observed between 1300 and 1200 cm -1, characteristicof the asymmetric extension of ester groups (C-O-C).– A broad and strong band was registered between 1200 and 1050 cm -1, characteristicof the symmetric extension of ester groups (C-O-C).–Comparisonwith the IR spectra library confirmedagreementwith a (DOP)plasticizer.

The transmission FTIR spectrum of the reinforcement fiber, as well as the spectrumof a polyethylene terephthalate, are presented in Fig. 2.14. The transmission spectrumexhibited characteristic bands typical of polyethylene terephthalate (see Tables 2.4 and2.5). These were:– A strong band was observed around 1740 cm-1, characteristic of the carbonyl group(C=O bond) stretching in polyesters.– A broad and strong band was observed between 1300 and 1200 cm -1, characteristicof the asymmetric extension of ester groups (C-O-C).– A broad and strong band was registered between 1200 and 1050 cm -1, characteristicof the symmetric extension of ester groups (C-O-C).– A strong and sharp band was observed around 830 cm -1, characteristic of the flexionof an aromatic ring.


Figure 2.14: Transmission FTIR spectrum of the reinforcement fiber of a plastic hose

– The comparisonwith the IR spectra library confirmed a goodmatch with a polyethy-lene terephthalate (PET).

Conclusions: The analyzed plastic hose had the following layer composition:

– The core layer is composed of a blend of nitrile rubber, dioctylphthalate (DOP) plas-ticizer, and polyvinyl chloride.– The reinforcement is composed of polyethylene terephthalate (PET) fibers.– The exterior layer is composed of a blend dioctylphthalate (DOP) plasticizer andpolyvinyl chloride.– An extract rich in plasticizers was studied by gas chromatography combined withmass selective detector, and the presence of (DOP) plasticizer was confirmed.


Determining filler type in a polypropylene resin

Polypropylene pellets were analyzed to determine the filler type. The filler contentwas determined by carrying out a TGA study of the polypropylene resin, and the typeof filler was determined by a FTIR of the final ash obtained in the TGA. The samplepreparation was done by pressing a KBr pellet with the ash obtained after the TGAanalysis.The transmission FTIR spectrum of the final ash is presented in Fig. 2.15. For

comparison purposes the spectrum of the calcium hydroxide was also presented. TheFTIR spectrum of final ash registered a good coincidence with the calcium hydroxide,

42 2 Spectroscopy

generated by hydration of the calcium oxide produced during the thermal decomposi-tion of calcium carbonate in the TGA analysis.

Conclusions: The FTIR study of the residual ash of the TGA analysis allowed theconclusion that the filler in the polypropylene resin was a calcium carbonate. Moredetail of the filler content and a confirmation of the type of filler are presented inChapter 3.

Figure 2.15: FTIR spectrum of the TGA ash


Determining the cause of failure of an industrial hose

A failed industrial hose, as shown in Fig. 2.16, was analyzed to determine the causeof the failure. The hose was composed of an approximately 200 μm-thick innerUHMWPE layer that should act as the chemically resistant layer.Surrounding it is a thick structural EPDM layer that is reinforced with polyester

fibers and helically wrapped steel wires. When the hose failed, it was being used topump sulfuric acid at a concentration of 93%. The day of the failure the ambienttemperature reached 33 ◦C, but it had been warmer during the days prior to the failure.Because the hose could not be destroyed, a colonoscope, used to perform colono-

scopies on humans, was employed to photograph the inside of the hose so that theinner surface could be analyzed. The photographs in Fig. 2.17 reveal a helical crack,very deep in some areas, that ran along a seam cause by the manufacturing processof the hose. Furthermore, to determine if other regions of the hose had already beenattacked by the sulfuric acid, a series of X-rays were taken using a high resolutionX-ray machine to perform mammograms.


Figure 2.16: Photographs of the failed hose

Figure 2.17: Series of images of the inner surface of the failed hose generated with a colonoscope

The two X-rays shown in Fig. 2.18 reveal a section on the left where the steelwires have not been influenced by the sulfuric acid, and the image on the right showsextensive corrosion on the wire surfaces in the regionswhere the cracks (as determinedby the colonoscope) were deep, implying chemical attack by the sulfuric acid.Furthermore, the crack surfaces were analyzed using microscopy and SEM, as

shown in Fig. 2.19. The images reveal that the cracks originated in the the inside of thehose and traveled from theUHMWPE layer toward theEPDM layers. Furthermore, theimageswith the 50μm scale reveal a nodular surface quality that points to acid-etching

44 2 Spectroscopy

Unaffected Corroded

Figure 2.18: X-ray (mammography machine) images of an unaffected and a corroded section of thehose

1mm

Figure 2.19: SEM images of the crack surface in the failed hose; the top photograph shows theregion where the SEM images where taken

effects. Therefore, it can be deduced that the cracks were caused by environmentalstress cracking. Other SEM images also revealed etching and cracking of the surfacesadjacent to the rupture zone.To confirm if chemical attack occurred prior to rupture, an infrared (IR) spectrum

was performed on the UHMWPE lining, as well as on the polyester fibers and EPDMrubber casing. The IR spectra for the inner liner taken at various locations along


the hose, including the region where the rupture occurred, show evidence of acidpenetration into the molecular structure of the liner, leaving no doubt that chemicalattack by sulfuric acid occurred on the UHMWPE layer.

4000 8001000150020003000 600cm-1

Abs

orpt

ion

Standard polyethylene

UHMWPE liner of the failed hose

Methasulfonic acid

Figure 2.20: IR spectra of a standard polyethylene (top), UHMWPE liner of the failed hose (middle)and of methasulfonic acid (bottom)

Figure 2.20 presents a comparison of a spectrum performed on the failed hose nearits surface to a standard polyethylene and a spectrum of methasulfonic acid. It is clearthat the spectrum of the acid shows commonalities with the spectrum taken of thefailed hose. Clear sulfuric acid modifications are visible at 1200 and 1700 cm -1. Insimilar spectra, generated with the polyester fibers in the failed hose, the presence ofteraphthalic acid, a chemical produced during degradation of polyester, was detected.

2.2 RAMAN SPECTROSCOPY

To illustrate how Raman spectroscopy2 works one should consider what happens to a beamof monochromatic light when it is directed to a material. Some of the light will be reflected,some will be absorbed, and some will be transmitted through the material. Most of thereflected light will have the samewavelength as the incident light, but a small fractionmay beshifted in wavelength because of the vibrations and rotations of the molecules in the sample.This wavelength-shifted light is what is seen in a Raman spectrum [10]. Each peak in thespectrum represents amolecular vibration that causeda shift in thewavelength of the scattered

2Parts of this section were written by Javier Cruz of the Polymer Engineering Center at the University ofWisconsin-Madison.

46 2 Spectroscopy

or reflected light. The intensity of the peak is directly proportional to the concentrationof the species in the sample. Hence, the Raman scattered light from a sample is simplythe sum of the individual scattering from all the atom bonds that generate that particularvibration. One of the main benefits of Raman spectroscopy that leads to its vast possibilitiesin polymeric reactions is that the Raman signal is strong in long polymer chains where thedipole moments, which are the basis for IR detection, are in many occasions canceled out[10]. The Raman scatter is dependent on changes in polarizability, therefore, being quitesensitive to vibrations in symmetrical molecules and larger atoms [8]. IR measurements arerecording the absorption that arises due to a direct resonance between molecular vibrationalfrequency and IR radiation. This resonance interaction leads to a change in dipole moment.Therefore, when an IR photon encounters the molecule, it is absorbed, and the molecule iselevated to a higher energy level relative to the photon energy absorbed [9]. Raman scatteringon the other hand, involves two steps. The first is when the photon impacts the sample andthe second when the emitted radiation, which contains the Raman scattering, leaves thesample and is collected. During Raman scattering there is a change in the polarizabilityof the molecule, but a dipole moment is not required because it is being induced by theinteraction of the polarizability and the incoming radiation [9]. The polarizability may bedescribed as a tensor value with two Cartesian components; one related to the incomingenergy and one to the scattered energy, which are caused by polarization. Polarization is theforce that light can apply to an electron cloud in the direction perpendicular to the beam oflight. For Raman scattered light the polarizationwill be in the same direction as the changingpolarizability caused by the induced dipole moment on the electron cloud. For example, ifthe incoming light causes an electron cloud movement in the same direction fromwhich it iscoming, then the polarizabilitywill also be in the same direction andwill not induce a Ramanscatter. This is because the scattered light will have the same polarization as the incident lightand there will be no induced dipole. If the electron cloud is moved in a different direction(induced dipole), then the scattered light will have a different polarization from the incidentlight, therefore, containing Raman scattering. The emitted radiation consists of two types ofscatterings: Rayleigh and Raman. Rayleigh scattering is the light that is emitted at the sameenergy level as the incoming radiation; whereas Raman radiation is shifted in frequency andthus in energy. The scattering effects can be represented with energy level diagrams such asthe one shown in Fig. 2.21.A previouslymentionedmonochromatic incident radiation,such as a laser is emitted to the

sample. The scattered radiation is then measured to provide the Raman spectrum. Scatteredlight is shifted from200 cm-1 by asmuch as 4000 cm-1 from the incident light in both positiveand negative direction X, based on the molecules absorbing or releasing energy. As maybe seen in Fig. 2.21, Rayleigh scattering is an elastic scatter. Therefore, the energy level ofthe molecule does not change from an initial to a final state. Raman scattering is a measureof the wavelength and intensity of inelastically scattered light, where a molecule may endin a higher or lower energy level. In particle physics, inelastic scattering is a fundamentalscattering process in which the momentum of an incident particle is not conserved. In thisscattering process, the energy of the incident particle is lost or gained. During Stokes scatter,the final energy level is higher than the initial; anti-Stokes scattering is when the moleculewas already at an elevated vibrational energy state, leading to an energy release. There isbelieved to be symmetry in Stokes and anti-Stokes vibrations, but that is not necessarily the


case considering that a molecule may not shift to a lower level of energy than its lowest state[9, 10]. Disregarding the differences, Raman equipment generally reports only the Stokesscatter.

Virtual energy states

IR absorbance

Stokes (+)Raman scattering

Anti-Stokes (-)Raman scattering

Rayleigh scateringv=0

v=1

v=2

v=3

hvex

hvexhvexhvex

h(vex-vv)

h(vex+vv)

E0

Excitation energy

Vib

ratio

nal e

nerg

y st

ates

Figure 2.21: An energy level diagram showing Stokes, anti-Stokes, and Rayleigh scattering


Analysis of polybutadiene

In contrast to infrared spectroscopy that cannot detect C=C bonds because of sym-metry, Raman spectroscopy is useful for the characterization of polymers that containthese (C=C) bonds. This becomes particularly useful whenmonitoringpolymerizationprocesses, as well as vulcanization and curing reactions.For example, a Raman spectrum of a polybutadiene, which can contain 1,2-vinyl,

1,4-cis, and 1,4-trans units, can be used to quantify the amount of each unit. Eachone of these units is a strong Raman scatter with vibrations generating strong Ramanbands at 1639, 1650, and 1664 cm-1, respectively, as shown in Fig. 2.22 [11].Because the Raman scattering intensity is proportional to the concentration of each

unit, the spectrum can be used for the quantitative analysis of a polybutadiene sample.Because the spectrum contains overlappingbands, curve fitting techniques can be usedto separate the individual bands, assuming that each band is accurately represented us-ing a Gaussian distribution. Figure 2.23 [11] presents the three bands that resultedafter curve fitting.

48 2 Spectroscopy

Raman Shift (cm )-1

Rel

ativ

e In

tens

ity

1620 1640 170016801660

1,2-vinyl

1,4-trans-PB1,4-cis-PB

Figure 2.22: Portion of a Raman spectrum of a polybutadiene sample

Raman Shift (cm )-1

Rel

ativ

e In

tens

ity

1620 1640 170016801660

1,2-vinyl 13%

Cis-1,4-PB 38%

Trans-1,4-PB 38%

Baseline

Figure 2.23: Fitted Gaussian curves that emulate the bands corresponding to the 1,2-vinyl, 1,4-cis,and 1,4-trans units in the polybutadiene sample



Curing reaction of an epoxy resin (EP)

The epoxy resin spectrum also contains many peaks throughout the whole spectrumthat may be used for direct conversion analysis including 3004 cm -1 (CH2 stretch ofepoxy) in the higher frequencies, 1255 cm-1 (oxirane ring vibration) and 1350 cm-1

around the area of interest. Many studies have focused on the use of the peak at1255 cm-1 because of the higher intensity as compared to other peaks, but a maindisadvantage is that this frequency region remains with a residual peak after full con-version, as shown in Fig. 2.24 [12]. To account for this, one must generate a spectrumafter a long period of time to be defined as a full conversion spectrum, and the residualpeak of this spectrum is then considered 100% conversion. The problem with thismethod is that there is never a full epoxide conversion due to the diffusive reactionstage that occurs at infinite viscosities. Peak 1350-1, associated with the reaction ofthe epoxide ring and amine group, will be used for analysis because this peak, thoughsmall, fully disappears because of the crosslinking reaction. Peak 1186 -1 (associatedwith C-H in-plane bending in the backbone [13, 14]) was used as the basis of nor-malization since this peak would not undergo changes in intensity due to the curingreaction. Cruz et al. [12] also studied the effect of pressure on the cure of epoxy

1255 cm-1

1186 cm Reference-1

Cou

nts

0.2

1.2

1.0

0.8

0.6

0.4

1100 1500140013001200-1Raman shift (cm )

1350 cm-1

1.8

1.6

1.4

Figure 2.24: Spectral region for peaks of interest for epoxy resin system, three peaks noted: Peakused for direct conversion (1350 cm-1); peak that may be used for conversion analysis but does notfully disappear during conversion (1255 cm-1); reference peak for normalization (1186 cm-1)

resins using a high pressure reactor. Here, the Raman spectrumwas measured througha 1-inch quartz window, while the inside of the reactor was pressurized to 1000 and2000 psi. Figure 2.25 compares the degree of cure at 1000 and 2000 psi to the cure atatmospheric pressure.

50 2 Spectroscopy

0 543210

0.2

1.0

0.8

0.6

0.4

2000 psi

Atmospheric pressure

1000 psi

Figure 2.25: Conversion analysis for epoxy resin resin cured isothermally at 30 ◦C under varyingpressure


Curing reaction of an unsaturated polyester (UPE)

Figure 2.26 [12] provides an image of a small area of the full spectrum that was usedfor the curing analysis of unsaturated polyester resin and notes the peaks of interest.

1632 cm-1

1732 cm Reference-1

Cou

nts

0.5

3.0

2.5

2.0

1.5

1.0

1550 1750170016501600-1Raman shift (cm )

Figure 2.26: Spectrum interest area for UPE resin during cure. Peaks used for direct conversionanalysis (1632 cm-1) and the reference peak for normalization (1732 cm-1) are shown in the graph

2.3 Energy Dispersive X-Ray Spectroscopy 51

The peak at a frequency of 1632 cm-1 results from the vinyl stretching for the styreneC=C bond that is being consumed during the crosslinking reaction. Therefore, a peakheight of zero corresponds to a 100% conversion or consumption of the C=C doublebonds. Any residual peak will then reflect an incomplete conversion. Peak 1732 cm -1

is created by carbonyl (C=O) stretching vibration in the UP molecule, which does notplay a role in the curing reaction, is not expected to change or interact with the reactionvibrational changes and thus is used as basis of normalization.

2.3 ENERGY DISPERSIVE X-RAY SPECTROSCOPY

Energy dispersiveX-ray spectroscopy (EDS) is an analytical technique used to determine theelemental composition of a component in parts as small as a cubicmicron. EDS is an integralpart of the scanning electron microscope (SEM). When taking an SEM image, the surfaceunder consideration is bombarded with an electron beam. A schematic of an EDS systemis depicted in Fig. 2.27. The bombardment of electrons or photons causes an excitationbetween the atoms, which results in a release of excess energy in the form of X-rays. Whenthe sample surface is bombarded by the electron beam, some electrons are removed fromthe atoms on the sample surface. This results in electron vacancies which must be filledwith electrons from a higher shell. As a result, an X-ray is emitted to balance the energydifference between the two electrons. This process is schematically depicted in Fig. 2.28.

Emitted X-ray

Electron beam

Analyzer

Cou

nt

Energy (keV)

Si (Li) detector

Amplifier

Specimen

Figure 2.27: Schematic diagram of an energy dispersive X-ray spectroscopy system

The amount of energy released is characteristic of the atoms it excites, forming variouspeaks in the energy spectrum, according to the composition of the material. This is becauseevery chemical element has a unique electronic structure and, therefore, a particular responseto electromagnetic waves.It should be noted that many specific elements exhibit multiple peaks, and that peaks from

various chemical elements will overlap somewhat with each other. The intensities or areas ofthe various peaks of a specific spectrum are proportional to the concentration of that specificelement, making EDS not only a qualitative but also a quantitative composition diagnosticstool.

52 2 Spectroscopy

M L K

Photon

Electron lifted into continuum

M L K

Vacancy

Electron from outer shell fills the vacancy

Emitted X-ray

.Figure 2.28: Schematic diagram of the electron activity in EDS

C

Pb

Pb1000

0

5000

4000

3000

2000

10987654321 1211

keV

Cou

nt

Figure 2.29: Spectrum of a poly[N,N-p-phenylene bisacryl (methacryl)amide] showing the presenceof lead

The main elements of an EDS setup are:

• Electron beam source – An electronic beam is generated and focused using a cathodein conjunction with a magnetic lens

• X-ray detector – An X-ray detector is used to convert the X-ray energy into a voltagesignal

• Pulse processor – A pulse processor receives the voltage signal from the detector andpasses it to the analyzer

• Analyzer – The system that processes the data and displays the spectraBecause an electron beam can be accurately controlled, one can collect a spectrum from

a point or particle the size of only a cubic micrometer. Similarly, one can sweep a line oran area generating an X-ray map that depicts the elemental composition of a given surface.As an example, Fig. 2.29 [15] presents the resulting spectrum of a poly[N,N-p-phenylene

2.3 References 53

bisacryl (methacryl)amide] after polymerization. The graph shows significant quantities oflead on the surface analyzed using an SEM.The limitations of EDS are:

• An EDS system detects the presence of an element up to 0.1% concentration.• EDS cannot detect elements below carbon in the periodic table.• EDS has only limited detection capabilities for elements below sodium in the periodictable.

References

1. M. C. Garry, M. P. Fuller and Z. Stanek. An FTIR liquid analyser. American laboratory, 1990.

2. Nicolet. Sample handling training course handbook.

3. ASTMD 5576. Practice for determination of structural entities in polyolefins by FTIR. Americanstandard testing materials ASTM, 803:584–586.

4. J. N. Lomonte. IR determination of vinylidene unsaturation in polyethylene. Analytical chemistry,pages 129–131, 1962.

5. R. T. Conley. Infrared spectroscopy. Allyn and Bacon Inc. 2nd edition, 1972.

6. J. D. Sierra, C.Gartner andR.Avakian. Newpolyolefins characterization by instrumental analysis.ANTEC, 1998.

7. J. D. Sierra, S. Ospina, N. Montoya, M. P. Noriega, and T. A. Osswald. Characterization ofpolyethylene blends byusing novel techniques such as the successive self-nucleation and annealing(SSA) and the Fourier self-deconvolution IR spectroscopy (FSD-IR). ANTEC, 2000.

8. E.G. Brame Jr. and J.G. Graselli. Infrared and Raman Spectroscopy, Part C, page 873. MarcelDekker, Inc., NewYork, 1999.

9. I. R. Lewis andH.G. Edwards. Handbook of Raman Spectroscopy: From the Research Laboratoryto the Process Line, volume 2. Marcel Dekker, Inc. New York, 2001.

10. M.J. Pelletier. Analytical Applications of Raman Spectroscopy. Blackwell Science, MA, 1999.

11. N.N. Microstructural analysis of polybutadiene. RamanRXN Systems Applications Note, (403),2003.

12. J. C. Cruz, T. A. Osswald, and M. Kemper. Monitoring curing reactions of thermosets under highpressure by use of Raman spectroscopy. In SPE-ANTEC Tech. Papers, pages 2129–2133, 2007.

13. J.F. Aust, K.S. Booksh, C.M. Stellman, R.S. Parnas, and M.L. Myrick. Applied Spectroscopy,51:247–252, 1997.

14. R.E. Lyon, K.E. Chike, and S.M. Angel. Journal of Applied Polymer Science, 53:1805–1812,1994.

15. O. A. Al-Fulaij, A. A. Elassar, and A. El-Dissouky. Synthesis, characterization, and ligating be-havior of poly[n,n-p-phenylene bisacryl (methacryl)amide]. Journal of Applied Polymer Science,101:2412–2422, 2006.

55

CHAPTER 3

GAS CHROMATOGRAPHY ANDSELECTIVE MASS DETECTION

Gas chromatography (GC) is a characterization technique that separates a complex mixtureof substances according to volatility and interaction with a stationary phase (column). Oncethe components of the mixture are separated, it is possible to quantify (and sometimesidentify) each substance with the help of a proper detector. In gas chromatography, themobile phase is a gas and the stationary phase is a liquid or a solid. Gas chromatography is avery useful technique for polymer analysis, particularly for following determination analysissuch as residual monomer, residual odors, volatiles, additives, nature of contamination, andidentification of comonomers after a pyrolisis [1, 2, 3]. Even at trace concentration, anysubstance with a volatilization temperature below 320 ◦C and a molecular weight below 600g/mole can be analyzed by gas chromatography. Recent developments in high temperaturegas chromatography (HT-GC), column injectors and programmed temperature volatilization(PTV) have extended the molecular weight analysis up to 1500 g/mole.

3.1 GAS CHROMATOGRAPHY INSTRUMENTATION

The gas chromatograph comprises an injector, gases control unit, column, detector and dataanalysis unit. A schematic diagram of a gas chromatograph is presented in Fig. 3.1.

56 3 Gas Chromatography and Selective Mass Detection

4 987651x10

4x10

3x10

2x10

6

6

6

6

Time

Abun

Column

Column oven

Flow controller

Carrier gas

Detector

Waste

Sample injector

Figure 3.1: Schematic diagram of a gas chromatograph

Injectors: The main injectors used for polymer analysis are [4]:

• Split/splitless – The split/splitless injector is a device of a chromatograph that injectsa liquid (eventually a gas) sample, vaporizes the sample in the injector, mixes thesample with the carrier gas, and directs the sample into the column. For a reliablechromatographic analysis, the complete sample (without discrimination and decom-position) will be sent to the column by the injector. In the split operationmode, only afraction of the vaporized sample is sent to the column (according to a predefined splitratio), while in the splitless operation the majority of the sample is sent to the column.The splitless operation mode is used for diluted samples (trace analysis), while thesplit operation mode is used for concentrated samples. Exchangeable accessories ofthe split/splitless injector are the septum and the liner.

• Cool on-column – The cool on-column injector is a device of a chromatograph thatallows the injection of the sample into the column. Because the sample enters directlyinto the column, the advantages expected by this system may include less discrimina-tion of low volatility compounds, less adsorption of active compounds, less degrada-tion of thermal sensitive compounds, and better sensitivity for trace compounds. Thisinjector is particularly useful for analysis of high molecular weight additives.

• Programmed temperature volatilization (PTV) – In the PTV injector, the sample isintroduced into the liner in the liquid state; it is then vaporized and transferred intothe column in the gaseous state. High temperatures (up to 600 ◦C) are requiredto obtain enough vapor pressure to allow a quantitative transfer of high molecularweight materials onto the column in a reasonably short time. Although the injectionreproducibility is lower than the on-column injector, some advantages of the PTVinjector include ease of automation and reduced contamination of the column.

• Valve/loop–Thevalve/loop injector is particularlyuseful for gas analysis, for example,in pyrolisis of polymers.

Columns: The column is the support of the stationary phase where the separation of thesample components takes place and, for this reason, is the heart of gas chromatography. Themain requirements of a chromatographic column are:

3.1 Gas Chromatography Instrumentation 57

• Low bleed and high thermal stability – This is particularly important in mass selectivedetectors (MSD)

• Low superficial activity – Particularly important to allow elution of compoundsat tracelevel

• High selectivity – This gives the ability to selectively retain substances based onphysical and chemical characteristics, associated with the polarity of stationary phase

• High efficiency and resolution – Allows the production of sharp, well-defined, andseparated peaks

• Durability and low cost

The parameters considered for a proper selection of the column are:

• Polarity – A column with low polarity separates the compounds according to theboiling point, while the high polarity column separates by dipole-dipole interactions.Intermediate polarity columns separate by means of both mechanisms. The typicalstationary phases used in gas chromatography are reviewed in Table 3.1.

Table 3.1: Typical stationary phases used in GC

Stationary phase Trade names Typical applications

100%Dimethylpolysiloxane HP-1, Ultra 1, DB-1, SE-30, Rtx-1, MXT-1, OV-1, PE-1, SPB-1,CP-Sil 5

Nonpolar. Amines, hydro-carbons, pesticides, polychlori-nated biphenyl PCBs, phenols,sulphur compounds

5%-Difenil-95%Dimethylpolysiloxane

HP-5, HP-5MS Ultra 5, DB-5,DB-5MS, Rtx-5, Rtx-5MS, OV-5, PE-2, SPB-5, CP-Sil 8

Nonpolar. Semivolatiles, alka-loids, halogenated compounds,hydrocarbons, drugs, fatty acidmethyl esters (FAMEs)

50%-Difenil-50%Dimethylpolysiloxane

HP-50, DB-17, DB-17ht, OV-17,SPB-50, Rtx-50, CP-Sil 19, PE-17

Intermediate polarity. Pesti-cides, glycols, steroids, drugs

14%-cyanopropyl-86%Dimethylpolysiloxane

HP-1701, DB-1701, Rtx-1701,OV-1701, PE-1701, SPB-1701,SPB-7, CP-Sil 19CB

Intermediate polarity. Pesti-cides, halogenated compounds,halogenated aromatic com-pounds

Polyethylene glycol (PEG) HP-20M, HP-INNOWax, Car-bowax 20M, DB-WAX, Supel-cowax 10, MTX-Wax, PE-CW,CP-Wax 52CB

Polar. Acids, alcohols, aldehy-des, acrylates, essential oils


• Diameter – As the internal diameter increases, so does the capacity, but the resolutiondecreases. The typical diameter of a column is in the range of 0.53 to 0.20 mm. Highdiameter (0.32 and 0.53 mm) columns are preferred for high injection volume andpurge and tramp injection, but low diameter columns (0.20 to 0.25 mm) are used forhigh resolution and GC/MSD chromatography.

• Layer thickness – In modern chromatography columns (wall-coated open-tubular col-umn (WCOT)), the stationary phase is deposited over a fused silica tube (coated withpolyimide polymer for mechanical resistance) in a thin layer. As the stationary phasethickness increases, the resolution normally increases; however, the retention of com-pound and time of analysis both increase. The stationary phase thickness has to beselected in accordance with the physical state and the volatility of compounds to beanalyzed, as follows:

– Thick layers of stationary phase (3 to 5 microns) are preferred for gases andextremely volatile compounds (volatiles near to room temperature).

– Intermediate layers of stationary phase (1 to 3 microns) are preferred for volatilecompounds that elute at temperatures up to 200 ◦C.

– Thin layers of stationary phase (0.25 to 1.00 microns) are preferred for com-pounds that elute at temperatures in the range of 200 to 300 ◦C.

– Extremely thin layers of stationary phase (0.10 to 0.25 microns) are preferredfor high molecular weight compounds that elute at temperatures above 300 ◦C.

• Length – As the length increases and the diameter decreases, the efficiency of columnincreases (as the number of equivalent theoretical distillation plates increases). Typicalcolumn lengths are 15, 30, 50, 60, and 105 m. Columns of 30 m are universally usedin GC analysis, while columns of 50, 60, and 105m are used for the evaluation of verycomplex samples and low boiling point samples.

Detectors: The most commonly used detectors in gas chromatography are:

• Electrolytic conductivity detector (ELCD) – With this type of detector, halogen con-taining compounds catalytically react (reduction)with hydrogen to produce strong acidby-products (dissolved in the working fluid). The increase of electrolytic conductivityis registered because of the dissociation of the acid by-products. This detector can bemodified for nitrogen- and sulfur-containing substances.

• Electron-capture detector (ECD) – With this type of detector, compounds are ion-ized by capturing electrons, which are produced by the interaction of carrier gasmolecules (typically, nitrogen or argon/methane) with particle emissions from a ra-dioactive source (typically, 63Ni). The ECD detector is one of the most sensitivedetectors, especially for halogenated compounds.

• Flame ionization detector (FID) – With this type of detector, hydrocarbon-containingcompounds are ionized in a hydrogen-air flame. The FID is considered a universaldetector because it responses strongly to the majority of organic compounds.

• Flame photometric detector (FPD) – With this type of detector, heteroatomic com-pounds are burned in a hydrogen-air flame, and the atomic emissions in the visible


range are filtered and detected by a photomultiplier detector. Different filters may beselected for specific atoms (sulfur, tin, or phosphorous). The FPD is considered a verysensitive and selective detector.

• Nitrogen/phosphorous detector (NPD) – With this type of detector, nitrogen or phos-phorous compounds are catalytically ionized on a heated surface (of rubidium orcesium) in a reductive atmosphere. The NPD is more sensitive and selective than theFID detector.

• Photo-ionization detector (PID) – With this type of detector, compounds are ionizedwith photons in the UV range. The energy of photons can be increased to respond toaromatics and olefins.

• Thermal conductivity detector (TCD) – With this type of detector, the differentialthermal conductivity of carrier gas and a reference gas is measured. Compounds fromthe column change the thermal conductivity of carrier gas making the detection ofchromatographic peaks possible. This detector is considered a moderate sensitivityuniversal detector and is widely used in gas analysis.

• Mass selective detector (MSD) – With this type of detector, the compounds and thecarrier gas eluted from the column are bombarded with high-energy electrons andfragmented in a characteristicmass spectrum,which canbe used to qualify andquantifythe compounds.

Mass selective detector: In the MSD detector, the fragmentation process (under con-trolled conditions) of the compounds and the carrier gas produce a mass spectrum charac-teristic of their chemical structure that can be used not only for quantification purposes, butalso for identification purposes. Themass spectrum can be compared to a humanfingerprint.Figures 3.2 to 3.4 illustrate some of the most important fragmentation reactions for a dibutylphthalate (DBP) plasticizer, a triphenyl phosphate plasticizer (TPP), and a tricresyl phos-phate plasticizer (TPP). The characteristic mass fragments of these plasticizers are presentedin Table 3.2.

Table 3.2: Characteristic mass fragments of the some plasticizers

Plasticizer Mass fragments

Dibutyl phthalate (DBP) 149, 223, 205, 104, 93, 121, 160, 135

Triphenyl phosphate 326, 77, 44, 215, 170, 233, 94, 65, 152, 139, 115, 249

Tricresyl phosphate 368, 165, 243, 261, 91, 198, 65, 107, 180, 277

3.2 CORRELATION OF ADDITIVE STRUCTURE AND MASS SPECTRA

As previously, mentioned the mass fragmentation spectrum is a characteristic fingerprint ofthe chemical substance, so it can be used to identify unknown substances by comparisonwith mass spectrum libraries and the mass spectrum of a reference. Because of computer


COO

COO

-C4H9

H

+

-H2O

-C4H9

223

H+2H

205

-OC4H9

-C4H9 COOH

CO

O

CO+

COO

CO

COOH

Figure 3.2: Fragmentation process of dibutyl phthalate (DBP) plasticizer

OP

OO

O

93233326

+

. .

. .. .

. .

. .

. .. .

. .. .

. .

. .

. .. .

. .. .

. .OP

OO

O

Figure 3.3: Fragmentation process of triphenyl phosphate plasticizer

CH3

H OH

CH3

CH3

H HO

CH3

165

198

+

-H2O

-CH3

+

++ +

CH2

Figure 3.4: Fragmentation process of tricresyl phosphate plasticizer


technology developments, the comparison of a mass spectrum of an unknown substance canbe done in a short time with the help of a complete library of 200,000mass spectra. Themostrepresentative mass fragments are presented in the Table 3.3 for a selected list of additivesused in polymers.

Table 3.3: Characteristic mass fragments for several additives [5, 6]

Additive Molecular Characteristicweight, (g/mol) mass fragments, (m/z)

Plasticizers

Triphenyl phosphate (TPP) 326 326, 325, 77, 65, 39, 51, 169, 170,233, 96

o-Tricresyl phosphate (TOCP) 368 165, 91, 179, 181, 368, 277

Tricresyl phosphate (TCP) 368 368, 367, 91, 165, 179, 369, 198

Dimethyl phthalate (DMP) 222 163, 77, 164, 135, 92, 50, 149

Dibutyl phthalate (DBP) 278 149, 106, 104, 80, 61, 223, 205

Bis(2-ethylhexy) phthalate (BEHP) 390 149, 150, 41, 76, 104, 223, 167, 279

Di-isooctyl phthalate (DIOP) 390 149, 167, 57, 70 41, 71

Diisodecil phthalate (DIDP) 446 149, 57, 167, 307

Diundecyl phthalate (DUP) 474 149, 43, 57, 41, 55, 71

Bis(2-ethylhexy) sebacate (DEHS) 426 185, 57, 112, 71, 70, 43

Bis(2-ethylhexy) adipate, (DEHA) 370 129, 57, 71, 70, 112, 147, 43

Diisooctyl adipate (DIOA) 370 129, 57, 55, 41, 43, 70

Butyl bencyl adipate 292 91, 129, 111, 101

Slip additives

Oleamide 281 59, 72, 55, 41, 43, 281

Erucylamide 337 59, 72, 55, 41, 43, 69, 137, 337

Stearamide 283 59, 72, 28, 43, 57, 55, 41, 283

Antioxidants and UV stabilizers

Benzophenone 182 105, 77, 182, 51, 50

Benzotriazole 119 119, 64, 91, 63, 38, 52

BHT 220 205, 57, 220, 206, 145, 177


3.3 SELECTED STANDARDS FOR GAS CHROMATOGRAPHY TESTING

This section presents a selected number of standardized tests for gas chromatography testing.They are ASTMD5508 for determination of residual monomer in rubber and ASTMD3452for identification of polymers and blends for rubbers. Some widely used ISO standard testsfor gas chromatography methods are listed in Table 3.7.

Table 3.4: Determination of residual acrylonitrile monomer in styrene-acrylonitrilecopolymer resins and nitrile-butadiene rubber by headspace-capillary gas chromatography(HS-CGC)

Standard ASTM D5508-94a

Scope This test method covers the determination of the residual acrylonitrile (RAN)content in nitrile-butadiene rubbers (NBR), styrene-acrylonitrile (SAN) copoly-mers, and rubber-modified acrylonitrile-butadiene-styrene (ABS) resins. Anycomponents that can generate acrylonitrile in the headspace procedure will con-stitute an interference. The presence of 3-hydroxypropionitrile in latex formlimits this procedure to any rubbers and resins.

Specimen Thepolymer test unit (sample) should be a 1 in. (45mm) cube. All test specimensshould be taken from the interior of the part to minimize the contribution ofsurface effects on the residual-acrylonitrile level. All polymer-test units mustbe %ept in sealed containers.

Apparatus Gas chromatograph with a NPD detector (nitrogen phosphorous specific de-tector), automated headspace sampler, fused silica porous-layer-open-tubular(PLOT) capillary column, GS-Q, 30 m x 0.53 mm inside diameter, variablerestrictor, data-recording device, wrist-action shaker, balance, headspace vials,aluminum crimp caps, septa, crimper.

Test procedures Two dispersions (in o-dichlorobenzene) are prepared and sealed in headspacevials for each polymer; one vial contains the polymer in solvent while the secondvial contains the polymer, solvent, plus a %nown standard addition of acryloni-trile (AN). The vials are agitated in a wrist-action shaker for 16 hours underambient temperature. The vials are agitated and thermally equilibrated in thehead space. After the equilibrium time, an aliquot from the headspace is in-jected into the gas chromatograph and the acrylonitrile (AN) peak response isdetermined. The acrylonitrile (AN) peak is converted to a relative residual acry-lonitrile (RAN) concentration by using a standard addition methodology.

Values and Units Parts per billion (ppb or ng/g) of residual acrylonitrile monomer


Table 3.5: Standard practice for rubber–Identification by pyrolysis-gas chromatography- PART 1. IDENTIFICATION OF SINGLE POLYMERS


Scope This practice is a guide to the identification of polymers in raw rubbers and curedand uncured compounds, based on a single polymer, by the gas chromatographicpatterns of their pyrolysis products (pyrograms).This practice will identify the following polymers:- Polyisoprene of natural or synthetic origin,- Butadiene-styrene copolymers,- Polybutadiene,- Polychloroprene,- Butadiene-acrylonitrile copolymers,- Ethylene-propylene copolymers and related terpoly-mers, and- Isobutene-isoprene copolymers.- This practice will not differentiate the following polymers:- Natural polyisoprene from synthetic polyisoprene.- Butadiene-styrene copolymers produced by solution and emulsion polymer-ization. It is sometimes possible to distinguish butadiene-styrene copolymerscontaining different amounts of styrene as well as random polymers from blockpolymers.- Polybutadiene with different microstructures.- Different types of polychloroprenes.- Butadiene-acrylonitrile copolymers with different monomer ratios.- Ethylene-propylene copolymers with different monomer ratios, as well as thecopolymers from the related terpolymers.- Isobutene-isoprene copolymers (butyl rubbers) fromhalogenated butyl rubbers.- Polyisoprene containing different amounts of cis-trans isomers.- The practice does not identify ebonite or hard rubbers.

Specimen For thermal conductivity detection and electrically heated platinum filaments,a sample size of approximately 3 mg has been found satisfactory. This couldbe increased or decreased depending on the composition of the sample and thecapacity of the probe.For flame ionization and either Curie point apparatus or electrically heated plat-inum filaments, a sample size ranging from 0.2 to 2.0 mg has been found satis-factory.

Apparatus Pyrolysis devices - The applicability of this practice has been checked on thefollowing types:- Quartz tubes, electrically heated at a prefixed temperature.- Platinum filaments, electrically heated.- Small coils of ferromagnetic wire, heated to the Curie point temperature.- Gas chromatograph- Dual-column operation and temperature programming is recommended.- Gas chromatographic columns




- Carrier gas

Test procedures The pyrograms of%nown rubber are used for identification of unknown rubbers.The success of the method depends upon examining the %nown and unknownrubbers under exactly the same experimental conditions.The method started with an extraction according to the ASTM D297. Thesamples are pyrolized in different apparatus and the volatile components areanalyzed by gas chromatography using different detectors.

Values and Units Identification of polymers and their relative ratios and not the absolute levels ofthe polymers in the compounds being studied.

Table 3.6: Standard practice for rubber–Identification by pyrolysis-gas chromatography- PART 2. IDENTIFICATION OF BLENDS OF POLYMERS


Scope This practice is a guide to the identification of blends of rubbers in the raw, vul-canized, and unvulcanized state by the gas chromatographic patterns of pyrolysisproducts (pyrograms).Implementation of this guide presupposes aworking%nowledge of the principlesand techniques of gas chromatography, sufficient to carry out the practice, aswritten, and to interpret the results correctly.Two methods are described, depending upon the nature of the blend.

MethodA - Thismethod is used when styrene-butadiene copolymers are absent.The absence of the styrene peak, in a preliminary pyrogram, indicates this typeof blend.This method is used to identify blends of the following:- Polyisoprene of natural or synthetic origin,- Butadiene,- Isobutene-isoprene copolymers, and- Halogenated isobutene-isoprene rubbers.

MethodB - Thismethod is usedwhen butadiene-styrene copolymers are present.The presence of the styrene peak, in a preliminary pyrogram, indicates this typeof blend.The method fails if other styrene polymers or copolymers or unextractablestyrene containing resins are present. Method B is suitable for the identificationof polybutadiene in blends with styrene-butadiene copolymers. If the presenceof polybutadiene in the unknown rubber can be excluded, useMethod A.MethodB will identify butadiene-styrene copolymers with blends of the following:- Polyisoprene of natural or synthetic origin,




- Butadiene, and- Isobutene-isoprene copolymers and halogenated isobutene-isoprene rubbers.Methods A and B will not differentiate the following in blends:- Natural polyisoprene from synthetic polyisoprene,- Polybutadiene containing different microstructures,- Isobutene-isoprene copolymers and their related halogenated rubbers, and- Styrene-butadiene copolymers at different ratios or microstructures

Specimen For thermal conductivity detection and electrically heated platinum filaments,a sample size of approximately 3 mg has been found satisfactory. This couldbe increased or decreased depending on the composition of the sample and thecapacity of the probe.For flame ionization and either Curie point apparatus or electrically heated plat-inum filaments, a sample size ranging from 0.2 to 2.0 mg has been found satis-factory.

Apparatus Same apparatus as Part 1 in addition to the following:All the devices in accordance with pyrolysis devices may be used in Part 2, butthe Curie point device is especially recommended when Method B is used.For gas chromatograph, dual-column operation and temperature programmingis strongly recommended, especially when Method B is used.Nitrogen is the preferred carrier gas when the Curie point device is used. Itshould not be used with a thermal conductivity detector.

Test procedures Thepyrogramsof%nown rubbers are used for identification of unknown rubbers.The success of the method depends upon examining the %nown and unknownrubbers under exactly the same experimental conditions.The method started with an extraction according to the ASTM D297 (sections18 and 25). The samples are pyrolized in different apparatus and the volatilecomponents are analyzed by gas chromatography using different detectors.

Values and Units Identification of polymers and their relative ratios and not the absolute levels ofthe polymers in the compounds being studied.


Table 3.7: Widely used ISO standard tests for gas chromatography methods

Standard Number Tittle

16014-1:2003 Plastics – Determination of average molecular mass and molecular mass dis-tribution of polymers using size-exclusion chromatography – Part 1: Generalprinciples

8974:2002 Plastics – Phenolic resins – Determination of residual phenol content by gaschromatography

11337:2004 Plastics – Polyamides – Determination of ε-caprolactam and ω-laurolactam bygas chromatography

2561:2006 Plastics – Determination of residual styrene monomer in polystyrene (PS) andimpact-resistant polystyrene (PS-I) by gas chromatography

6401:1985 Plastics –Homopolymer and copolymer resins of vinyl chloride –Determinationof residual vinyl chloride monomer – Gas chromatographic method

4581:1994 Plastics – Styrene/acrylonitrile copolymers – Determination of residual acry-lonitrile monomer content – Gas chromatography method

13741-2:1998 Plastics/rubber – Polymer dispersions and rubber latices (natural and synthetic) –Determination of residualmonomers and other organic components by capillary-column gas chromatography – Part 1: Direct liquid injection method – Part 2:Headspace method


Plasticizer Identification in a Flexible PVC Compound

In this case study, a flexible PVC formulationwas analyzed to determine the plasticizertype and content. After the size reduction of one gram of the sample, the plasticizerwas extracted with a Soxhlet extractor during 6 hours and with 250 ml of ethylicether. The extract was analyzed by gas chromatography and mass selective detectortechnique. A Soxhlet extractor, schematically depicted in Fig. 3.5, is a device used toextract compounds that have a limited solubility in a solvent. When testing sampleswith high solubility in the solvent, a filtration process must take place to separate thesolids from the solvent. The solid to be tested is first placed in the thimble, whichcontains thick filter paper. After bringing the solvent to reflux, the vapor is allowed tomove up the distillation arm to flood the chamber holding the solid. The warm solventdissolves part of the solid. When filled, the chamber is emptied by a side siphon tothe distillation flask. After each cycle, which could be repeated over several hours or


days, the non-volatile compound dissolves in the solvent that is eventually extractedfor analysis. The advantage of a Soxhlet extractor is that the same solvent is passedthrough the system over each cycle.

Stirrer

Still pot

Distillation path

Thimble

Solid

Siphon top

Siphon exit

Expansion adapter

Condensor

Cooling water in

Cooling water out

Figure 3.5: Schematic diagram of a Soxhlet extractor.

A first step of the study was a qualitative analysis to identify the type of plasticizer.In this analysis, the extract was injected in the split/splitless port of the chromatographand analyzed according to the conditions in Table 3.8.From the plasticizer extract, the chromatogramshown in the Fig. 3.6was generated.

Two peaks were obtained, one at 9.70 minutes, corresponding to the internal standard(dibutyl phthalate, DBP) and one at 12.25 minutes, corresponding to the unknownplasticizer. The representative mass fragments of the 9.70-minute peak are presentedin Table 3.9 and exhibit the characteristic mass fragments of dibutyl phthalate (DBP).The mass spectrum of this peak was compared with the library spectra, and a goodmatch with the DBP mass fragment spectrum was observed.

Figure 3.6: Chromatogram of plasticizer extract of flexible PVC compound [7, 8]


Table 3.8: GC/MSD analysis conditions to determine a plasticizer in a PVC compound

Parameter ValueGas chromatography

Column HP5MS

Carrier gas High purity He

Injection port Split

Split ratio 50:1

Injector temperature, ◦C 250

Injection volume, μ l 1

Initial temperature of column, ◦C 80

Final temperature of column, ◦C 300

Heating rate, ◦C/min 20

Internal standard Dibutyl phthalate DBP

Mass selective detector

Detection mode Scan

Mass range detection, a.m.u.1 50-800

Mass resolution, a.m.u. 0.1

Tune substance PFTBA

Interface temperature, ◦C 290

Quadrupole temperature, ◦C 106

Ion source temperature, ◦C 230

Table 3.9: Characteristicmass fragments of the twopeaks observed in the chromatogram

Retention time, min Mass fragments

9.70 149, 223, 205, 104, 121, 93, 135

12.25 149, 167, 279, 113, 104, 83, 132, 97

The representative mass fragments of the 12.25-minute peak is presented in Ta-ble 3.9. The unknown plasticizer exhibited the characteristic mass fragment of bis(2-ethylhexyl) phthalateBEHP and exhibited a goodmatchwith theBEHPmass fragmentspectrum of the library.

1a.m.u.: atomic mass units


COO

COO

C8H15

2H

COOH

CO

O

H+

279

COOH

C

OH

OH

167

-H2O CO

COOH+

Figure 3.7: Fragmentation process of 12.247-minute peak [7, 8]

Figure 3.8: Calibration line for quantification of BEHP [7, 8]

The main fragmentation scheme of the BEHP is also presented in the Fig. 3.7. Thisconfirms that the main mass fragments are 279, 167, and 149 a.m.u. (see Table 3.3).Once the plasticizer of the flexible PVC compound is identified, the next step of thestudy is a quantification of this substance. Five standards of %nown BEHP concen-tration were prepared and measured in the GC/MSD equipment. The calibration line,which is the correlation of signal area against concentration in ppm, is presented inFig. 3.8.The extracts were run four times. For each sample, the percentage by weight in the

flexible PVC compound was calculated taking into account the concentration in theextract, the extracted weight of sample, and the recovering factor. The results of thequantification are presented in Table 3.10, where a good reproducibility of the valuesis observed and an average percentage by weight of 35% was registered.Conclusions: Using the GC/MSD study, it was found that a bis(2-ethylhexyl) ph-

thalate (or the dioctyl phthalate, BEHP) plasticizer at 35% by weight was present inthe flexible PVC compound.


Table 3.10: Percentage by weight of the flexible PVC compound

Run number BEHP percentage by weight, %

1 34.5

2 35.6

3 34.6

4 35.1

Average 35.0

Standard deviation 0.4

Coefficient of variation 1.3


Slip Agent Quantification in a Plastic Film

Polypropylene pellets were analyzed by gas chromatography and a flame ionizationdetector (FID)2 to determine the amount of the slip agent erucamide present in thematerial.Before the tests, the sample was ground to a very fine dust (20-mesh) using a

mill. This grinding procedure was crucial to obtain a reproducible and exact value oferucamide content. About 3 g of the dust was extracted using a Soxhlet extractor with50 ml of dichloromethane during a period of two hours.The quantification procedure was done based on some guidance from the ASTM

D6042-96 test [9]. The response factor of erucamide was first obtained analyzing astandard of %nown concentration of erucamide doped with 118 ppm of Tinuvin � 770as internal standard indicated was the norm. A solution with the extract of polypropy-lene pellets was prepared and doped with 118 ppm of Tinuvin� 770.The results of four runs of the extract analyzed in the GC/FID are presented in

Table 3.11. The obtained chromatogram is presented in Fig. 3.9. The chromatogramexhibits two peaks of high intensity, one around 14.62 minutes corresponding to theerucamide, and one around 16.23 minutes corresponding to the Tinuvin� 770 used asan internal standard.Conclusions: The erucamide content of the polypropylene pellets was successfully

determined by using gas chromatography (GC) combined with the flame ionizationdetector (FID). The erucamide content in polypropylene pellets was 1509 ppm, whichwas in accordance with the value reported by the raw material manufacturer (1500ppm).

2A flame ionization detector is used in conjunction with a gas chromatographer after the components elute fromthe column. The system burns the components using a hydrogen-air flame to produce ions. The ions result in anelectric current that produces a signal in the detector.


Figure 3.9: Representative chromatogram of the erucamide quantification

For validation of the method, an additional analysis by high performance liquidchromatographyHPLC (sometimes also referred to as high-pressure liquid chromatog-raphy) was done, and a value of 1503 ppm was obtained.

Table 3.11: Data for quantification of erucamide in polypropylene pellets

Run Erucamide Tinuvin 770 Area ppm ofarea area relationship erucamide

1 58 777 135 61 429 819 0.96 1 502

2 61 898 255 64 032 399 0.97 1 517

3 64 478 223 66 399 419 0.97 1 524

4 67 621 542 71 084 534 0.95 1 493

Average 1 509

Standard deviation 14

Coefficient of variation 0.93


Analysis of Plasticizer in PVC Film

A PVC film used as a wrapper was analyzed to identify the nature of the formulatedplasticizer. After a size reduction, the sample was dissolved in tetrahydrofuran (THF)and precipitated with methanol. The precipitate was removed by means of centrifuga-tion and the extractwas analyzedby gas chromatographycoupledwith amass selectivedetector. Because the purpose of the analysis was the identification of plasticizers, alow bleeding septum for the injector was necessary.


Figure 3.10: Chromatogram of a wrapping PVC film plasticizer extract

Table 3.12: Peaks observed in chromatogram of awrapping PVCfilm plasticizer extract

Retentiontime, min

Compound Matching % Mass fragment % Area

6.65 Butyl hydroxytoluene (BHT)

97 205,220,145,177,57,105 2.20

7.29 broad Diethyl phtha-late (DEP)

97 149,177,105,76,65,121,222 3.70

12.49 Di-2-ethylhexyl adi-pate (DEHA)

87 129,57,70,112,43,70,147,83,241 5.00

13.31 Di-2-ethylhexyl ph-thalate (BEHP)

83 149,167,57,71,279,113,207,177 89.10

The obtained chromatogram is presented in Fig. 3.10. The chromatogramexhibitedfour peaks of different intensities and the main information of every peak is presentedin Table 3.12. The table shows for every retention time, the most probable compoundaccording to the best match with the mass spectra library. The match can be confirmedby the most intense mass fragment (see Table 3.2). To obtain a relative concentrationof every plasticizer, a percentage of total areas is calculated. The butyl hydroxytoluene (BHT) found in the chromatogramwas attributed to the THF solvent, becausethis compound is used as an antioxidant of this particular solvent. According toTable 3.12, the main plasticizer is a di-2-ethylhexyl adipate (DEHA) and the presenceof other plasticizers in minor concentrations was detected. These minor plasticizerswere diethyl phthalate (DEP) and di-2-ethylhexyl phthalate (BEHP).Conclusions: Gas chromatography combinedwith amass selective detector,proved

to be a very useful technique for the identification of the plasticizer in the PVC filmwrapper. According to the performed analysis, the main plasticizer of the film was

3.3 References 73

a di-2-ethylhexyl adipate DEHA. Other plasticizers in minor concentrations (diethylphthalate (DEP) and di-2-ethylhexyl phthalate (BEHP)) were observed.

References

1. G. Stilianos Rowis and J. W. Fedora. Use of a thermal extraction unit for furnace-type pyrolisis:Suitability for the analysis of polymers by pyrolisis/GC/MS. Rapid communications in massspectrometry, 10:82–90, 1996.

2. Frontier Laboratories Ltd. Composition Analysis of Fully Aromatic Polyester by Py-GC UtilizingReactive Pyrolisis. Double-Shot Pyrolyzer� Application Note PYA2-004E. Frontier LaboratoriesLtd.

3. T. Wampler. Analysis of an Acrylic Copolymer Using Pyrolisis-GC/MS. Perkin Elmer, 2005.

4. K. Grob. Split and splitless injection for quantitative gas chromatography. Wiley CVH, 2001.

5. F. McLafferty and F. Turecek. Interpretation of mass spectra. Wiley, 1993.

6. National Institute for Standard Technology. NIST standard reference database number 69, 2005.

7. J. D. Sierra and S. A. Ospina. Characterization of PVC compounds using gas chromatographycoupled with mass selective detector. III International Seminar of PVC Technology, 1998.

8. J. D. Sierra. Experiences in characterization of virgin PVC compounds and PVC containingrecycled material. PETCO Second Andean PVC Forum., 2006.

9. ASTMD6042-96. Determinationofphenolic antioxidants and erucamide slip additives in polypropy-lene homopolymer formulations using liquid chromatography. American standard testing mate-rials ASTM, 1996.

75

CHAPTER 4

THERMAL PROPERTIES

The heat flow through a material is controlled by heat conduction, determined by the thermalconductivity, K . However, at the onset of heating, the polymer responds solely as a heatsink, and the amount of energy per unit volume stored in the material before reaching steadystate conditions is controlled by the density, ρ, and the specific heat, Cp, of the material.These three thermal properties can be combined to form the thermal diffussivity, α using

α =k

ρCp. (4.1)

4.1 THERMAL CONDUCTIVITY

When analyzing thermal processes, the thermal conductivity,K , is the most commonly usedproperty that helps quantify the transport of heat through a material. By definition, energy istransported proportionally to the speed of sound. Accordingly, thermal conductivity followsthe relation

k ≈ Cpρul (4.2)

where u is the speed of sound and l the molecular separation. Amorphous polymers showan increase in thermal conductivity with increasing temperature, up to the glass transition

76 4 Thermal Properties

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-200 -150 -100 -50 0 50 100 150 200 250

Temperature

oC

POM

PA6

PC

PIB

PSPVC-U

PVC, 40% DOP

PA610In air 20/65

In water

PA6

PA66

PA66

W/m/K

PP

HDPE

Figure 4.1: Thermal conductivity of various thermoplastics

1.2

1.1

1.01 250 500 750 1000

( bar)Pressure, P

T = 230 °C PP

HDPE

LDPE

PS

PC

Var

iatio

n in

ther

mal

c

ondu

ctiv

ity(k

/k 1

bar )

Figure 4.2: Influence of pressure on thermal conductivity of various thermoplastics

temperature,Tg . AboveTg, the thermal conductivity decreases with increasing temperature.Because of the increase in density upon solidification of semicrystalline thermoplastics, thethermal conductivity is higher in the solid state than in the molten. In the molten state,however, the thermal conductivity of semicrystalline polymers reduces to that of amorphouspolymers as can be seen in Fig. 4.1.Furthermore, it is not surprising that the thermal conductivity of melts increases with

hydrostatic pressure. This effect is clearly shown in Fig. 4.2. Figures 4.3 and 4.4 present thecombined effect that pressure and temperature have on the thermal conductivity of PS andPE, respectively.As long as thermosets are unfilled, their thermal conductivity is very similar to amorphous

thermoplastics. Anisotropy in thermoplastic polymers also plays a significant role in ther-mal conductivity. Highly drawn semicrystalline polymer samples can have a much higherthermal conductivity as a result of the orientation of the polymer chains in the direction ofthe draw.


0.14

0.16

0.18

0.2

50 100 150 200 250

PS

750

500

250

1

Pressure(bar)

Temperature

oC

Wm K

Figure 4.3: Influence of pressure and temperature on the thermal conductivity of PS

0.24

0.26

0.28

0.3

0.32

50 100 150 200 250 300

PE-LD PE-HD

1

1000

750

500

250

1

1000

750

500

250

oC

Temperature

Pressure(bar)

Pressure(bar)W

m K

Figure 4.4: Influence of pressure and temperature on the thermal conductivity of PE-LD and PE-HD


0 50 100 150 200 250(°C)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Temperature, T

PE-LD

PE-LD + GF (40% wt) -orientation

PE-LD + GF (40% wt) ll -orientation

PE-LD + Quartz powder 60% wt

The

rmal

con

duct

ivity

, k (

W/m

/K)

Figure 4.5: Influence of filler on the thermal conductivity of PE-LD

Closedcells

10-2

10-1

100

101

102

103

1 0.5 0 0.5 1

Open cells

Polymer/metalFoams

Metal inpolymer

Volume fractionof gas

Volume fractionof metal

The

rmal

con

duct

ivity

, kW

/m/K

Polymerin metal

Figure 4.6: Thermal conductivity of plastics filled with glass or metal

For amorphous polymers, the increase in thermal conductivity in the direction of thedraw is usually not higher than a factor of two. The higher thermal conductivity of inorganicfillers increases the thermal conductivity of filled polymers. Nevertheless, a sharp decreasein thermal conductivity around the melting temperature of crystalline polymers can still beseen with filled materials.The effect of fillers on thermal conductivity for PE-LD is shown in Fig. 4.5, where the

effect of fiber orientation as well as the effect of quartz powder on the thermal conductivityof low density polyethylene are shown.Figure 4.6 demonstrates the influence of gas content on expanded or foamed polymers

and the influence of mineral content on filled polymers.Figure 4.7 compares theorywith experimental data for anepoxyfilledwith copperparticles

of various diameters. The figure also compares the data to the classic model given byMaxwell.With fiber-reinforced systems, one must differentiate between the longitudinal and the

transverse directions to the fibers. For high fiber content, one can approximate the thermal


10 0 20 30 40 50 60 0

0.4

0.8

1.2

1.4

1.6

1.0

0.6

0.2

Maxwell

Knappe

The

rmal

con

duct

ivity

, k(W

/m/K

)

25 μm11 μm

46 μm100 μm

Experimental data(Temperature 300K)

Concentration, φ (%)

Figure 4.7: Thermal conductivity versus volume concentration of metallic particles of an epoxyresin. Solid lines represent predictions using Maxwell and Knappe models

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 100 200 300 400 500

PC

PVCPMMA

PS

PSII

PMMAII

PVCII

PCII

Stretching

%

Figure 4.8: Thermal conductivity as a function of % stretch, parallel and perpendicular to thedirection of stretch

conductivity of the composite by the thermal conductivity of the fiber. Similar to fiberorientation of reinforced polymers, the molecular orientation plays a significant role in thethermal properties of a polymer. Figure 4.8 presents the effect of stretch on the thermalconductivity of various amorphous polymers.The thermal conductivity can be measured using the standard tests ASTM C177 and

DIN 52612. A new method currently being balloted (ASTM D20.30) is preferred by mostpeople today.


4.2 SPECIFIC HEAT AND SPECIFIC ENTHALPY

The specific heat,C, represents the energy required to change the temperature of a unit massof material by one degree. The specific enthalpy represents the energy of a material per unitmass at a specific temperature. The specific heat can bemeasured at either constant pressure,Cp, or constant volume, Cv .Because the specific heat at constant pressure includes the effect of volumetric change,

it is larger than the specific heat at constant volume. However, the volume changes of apolymer with changing temperatures have a negligible effect on the specific heat. Hence,one can usually assume that the specific heat at constant volume or constant pressure are thesame. It is usually true that specific heat only changes modestly in the range of practicalprocessing and design temperatures of polymers. However, semicrystalline thermoplasticsdisplay a discontinuity in the specific heat at the melting point of the crystallites. This jumpor discontinuity in specific heat includes the heat that is required to melt the crystallites,which is usually called the heat of fusion. Hence, specific heat is dependent on the degreeof crystallinity.The chemical reaction that takes place during solidification of thermosets also leads to

considerable thermal effects. In a hardened state, their thermal data are similar to those ofamorphous thermoplastics.

0 50 100 150 200

Temperature , T

2.4

1.6

0.8

2.4

1.6

0.8

0a) Amorphous thermoplastics

32

24

16

8

0b) Semi-crystalline thermoplastics

c) Thermosets (phenolic type 31)

Polyvinyl chloride

Polycarbonate

(°C)

Polystyrene

LDPE

HDPE

UHMWPE

After curing

Before curing

Spe

cific

hea

t,

(K

J/kg

)

Figure 4.9: Specific heat curves for selected polymers of the three general polymer categories

Figure 4.9 shows specific heat graphs for the three polymer categories. The graphs thatpertain to polyethylene have the heat of fusion lumped into the specific property curve.Similarly, the graph for phenolic presents the effect of cure.


Figure 4.10: Measured specific heat versus temperature of HDPE

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

-250 -200 -150 -100 -50 0 50 100 150 200 250

PB

PP

PE

PA6

PSPC

PVCPMMA

POM

Diamond

PTFE

Air

Polysulfone

5.04.84.64.44.24.0

Cp

Temperature (oC)

Water

Figure 4.11: Specific heat curves for selected polymers

While heating the sample when measuring specific heat, one can also record the total heatconsumed. This information is important when predicting the heat required during meltingin a specific process. Figure 4.10 shows a measured specific heat graph, as well as the totalheat consumed, of a HDPE under a heating program. The melting point of this materialis observed at 133 ◦C. Figure 4.11 presents the specific heat of several thermoplastics as afunction of temperature and compares them to the curves for air, diamond, and water.


0

200

400

600

0 50 100 150 200 250

Temperature

PMMAPVC-U

PC

PS, SAN, ABS

20 oC

kJ/kg

Figure 4.12: Specific enthalpy curves for selected amorphous polymers

0

200

400

600

800

0 50 100 150 200 250 300

Temperature

PA610

PA 66

PA 6

PA6-GF 30

20 oC

kJ/kg

Figure 4.13: Specific enthalpy curves for various polyamides

Specific enthalpy curves for selected amorphous thermoplastics are presented in Fig. 4.12.Figure 4.13 presents the specific enthalpy for various polyamides, while Fig. 4.14 shows thecurves for other semicrystalline polymers.The specific heat can also be affected by the filler and reinforcements. In most cases,

temperature dependence of Cp on inorganic fillers is minimal and need not be taken intoconsideration.


0

200

400

600

800

1000

0 100 200 300 400

Temperature

PET

PE-HD PP POM

PE-LD

PBT

PTFE

PCTFE

20 oC

kJkg

Figure 4.14: Specific enthalpy curves for selected semicrystalline polymers

0.45

0.55

0.65

0.75

0.85

0.95

1.05

1.15

1.25

1.35

0 100 200 300 400

PE-HDPP-H

PS, ABS

PA6SAN

PA66PC+ABS

PA610

CA

PMMA

PCPBT

PPS+ LCP(PET)POMPVC-P

PVC-U ETFE

PPS

PTFE

Pressure 1 bar

oC

cm3/g

Temperature

Figure 4.15: Specific volume as a function of temperature at 1 bar for selected thermoplasticpolymers


Figure 4.16: Measured pvT diagram of ABS as a function temperature

4.3 DENSITY

The density or its reciprocal, the specific volume, is a commonly used property for polymericmaterials. As with other properties, the specific volume is greatly affected by the temper-ature. Figure 4.15 shows the specific volume at atmospheric pressure for several plasticsas a function temperature. However, the specific volume is also affected by the processingpressure and is therefore often plotted as a function of pressure, as well as temperature, inwhat is known as a pvT diagram.A measured pvT diagram is shown, using ABS as an example, in Fig. 4.16. This diagram

was obtained under a cooling program.The two slopes in the curves represent the specific volume of the melt and of the glassy

amorphous ABS separated by the glass transition temperature. The curves clearly show theglass transition temperature, Tg ≈ 100 ◦C for the ABS cooled at 1 bar.The density of polymers filled with inorganic materials can be computed at any tempera-

ture using the rule of mixtures. Density measurements can be done using standard tests ISO1183 and ASTM D792, presented in Table 4.1.

4.4 THERMAL DIFFUSIVITY

Thermal diffusivity, defined in Eq. 4.1 at the beginning of this chapter, is the materialproperty that governs the process of thermal diffusion over time. The thermal diffusivity inamorphous thermoplastics decreases with temperature. A small jump is observed around theglass transition temperature due to the decrease in heat capacity at T g. Figure 4.17 presentsthe thermal diffusivity for selected amorphous thermoplastics.


-200 -100 0 100 200 300

Temperature , T (o C)

0.0

PET

PCPVC

HIPS

PS

PMMA

2.4 10-7

2.0 10-7

1.6 10-7

1.2 10-7

0.8 10-7

0.4 10 -7

The

rmal

diff

usiv

ity (

m2 /

s)

Figure 4.17: Thermal diffusivity as a function of temperature for various amorphous thermoplastics

Table 4.1: Standard methods of measuring density of polymers (Shastry)

Standard ISO 1183 : 87 D792 - 98 Method A or B, orD1505 - 88 (Reapproved in 1990)

Specimen geometry The specimen shall be of convenientsize to give adequate clearance be-tween the specimen and the beaker(a mass of 1 – 5 g is often conve-nient). This specimen shall be takenfrom the center portion of the ISO3167 multipurpose test specimen.

Single piece of material of any sizeor shape that can be convenientlyprepared, provided that its volumeshall be not less than 1 cm3 andits surface and edges made smooth,with a thickness of at least 1 mmfor each 1 g weight (D792 re-quirements). The test specimensshould have dimensions that permitthe most accurate position measure-ment of the center of volume of thesuspended specimen. When the in-terfacial tension affects the equilib-rium position of the specimens inthe thickness range from 0.025 –0.051 mm, then films no less than0.127 mm thick should be tested (D1505 requirements)

Conditioning Including any post molding treat-ment, shall be carried out at 23 ◦C±2 ◦C and 50 ±5 % R.H. for a min-imum length of time of 88h, ex-cept where special conditioning isrequired as specified by the appro-priate material standard.

At 23±2 ◦Cand50±5%relative hu-midity for no less than 40h accord-ing to D618 - 95.



Standard ISO 1183 : 87 D792 - 98 Method A or B, orD1505 - 88 (Reapproved in 1990)

Test procedures Any one of the four methods – im-mersion in liquid, pyknometer, titra-tion, or density gradient column.

D 792 – displacement in wa-ter (Method A) or other liquids(Method B) D1505 – density gradi-ent column.

Three specimens are required forMethod D (density gradient col-umn).

Several specimens are required forD792.Three specimens are required forD1505.

Values and units Density⇒kg/m3 Density⇒kg/m3

Temperature, T ( o C)

-200 -100 100 200 -150 -50 50 150 250 0

-7

-7

1.5 10

-7

-7

-7

0.0

PTFE

PE-LD

PP

PE-HD

3.0 10

2.5 10

2.0 10

-7

1.0 10

0.5 10

The

rmal

diff

usiv

ity (

m2 /

s)

Figure 4.18: Thermal diffusivity as a function of temperature for various semicrystallinethermoplastics

Adecrease in thermal diffusivity,with increasing temperature, is also observed in semicrys-talline thermoplastics. These materials show a minimum in the thermal diffusivity curve atthe melting temperature, as demonstrated in Fig. 4.18, for a selected number of semicrys-talline thermoplastics. It has also been observed that thermal diffusivity increases with anincreasing degree of crystallinity and that it depends on the rate of crystalline growth, hence,on the cooling speedThermal diffusivity for common thermoplastics as a function of temperature under real

processing conditions is not available. One known possibility to obtain thermal diffusivity"values" as a function of temperature is calculating them from the properties observed inEq. 4.1. It is not surprising that the intent to use values of thermal diffusivity calculatedfrom those three values can lead to bad results [1], because the three variables involved inthe thermal diffusivity calculation are measured under different conditions: density mea-surements are made at atmospheric pressure and at higher pressures, thermal conductivity


is generally measured under stationary conditions of heat flow, and in the measurement ofthe heat capacity, the cooling and heating rates are much lower than those usually reachedduring polymer processing, among other reasons [2].All the methods for measuring the thermal diffusivity are based on the generation of a

thermal disturbance. During the propagation of this disturbance, it is possible to obtain therequired data to determine the thermal diffusivity. There are several possibilities of contactand contactless methods to generate a disturbance and its propagation. It is possible toclassify them depending on the geometry of the disturbance source (spot, line, and surface)and the disturbance type as a function of time (pulse, continuous functions, i.e., linear,exponential, and step function, or cyclical functions).Some of the sample contact methods are:

• Spot Source

– Pulse disturbance (flash technique)

– Continuous or cyclical disturbance (hot-spot technique)

• Line Source

– Continuous or cyclical disturbance (hot wire)

• Surface Source

– Continuous disturbance (hot disc, Shoulberg - technique)

– Cyclical disturbance (heat wave, A.C.- Joule, Angstrom method)

– Step disturbance (new quenching technique)

Some of the contactless methods are:

• Spot Source

– Pulse disturbance (flash technique)

– Cyclical and pulse disturbance (infrared radiometry, mirage effect technique)

• Line Source

– Pulse disturbance (pulsed photothermal radiometry)

– Cyclical disturbance (converging thermal wave technique, forced rayleigh lightscattering, FRLS, RLS)

• Surface Source

– Cyclical disturbance (thermal wave-interpherometry (TWI), photoacustics)

– Pulse and cyclical disturbance (infrared imaging)


4.4.1 New Developments in Thermal Diffusivity Measurement

In related research activities at ICIPC in Colombia and under collaboration with the IKVin Germany [2, 3], a new quenching method to directly obtain the thermal diffusivity fromtemperature measurements under real processing conditions for injection molding has beendeveloped.1

Figure 4.19: Thermal diffusivity of HDPE measured with the new method

1The method uses the approximated expression of the numerical solution of Fourier’s equation for the case of aone-dimensional heat flow which simplifies to

∂T∂t

= α(T, x)∂2T∂x2 .

To determine the thermal diffusivity α, this equation is written in a finite difference expression, which de-fines α as the quotient between a forward difference approximation for the time derivative and a central differenceapproximation for the space derivative, built from temperature values Ti-1,j , Ti,j , Ti+1,j and Ti,j+1 that are thevalues for three positions xi-1 = xi-Δx, xi+1 = xi+Δx for the time t = j and the temperature in position xi

for the time t+Δt.

α(Ti,t, xi) = Δx2

Δt

Ti,j+1-Ti,j

Ti-1,j -2Ti,j+Ti+1,j

According to this equation, it is necessary to know the temperature history for three points uniformly dis-tributed over the thickness of the domain and separated by distances Δx. The calculated diffusivity is valid forposition xi and a corresponding temperature Ti,j .


This method demands very precise measurements of temperature profiles T (x, t) duringthe process for different points (xi) equally distributed over the thickness of the mold cavity.From these temperature profiles, it is then possible to obtain the thermal diffusivity by solvinga very simple inverse heat conduction problem [1].Figure 4.19 presents the thermal diffusivity of a HDPE as a function of temperature and

of the distance from the cavity wall (X) obtainedwith this new technique using a 4 mm thickplate, with a 230 ◦C melt temperature, a 40 ◦C mold temperature, and a cavity pressure of120 bar [2]. These measurements show a minimum in the thermal diffusivity curves at thecrystallization temperature, Tc ≈ 124.6 ◦C.


Measuring Thermal Diffusivity of a Polypropylene

A complete set of injection molding experiments was carried out with a polypropy-lene to study the dependency of thermal diffusivity on processing conditions [3]. Asexpected, the resulting thermal diffusivity values show a remarkable dependence oftemperature and consequently, because of different local cooling rates, the thicknessof the part. The peak of thermal diffusivity is closely related to the crystallizationtemperature and shows a dependence of cavity pressure and cooling rate.A mathematical model to describe the thermal diffusivity was developed, due to

the fact that simulation programs require material data in the form of a model, oras table values when the property can be expressed using single values. The modeltakes into account melt temperature, internal cavity pressure during packing, moldwall temperature, and thickness of the injected part.Themodel describes thermal diffusivity as a function of temperature for a particular

location over the thickness and uses a dimensionless temperature θ ∗ and position x∗

definedby θ∗ = T−Tw

Tc−Twfor themelt region θ∗ � 1 and for the solid region θ∗ � 1. Here

Tw is the wall temperature and Tc is a temperature value related to the crystallizationtemperature of the material under local pressure and local cooling rates. The thermaldiffusivity for the melt (α = αmelt) is described by

αmelt =A1-A2

1+exp(

(1-θ∗)A3

)+A2; θ∗ � 1 (4.3)

The crystallization and solid region are described separately by Eqs. 4.4 and 4.5:

αcryst = A1+A4 · A5 · (1-θ∗) · exp(A5 · (1-θ∗)); θ∗ � 1 (4.4)

αsolid = A6 · exp

(-A7

(1-θ∗)

); θ∗ � 1 (4.5)

The parameters Ai are a function of the dimensionless coordinate for position x ∗

where s is the part thickness.

Ai = a0,i+a1,i · x∗+a2,i · x∗2 where x∗ = x/(s

2) (4.6)


These Ai parameters have a very noticeable dependency on processing conditionsand can be described expressing the bj (j=1,2,3) coefficients by Eq. 4.7. In order tosimplify the description of all these parameters,only the parameterA 4, which describesthe effect of crystallization, was considered as a linear function of x* (b 2 = 0 for allA-parameters, and b1 = 0 for all but not for A4).

bi = c0,i+cd,i · d+cp,i · p+cTM,i · TM+cTW ,i · TW (4.7)

Figure 4.20: Measured and calculated temperature evolution in the PP part

Table 4.2: Coefficients c for the calculation of the PP thermal diffusivity

A1 (b0) A2 (b0) A3 (b0) A4 (b1) A5 (b0) A6 (b0) A7 (b0) Tc (b0)

c0 7.03E-02 5.00E-03 5.50E-03 1.45E-01 1.39E+01 -2.30E-04 3.46E-01 1.07E+02

cd 2.88E-03 0 0 6.48E-03 3.87E-01 2.42E-03 -2.03E-02 3.11E+00

cp -2.63E-05 0 0 -6.44E-05 6.98E-03 5.38E-05 -2.17E-04 2.17E-02

cTm -2.96E-05 0 0 -3.51E-05 2.48E-02 1.44E-04 2.82E-04 -5.32E-02

cTw -4.50E-05 0 0 2.55E-04 -1.11E-01 -9.43E-05 2.26E-03 1.09E-01

The coefficients c are shown inTable 4.2. They are only valid for specific processingconditions and they were validated with experiments using the following conditions:

– Pressure – from 150 to 300 bar– Melt temperature – from 230 to 270 ◦C


– Mold wall temperature – from 20 to 60 ◦C, and– Part thickness – from 3 to 5 mm

Figures 4.20 and 4.21 show the measured evolution of thermal diffusivity and tem-perature over the thickness and is compared to the predicted values.

Figure 4.21: Calculated thermal diffusivity of PP with the new method

4.5 LINEAR COEFFICIENT OF THERMAL EXPANSION

The linear coefficient of thermal expansion is related to volume changes that occur in apolymer because of temperature variations and is well represented in the pvT diagram. Formany materials, thermal expansion is related to the melting temperature of that material,shown for some important polymers in Fig. 4.22. Similarly, there is also a relation betweenthe thermal expansion coefficient of polymers and their elastic modulus, as depicted inFig 4.23.Although the linear coefficient of thermal expansion varies with temperature, it is often

considered constant within typical design and processing conditions. It is especially highfor polyolefins, where it ranges from 1.5×10 -4K-1 to 2×10-4K-1; however, fibers and otherfillers significantly reduce thermal expansion. The linear coefficient of thermal expansionis a function of temperature. Figure 4.24 presents the thermal expansion coefficient for aselected number of thermoplastic polymers. The figure also presents thermal expansionperpendicular and parallel to the fiber orientation for a fiber-filled POM.A rule of mixtures is sufficient to calculate the thermal expansion coefficient of polymers

that arefilledwith powdery or small particles aswell aswith short fibers. In case of continuous


0

1000

2000

3000

4000

( 1/ oC)Linear thermal expansion coefficient, 106

Mo

Pt

Fe

Au Cu

Ba Al

Pb Li

NaRb

CsKSPolyoxymethylene

Polycarbonate

Polyethylene terephthalate

Polymethyl methacrylate

W

Graphite

0 20 40 10060 80

Mel

ting

tem

pera

ture

(k)

Figure 4.22: Relation between thermal expansion of some metals and plastics at 20 ◦C and theirmelting temperature

0

50

100

150

200

250

300

0.1 1 10 100 1000

PE-LD

PE-HD PP

CAB CP

CA

ABSPS PA-GF O…30

PC-GF

ABS-GF 20

EP-u. UP-GF 30-70

PF/UF/MF

kN/mm2

Al

TiC

FeCrGlas Graphite

MetalsFibers

For compression molding

Modulus

PC

10-1 100 101 102 103

μmmk

Figure 4.23: Relation between thermal expansion of some metals and plastics and their elasticmodulus


2

4

6

8

10

12

14

16

18

20

-80 -60 -40 -20 0 20 40 60 80 100 120 140 160

Temperature

oC

20•10 -5

K-1

-200 oC

-150 oC

-100 oCPOM

PEDensity=0.94

PTFE PVC-U

PMMA

PA6

PVC-P

POM-GF 30

ak = 7 kJ/m 2

ak= 5 kJ/m 2

⊥ Perpendicular to flow direction

ll Parallel to flow direction

27•10 -5

SB

Figure 4.24: Coefficient of thermal expansion of various plastics as a function of temperature

-1

-0.5

0

0.5

1

1.5

2

-80 -60 -40 -20 0 20 40 60 80 100 120

Temparature

PE 0.92PE 0.96 PP

PA

PS, SB, SAN, ABS, ASSA, PVC

PVCPPPA

oC

PE 0.96

PE0.92

-200 oc -274 oC

PE -1.82 -2.05 PC -1.04 -1.16 PPE -1.30 -1.35 UP ≈-1.40

Figure 4.25: Length change as a function of temperature for various thermoplastics; index for PEdenotes specific gravity

fiber-reinforcement, the rule of mixtures applies for the coefficient perpendicular to thereinforcing fibers. In fiber direction, however, the thermal expansion of the fibers determinesthe linear coefficient of thermal expansion of the composite. Extensive calculations arenecessary to determine coefficients in layered laminated composites and in fiber-reinforcedpolymers with varying fiber orientation distribution.


0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 7 8 9 10

Wall thickness

mm

%

PBT

PA6

PCABS

Figure 4.26: Wall shrinkage as a function of wall thickness for a selected number of thermoplastics

The temperature variation of the thermal expansion coefficients can be seen by the shapeof the curves in Fig. 4.25, which present % length change as a function of temperature forseveral thermoplastics.Molecular orientation also affects the thermal expansion of plastics. The thermal expan-

sion is often affected by the cooling time during processing. This is especially true withsemicrystalline polymers whose crystallization process requires time. For example, a thinpart that cools fast will have a lower degree of crystallinity and will therefore shrink less.This is illustrated in Fig. 4.26 in which the range of wall shrinkage as a function of wallthickness for two semicrystalline polymers (PA6 and PBT) and two amorphous polymers(PC and ABS) is presented. The figures show how the semicrystalline plastics are moreaffected by the increase in wall thickness. The coefficient of linear thermal expansion ismeasured using the standard tests ISO 11359 and ASTM E831, see Table 4.3.Thermal expansion data are often used to predict shrinkage in injection molded parts.

Injection molding shrinkage data are measured using ASTM D955 and ISO 294-4 tests, seeTable 4.4.


Table 4.3: Standard methods of measuring coefficient of linear thermal expansion(CLTE) (Shastry)

Standard ISO 11359 - 2 : 99 E831 - 93

Specimen Prepared from ISO 3167 multipur-pose test specimen cut from thespecimen taken from themiddle par-allel region.

Specimen shall be between 2 and10 mm in length and have flat andparallel ends to with ±25 microm-eters. Lateral dimensions shall notexceed 10 mm.

Conditioning No conditioning requirementsgiven. If the specimens are heatedor mechanically treated beforetesting, it should be noted in thereport.

No conditioning requirementsgiven. If the specimens are heatedor mechanically treated beforetesting, it should be noted in thereport.

Apparatus TMA TMA

Test procedures Three specimens are required. Mea-sure the initial specimen length inthe direction of the expansion test to±25 micrometers at room tempera-ture. Place the specimen in the spec-imen holder in the furnace. If mea-surements at sub-ambient tempera-tures are to be made, then cool thespecimen to at least 20 ◦C below thelowest temperature of interest.

Three specimens are required. Mea-sure the initial specimen length inthe direction of the expansion test to±25 micrometers at room tempera-ture. Place the specimen in the spec-imen holder in the furnace. If mea-surements at sub-ambient tempera-tures are to be made, then cool thespecimen to at least 20 ◦C below thelowest temperature of interest.

Heat the specimenat a constant heat-ing rate of 5 ◦C/min over the de-sired temperature range and recordchanges in specimen length andtemperature to all available decimalplaces. Determine the measurementinstrument baseline by repeating thetwo steps above without a specimenpresent. The measured change inexpansion length of the specimenshould be corrected for the instru-ment baseline.

Heat the specimenat a constant heat-ing rate of 5 ◦C/min over the de-sired temperature range and recordchanges in specimen length andtemperature to all available decimalplaces. Determine themeasurementinstrument baseline by repeating thetwo steps above without a specimenpresent. The measured change inexpansion length of the specimenshould be corrected for the instru-ment baseline.



Standard ISO 11359 - 2 : 99 E831 - 93

Record the secant value of the ex-pansion vs. temperature over thetemperature range of 23◦C to55 ◦C.

Select a temperature range froma smooth portion of the thermalcurves in the desired temperaturerange, then obtain the change in ex-pansion length over that temperaturerange.

Values and units Coefficient of linear thermal expan-sion micrometers/(m.◦C)

Coefficient of linear thermal expan-sion micrometers/(m.◦C)

Table 4.4: Standard methods of measuring injection molded shrinkage (Shastry)

Standard ISO 294 - 4 : 97 D955 - 89 (Reapproved 1996)

Conditioning At 23 ±2 ◦C between 16 h to 24 h,materials that show marked differ-ence in mold shrinkage if stored ina humid or dry atmosphere must bestored in dry atmosphere.

At 23 ±2 ◦C and 50 ±5 % relativehumidity for 1–2 h for "initial mold-ing shrinkage" (optional), 16 – 24 hfor "24 – h shrinkage" (optional),and 40 – 48 h for "48 – h or normalshrinkage"

Test procedures Mold at least five specimens, using a2-cavity ISO 294-3 Type D2 mold,equipped with cavity pressure sen-sor.

Molding in accordance with thePractice D3641 such that the mold-ing equipment is operated withoutexceeding 50 – 75 % of its rated.

Molding equipment complies withthe relevant 4.2 clauses in ISO 294-1 and ISO 294-3. In addition, ac-curacy of the cavity pressure sensormust be ±5%. Themachine is oper-ated such that the ratio of the mold-ing volume to the screw-stroke vol-ume is between 20 – 80 %, whenusing the injection molding condi-tions specified in Part 2 of the rele-vant material standard.

Molding in accordance with thePractice D3641 such that the mold-ing equipment is operated withoutexceeding 50 – 75%of its rated shotcapacity.

Perform mold shrinkage measure-ments on specimens which havebeen molded such that one or moreof the preferred "cavity pressure atpressure at hold pch" of 20, 40, 60,80, and/or 100 MPa is achieved.

No cavity pressure requirements aregiven.



Standard ISO 294 - 4 : 97 D955 - 89 (Reapproved 1996)

Allow molded specimens to cool toroom temperature by placing themon a material of low thermoconduc-tivity with an appropriate load topreventwarping. Any specimen thathas warpage > 3 % of its length isdiscarded.

Allow molded specimens to cool at23 ±2 ◦C and 50 ±5 % relative hu-midity. No warpage limits are spec-ified.

Measure the length and width ofthe cavity and the correspond-ing molded specimens to within0.02 mm at 23 ±2 ◦C.

Measure the length or diameter(both parallel and normal to theflow) of the cavity and the cor-responding molded specimens towithin 0.02 mm. Temperature re-quirement of the mold while mea-suring the cavity dimensions is notspecified.

Values and units * Molding shrinkage (16 – 24 h): %* reported as mean value of the fivespecimens measured

* Initial molding shrinkage:mm/mm (optional)* 24 h shrinkage: mm/mm (op-tional)* 48 h or normal shrinkage:mm/mm* reported as mean value of the fivespecimens measured

4.6 CURING BEHAVIOR

Both thermosets and elastomeric materials undergo a reaction process during processing.They can be classified in two general processing categories: heat-activated cure and mixing-activated cure thermosets. However, no matter which category a reactive polymer belongsto, its curing reaction can be described by the reaction between two chemical groups denotedby A and B which link two segments of a polymer chain.The reaction can be followed by tracing the concentration of unreactedAs or Bs, C A or

CB . If the initial concentration of A and B is defined as CA0 and CB0 , the degree of curecan be described by

c =CA0 − CB0

CA0

. (4.8)

The degree of cure or conversion, c, equals zero when there has been no reaction andequals one when all As have reacted and the reaction is complete. However, it is impossibleto monitor reacted and unreacted As and Bs during the curing reaction of a thermosetpolymer. It is known that the exothermic heat released during curing can be used to monitorthe conversion, c. When a small sample of an unreacted thermoset polymer is placed in adifferential scanning calorimeter (DSC), the sample will release a certain amount of heat,


QT . This occurs because every cross-link that forms during a reaction releases a smallamount of energy in the form of heat. For example, Fig. 4.27 shows the heat rate releasedduring isothermal cure of a vinyl ester at various temperatures.

Figure 4.27: DSC scans of the isothermal curing reaction of vinyl ester at various temperatures

Using the exothermic heat as a measure of cure, the degree of cure can be defined by thefollowing relation

c =Q

QT, (4.9)

whereQ is the heat released up to an arbitrary time t, and is defined by

Q =∫ t

0

Qdt. (4.10)

DSC data is commonly fitted to semi-empirical models that accurately describe the curingreaction. Hence, the rate of cure can be described by the exotherm, Q, and the total heatreleased during the curing reaction,QT , as

dc

dt=

Q

QT. (4.11)

With the use of Eq. 4.11, it is now easy to take the DSC data and find the models for dcdt that

best describe the curing reaction.During cure, thermoset resins exhibit three distinct phases: viscous liquid, gel, and solid.

Each of these three stages is marked by dramatic changes in the thermomechanical propertiesof the resin. The transformation of a reactive thermosetting liquid to a glassy solid generallyinvolves two distinct macroscopic transitions: molecular gelation and vitrification. Molecu-lar gelation is defined as the time or temperature at which covalent bonds connect across theresin to form a three-dimensional network which gives rise to long range elastic behavior in


Figure 4.28: Degree of cure as a function time for an epoxy resin measured using isothermal DSC

the macroscopic fluid. This point is also referred to as the gel point, where c = c g. As athermosetting resin cures, the cross-linking begins to hinder molecular movement, leadingto a rise in the glass transition temperature. Eventually, when T g nears the processing tem-perature, the rate of curing reduces significantly and becomes dominated by diffusion. Atthis point, the resin has reached its vitrification point. Figure 4.28, which shows the degreeof cure as a function of time, illustrates how an epoxy resin reaches a maximum degree ofcure at various processing temperatures.The resin processed at 200 ◦C reaches 100% cure because the glass transition temperature

of fully cured epoxy is 190 ◦C, less than the processing temperature. On the other hand, thesample processed at 180 ◦C reaches 97% cure, and the one processed at 160 ◦C reaches only87 % cure. Figures 4.27 and 4.28 also illustrate how the curing reaction is accelerated asthe processing temperature is increased. The curing reaction of thermally cured thermosetresins is not immediate, thus the blend can be stored in a refrigerator for a short period oftime without any significant curing reaction.The behavior of curing thermosetting resins can be representedwith the generalized time-

temperature-transformation (TTT) cure diagram developed by Enns and Gillham; it can beused to relate the material properties of thermosets as a function of time and the processingtemperature as shown in Fig. 4.29.The diagram presents various lines that represent constant degrees of cure. The curve

labeled c = cg represents the gel point and c = 1 the fully cured resin. Both curves havetheir corresponding glass transition temperatures, Tg1 and Tggel

, for the glass transitiontemperature of the fully cured resin and at its gel point, respectively. The glass transitiontemperature of the uncured resin, Tg0 , and an S-shaped curve labeled vitrification line,are also depicted. The vitrification line represents the boundary where the glass transitiontemperature becomes the processing temperature. Hence, to the left of the vitrification curve,the curing process is controlled by a very slow diffusion process. The TTT-diagramshows anarbitrary process temperature. The material being processed reaches the gel point at t = t gel


c=c1 c=c2 c=1

c=cg

Sol-gel glassy

Figure 4.29: Time-temperature-transformation (TTT) diagram for a thermoset

and the vitrification line at t = tg . At this point, the material has reached a degree of cure ofc1, and the glass transition temperature of the resin is equal to the processing temperature.The material continues to cure very slowly (diffusion controlled) until it reaches a degree ofcure just below c2. There are also various regions labeled in the diagram. The one labeledviscous liquid is where the resin is found from the beginning of processing until the gel pointhas been reached. The flow and deformation that occurs during processing or shaping mustoccurwithin this region. The region labeled charmust be avoided during processing,becuaseat high processing temperatures the polymer will eventually undergo thermal degradation.

4.7 THERMAL ANALYSIS AND MEASURING DEVICES

Thanks to modern analytical instruments, it is possible to measure thermal data with ahigh degree of accuracy. These data allow a good insight into chemical and manufacturingprocesses. Accurate thermal data or properties are necessary for everyday calculations andcomputer simulations of thermal processes. Such analyses are used to design polymerprocessing installations and to determine and optimize processing conditions. In the lasttwenty years, several physical thermal measuring devices have been developed to determinethermal data used to analyze processing and polymer component behavior.According to the International Confederation for Thermal Analysis and Calorimetry (IC-

TAC) and DIN 51005 standard, thermal analysis is a group of techniques that measure as afunction of temperature, diverse physical or chemical properties of the substance or mixture,and its reaction products under a controlled time-temperature program. Table 4.5 presentsthe main thermal analysis techniques, including the measured property and required instru-ment. In this book, only the DSC and TMA/DTG, the most common and important thermalanalysis techniques, will be reviewed in detail.


Table 4.5: Main thermal analysis techniques

Technique Property measured Instrument

Thermogravimetry (TGA/DTG) dmdT

or dmdtm: Mass Thermobalance

Differential thermal calorimetry (DTA) Ts−Tr Ts: sample temper-ature Tr: reference tempera-ture

DTA

Differential scanning calorimetry (DSC) dHdT

or dHdt

H : entalphy Calorimeter

Thermomechanical analysis (TMA) Deformation under oscilla-tory loads

Various instruments

Dynamic mechanical analysis. (DMA) Complex module and tan δunder oscillatory loads

Different instruments

Dilatometry Dimensional changes Dilatometer

Evolved gas analysis (EGA) Several techniques Different instruments

Thermooptometry Light emission or light trans-mittance

Differential photomet-ric calorimeter (DPC)

Dynamic electrical analysis (DEA) Current or electrical resis-tance, dielectric properties

Electrical conductivityof dielectric measure-ment equipment

Thermosonometry Sound speed Various instruments

Thermal analysis has awidefield of applications inpolymer and additives characterization.A complete list of physical and chemical properties and the recommended techniques ispresented in Table 4.6.

Table 4.6: Physical and chemical properties and the recommended techniques in thermalanalysis

PROPERTY DTA DSC TGA DPC TMA DMA DEA EGA

Expansion coefficient - - - - X - - -

Heat capacity - X - - - - - -

Melting heat - X - - - - - -

Melting temperature X X - - - - -

Glass transition temperature X X - - X X - -



PROPERTY DTA DSC TGA DPC TMA DMA DEA EGA

Crystallization temperature X X - - - - - -

Crystallinity - X - - - - - -

Degree of crystallinity - X - - - - - -

Chemical stability - X X X - - - X

Thermal stability - - X - - - - X

Mechanical stability - - - - - X - -

Elasticity module - - - - - X - -

Chemical composition - - X - - - - X

Moisture content - - X - - - - X

Crosslinking rate - X X - - - X -

Crosslinking degree - X - - - - X -

Dielectric constant - - - - - - X -

4.7.1 Differential Scanning Calorimetry (DSC)

Differential scanning calorimetry (DSC) is a thermal technique that measures the enthalpychanges, coupled with diverse physical and chemical events, suffered by a sample under acertain temperature-time program. By using the DSC technique, it is possible to evaluateheat absorbed or emitted by a sample during several thermal events, including glass tran-sition, melting, crystallization, crosslinking, chemical reaction, evaporation, and chemicaldecomposition. A schematic DSC thermogram illustrating the possible thermal events of apolymeric compound is presented in Fig. 4.30. Additionally, information of the peak tem-perature, start and end temperature, and onset temperature of the event can be determined.The heat capacity of a sample as a function of temperature can also be determined, if a properstandard is used for calibration, typically a sapphire standard. The rate of change of heat ca-pacity or enthalpy as a function of time (or temperature) can be determined, so the DSC is animportant tool for kinetic studies of chemical reactions, crosslinking, and thermo-oxidativedecomposition.DSC allows one to determine thermal transitions of polymers in a range of temperatures

between -180 ◦C and 600 ◦C. The DSC test requires samples that are in the mg range(< 20 mg).

Glass transition temperature: The glass transition temperature, usually denoted byTg, is a common property of amorphous and semicrystalline polymers. It is the temperatureat which the relaxationmechanism of the macromolecules stops when the polymer is cooled.The mobility of the chain segments is much lower below T g (it is known as frozen or glassymaterial). As a consequence, as the polymer reaches the glass transition temperature, a veryrigid and fragile nature is observed. Tg is registered in the DSC technique as a step in theheat capacity or in the heat flow. By convention,Tg is calculated as the temperature at whichhalf of the change in specific heat capacity has occurred.


Figure 4.30: Thermal events of a sample measured by DSC

Melting temperature: As a semicrystalline polymer is heated above Tg, at a certaintemperature the crystalline domains are desegregated and a viscoelastic fluid is obtained.This thermodynamic transition is usually denominated melting temperature, T m. Tm isobserved in the DSC technique as an endothermic peak in the heat capacity or in the heatflow, so a peak temperature (as well as start and end temperature) and a peak area (enthalpychange during melting) can be determined.

Crystallization temperature: As a semicrystalline polymer is cooled, at a certain tem-perature the crystalline domains are reordered and a crystalline polymer is obtained. Thisthermodynamic transition is usually denoted as crystallization, and it occurs around a tem-perature termed the crystallization temperature, T c. Tc is observed in the DSC technique asan exothermic peak in the heat capacity or in the heat flow, so a peak temperature (as wellas start and end temperature) and a peak area (enthalpy change during crystallization) canbe determined. As a rule, the crystallization temperature is always between the melting andglass transition temperatures, and depends on the cooling rate.A truly 100 % crystalline polymer structure cannot be obtained, so a measurement of the

degree of crystallinity is very useful. The degree of crystallinity, χ, is determined from theratio of the heat of fusion of a polymer sample,ΔHSC , and the enthalpy of fusion of a 100%crystalline sampleΔHC .

χ =ΔHSC

ΔHC(4.12)

Figure 4.31 shows a typical DSC curve measured under a heating program using a partlycrystalline polymer, such as PET sample. When following the curve from left to right, the


Figure 4.31: DSC heat flow of a PET sample

first jump or detectable deviation from the base line is Tg. The first area that is enclosedbetween the trend line and the base line is a direct measurement for the amount of heat,ΔH , needed for transition, in this case, the transition is crystallization (T c ≈ 151.6 ◦C), andthe area corresponds to the heat of crystallization. Finally, the second area that is enclosedbetween the trend line and the base line is a direct measurement for the amount of heat,ΔH ,needed for another transition. In this case, the transition is melting (T m ≈ 251.2 ◦C), andthe area corresponds to the heat of fusion.Table 4.7 is a useful review of glass transition temperatures, melting temperatures, and

100 % crystalline melting temperatures for thermoplastic polymers following the standardsASTM D3417 and ASTM D3418. Table 4.8 is a review of glass transition temperatures forelastomers.Specific heat, Cp, is one of the many material properties that can be measured with DSC.

During a DSC temperature sweep, the sample pan and the reference pan are maintained atthe same temperature. This allows the measurement of the differential energy required tomaintain identical temperatures. The sample with the higher heat capacity will absorb alarger amount of heat, which is proportional to the difference between the heat capacity ofthe measuring sample and the reference sample. It is also possible to determine the purity ofa polymer sample when additional peaks or curve shifts are detected in a DSC measurement.


Table 4.7: DSC characteristic data for selected polymers [4, 5]

Polymer Tg Tm 100 % crystallineΔHc Comments(◦C) (◦C Peak) (J

g)

LDPE -120 to -70 105 to 115 140 -

LLDPE -120 to -70 120 to 130 - -

HDPE -130 to -80 130 to 135 290 -

PP -10 to 0 165 to 176 207 Isotactic homopolymer

- - - Random copolymer

- - - Block copolymer

EVA -40 to 20 65 to 110 - VA content from 3 % to35 %

PVC 81 to 99 - - -

PS 80 to 113 - - Atactic homopolymer

HIPS 80 to 113 - - Styrene blocks

-80 to -20 - - Butadiene blocks

SAN 105 to 130 - - -

ABS -80 to -50 - - Butadiene blocks

100 to 110 - - Styrene blocks

120 to 130 - - Acrylonitrile blocks

PA6 40 to 85 180 to 230 190 Dry

- 180 to 230 190 Equilibrium moisture

PA66 50 to 70 225 to 265 200 Dry

- 225 to 265 200 Equilibrium moisture

PA11 40 to 50 180 to 200 224 -

PA12 40 to 50 175 to 190 95 -

PA610 50 to 65 210 to 233 209 -

PET 60 to 70 - Amorphous

80 250 to 285 115 Semicrystalline

PBT 25 to 75 190 to 250 142 -

PC 140 to 150 - -

POM -85 to -75 175 to 190 325 Homopolymer

-30 140 to 170 250 Copolymer

PMMA 106 to 115 - Atactic homopolymer

PTFE -73 to -20 190 to 335 82 to 115 -

PPO (PPE) 207 to 234 - -Continued on next page


Polymer Tg Tm 100 % crystallineΔHc Comments(◦C) (◦C Peak) (J

g)

PEEK 143 to 150 334 to 395 146 -

PSU 185 to 190 - -

PPS 85 to 110 275 to 290 - -

Table 4.8: Glass transition temperatures for selected elastomers [6]

Elastomer Tg◦C Elastomer Tg

◦C

Polyacrylate rubber (ACM ) -22 to -40 Butyl rubber (IIR) -66

Butadiene rubber (BR) -112 Natural rubber (NR) -72

Chlorinated polyethylene (CPE) Nitrile rubber (NBR) -45 to -20

Ethylene propylene terpolymer (EPDM) -55 Hydrogenated nitrile rubber(NBR)

-30

Silicone (FVQM) -70 Styrene butadiene rubber(SBR)

-50

Silicone (MVQ) -120 Polyether urethane rubber(EU)

-55

Thermal degradation is generally accompanied by an exothermic reaction which mayresult from oxidation. Such a reaction can easily be detected in a DSC output. By furtherwarming of the test sample, cross-linking may take place and, finally, chain breakage, asshown in Fig. 4.30.The differential scanning calorimeter is used to measure the melting, T m, and the glass

transition temperatures of polymers using the ISO 11357 and ASTM 3418 tests. Tables 4.9and 4.10 present the tests for melting and glass transitions, respectively.

Table 4.9: Standard methods of measuring melting temperature (Shastry)

Standard ISO 11357 - 3 : 98 D3418 - 97

Specimen Molding compound. Powders; granules; pellets ormolded part cut with a microtome,razor blade, hypodermic punch, pa-per punch or cork borer; slivers cutfrom films and sheets.



Standard ISO 11357 - 3 : 98 D3418 - 97

Apparatus DSCCalibrate the temperature measur-ing system periodically over thetemperature range used for the test.

DSC or DTAUsing the same heating rate to beused for specimen, calibrate thetemperature scale with the appropri-ate reference materials covering thematerials of interest.

Test procedures Sample mass of up to 50 mg is rec-ommended.

Sample weight of 5 mg is recom-mended. An appropriate samplewill result in 25 to 95 % of scaledeflection.

Perform and record a preliminarythermal cycle by heating the spec-imen at a rate of 10 K/min under in-ert gas from ambient to 30 K abovethe melting point to erase previousthermal history. Hold for 10 min attemperature. Cool to 50 ◦C belowthe peak crystallization temperatureat a rate of 10 K/min.

Immediately repeat heating underinert gas at rate of 10 K/min. Per-form and record a preliminary ther-mal cycle by heating the specimenat a rate of 10 ◦C/min under nitro-gen from ambient to 30 ◦C abovethe melting point to erase previousthermal history. Hold for 10 min attemperature. Cool to 50 ◦C belowthe peak crystallization temperatureat a rate of 10 ◦C/min. Repeat heat-ing as soon as possible under N2 atrate of 10 ◦C/min.

Values and units Tp- peak melting point(s) from thesecond heat cycle⇒ ◦C or K

Tm-melting point(s) from the sec-ond heat cycle⇒ ◦C

Table 4.10: Standard methods of measuring glass transition temperature (Shastry)

Standard ISO 11357 - 2 : 98 D3418 - 97

Specimen Molding compound. Powders; granules; pellets ormolded part cut with a microtome,razor blade, hypodermic punch, pa-per punch or cork borer; slivers cutfrom films and sheets.



Standard ISO 11357 - 2 : 98 D3418 - 97

Apparatus DSCCalibrate the temperature measur-ing system periodically over thetemperature range used for the test.

DSC or DTAUsing the same heating rate to beused for specimen, calibrate thetemperature scale with the appropri-ate reference materials covering thematerials of interest.

Test procedures Sample mass of 10 – 20 mg is satis-factory.

Sample weight of 10 – 20 mg is rec-ommended

Perform and record an initial ther-mal cycle up to a temperature highenough to erase previous thermalhistory, by using a heating rate of20 ◦C±1 K/min in 99.9 % pure ni-trogen or other inert gas.

Perform and record a preliminarythermal cycle by heating the spec-imen at a rate of 20 ◦C/min in airor nitrogen from ambient to 30 ◦Cabove the melting point to erase pre-vious thermal history.

Hold temperature until a steady stateis achieved (usually 5-10 min)

Hold for 10 min at temperature.

Quench cool at a rate of at least(20±1) K/min to well below the Tg

(usually 50 K below).

Quench cool to 50 ◦C below thetransition peak of interest. Holdtemperature until a steady state isreached (usually 5 – 10 min).

Reheat at a rate (20 ±1) K/min andrecord heating curve until all desiredtransitions are recorded.

Repeat heating as soon as possible ata rate of 20 ◦C/min until all desiredtransitions have been completed.

Values and units Tmg midpoint temperature⇒ ◦C Tm (Tg) midpoint temperature⇒ ◦C Tf (Tg) extrapolated onsettemperature ⇒ ◦C For most appli-cations the Tf is more meaningfulthan Tm and may be designated asTg in place of the midpoint of the Tg

curve.

Oxygen induction time (OIT) technique: Here, new stabilization additives packagefor LLDPE cable sheaths in phone cables was analyzed to determine its oxidation stabilityand to establish its effectiveness in comparison with the previous additives package used atthe company.


Table 4.11: Standard test method for oxidative-induction time of polyolefins by differ-ential scanning calorimetry

Standard ASTM D3895-04

Abstract This test method outlines a procedure for the determination of oxidative-induction time (OIT) of polymeric materials using differential scanningcalorimetry (DSC). This test is applicable to polyolefin resins that are ina fully stabilized/compounded form

Specimen Polyolefins specimen disks of 6.4 mm diameter, cut from a 250 μm thicksheet obtained by compression molding the sample.

Apparatus Differential Scanning Calorimeter (DSC)

Test procedures The sample and the reference pan are heated at a constant rate in aninert gaseous environment, typically nitrogen, to a specified temperature,usually 200◦C. Once the specified temperature has been reached, theatmosphere is switched to an oxidative atmosphere, usually oxygen,allowed to enter at sameflow rate. The specimen is then held at a constanttemperature until the oxidative reaction is displayed on the thermal curve.The time interval from when the oxygen flow is first inittiated to theoxidative reaction is referred to as the induction period. Aluminum pansare used in geomembrane and vapor-barrier film applications, while forwire and cable industrial applications, copper pans are used

Values and Units Average oxidative induction time, OIT in minutes

Two small samples of cable sheaths with the previous and the new additives packageweremeasured by DSC running an OIT (oxygen induction time) program at a constant heatingrate of 20 K/minute, under an inert gas atmosphere (nitrogen) until 200 ◦C. Afterwards theatmospherewas switched to oxygen and this was the start of the recording for the experimentuntil oxidation was observed (deviation from base line). Figure 4.32 shows the obtainedresults.From the figure it was clear that the new stabilization additives package presented a

much lower oxidation stability or lower value of OIT (time ≈ 25.7 min) than the previousone (time ≈ 43.1 min). Table 4.11 presents the standardized ASTM D3895 test method,used to determine the oxidative-induction time of polyolefins using a differential scanningcalorimeter.


Figure 4.32: OIT results from two additives packages for cable sheaths

Table 4.12: Standard test method for reaction induction time by thermal analysis

Standard ASTM E2046-03

Scope This test method is intended to measure the reaction induction time(RIT) of chemical materials undergoing exothermic reactions with aninduction period. This technique may be used for solids, liquids, orslurries of chemical substances. The RIT is a relative index value, notan absolute thermodynamic property, therefore, itmay change dependingupon experimental conditions.

Specimen The test specimen should be representative of the material being studiedand be prepared to have good thermal contact with the container. Spec-imen may be run in an unconfined or in a sealed container depending onthe condition required for a given application. The test specimen sizedepends on the sensitivity of the apparatus

Apparatus Test chamber, temperature controller, recording device, containers andbalance




Test procedures A specimen of the chemical compound is placed in a container that isheated to the temperature of interest. The specimen temperature and thedifference in heat flow or temperature between the test specimen and aninert reference are monitored until an exothermic reaction is recorded.The time from the attainment of the isothermal test temperature untilthe extrapolated onset of the exothermic reaction is taken as the reactioninduction time.

Values and Units 120 min at 100 (◦C)

Reaction induction time (RIT) technique: The reaction induction time technique isused to determine the onset of an exothermic reaction of a specific material, and is measuredusing the standardized ASTM E2046 testing method presented in Table 4.12.


Characterization of multilayer films for food applications

Here, a coextruded and laminated film was analyzed to determine the layer structure.This case was also presented in industrial application 2.1 which is focused on therequired FTIR and morphological analysis. Based on the FTIR analyses it was con-cluded that the film had 7 layers (morphology) consisting of, LDPE, LLDPE, EVOH,and PET (FTIR results).A 10 mg sample of the film was measured by DSC running a heating program at

a constant rate of 10K/minute and under nitrogen atmosphere. Figure 4.33 shows theobtained results. The figure presents four clear melting peaks at the following temper-atures, from left to right:

– Melting peak 1: 112.12 ◦C corresponding to LDPE– Melting peak 2: 123.83 ◦C corresponding to LLDPE– Melting peak 3: 175.66 ◦C corresponding to EVOH– Melting peak 4: 253.25 ◦C corresponding to PET

A confirmation of the proposed 7-layer structure was obtained. The film was amultilayer of PET laminated to a 5-layer coextruded film:

– PET / (LDPE-LLDPE) / Tie / EVOH / Tie / (LDPE-LLDPE)


Figure 4.33: Multilayer film measured by DSC


Elastomers formulation analysisHere, two elastomeric compoundswith different formulationswere evaluated using

theDSC analysis to determinewhich compoundwas compatible (criteria to be selectedfor industrial applications). The compatibility of a compound with the presence ofdifferent elastomers can be established when a unique glass transition temperature isobserved in a thermogram.The compositions of the two elastomeric compounds were the following:

• Compound 1– NBR (nitrile rubber)

– EPDM (ethylene propylene diene terpolymer)

• Compound 2– SBR (styrene butadiene rubber)

– BR (butadiene rubber)

Small samples of the two compoundsweremeasured byDSC running a T g determi-nation program, i.e., quenching in a nitrogen cooling can until -150 ◦C and afterwards


Figure 4.34: DSC measurement of NBR, Tg = -22.95 ◦C

Figure 4.35: DSC measurement of EPDM, Tg = -48.20 ◦C


Figure 4.36: DSC results of compound 1, Tg1 = -50 ◦C and Tg2 = -22.84 ◦C

Figure 4.37: DSC measurement of SBR, Tg = - 51.44 ◦C


Figure 4.38: DSC measurement of BR, Tg = -99.89 ◦C

Figure 4.39: DSC results of compound 2, Tg = - 47.33◦C


heating at a constant rate of 10 K/minute. The results are shown in the Figs. 4.34 to4.39.From the detailed DSC analysis presented in Figs. 4.35 to 4.39, it was possible to

conclude that the compound 2 was compatible and suitable for industrial applications,because it showed a unique glass transition temperature of T g = - 47.33 ◦C.


Analysis of elastomer curing for a sole rubber compound

Here, elastomer samples were obtained from the same rubber compound at differentlevels of vulcanization and in different times from a vulcanization press (T set= 150 ◦C)to determine the degree of their crosslinking or vulcanization. The crosslinking inelastomers can be observed in a DSC thermogram as an exothermal peak.The samples were measured by DSC under a heating program at a constant heating

rate of 20 K/minute and under nitrogen atmosphere. The results are shown in Figs.4.40 to 4.43.

Figure 4.40: Curve of sample 1 without previous vulcanization

From the detailed DSC measurements presented in Figs. 4.40 to 4.43, it waspossible to determine the degree of vulcanization of the samples by means of theheat of crosslinking (area under the exothermal peak). The degree of vulcanization iscalculated using Eq. 4.13.Degree of vulcanization

(%) =ΔH1 − ΔHx

ΔH1∗ 100 (4.13)


Figure 4.41: Vulcanization curve of sample 2 extracted at 5:40 min

Figure 4.42: Vulcanization curve of sample 3 extracted at 8:40 min


Figure 4.43: Curve of the fully vulcanized sample 4 extracted at 15 min

The obtained results are as follows:

Sample 1: ΔH1 = 9.244 J/g and degree of vulcanization = 0 %



Sample 4: ΔH4 was not detected and degree of vulcanization = 100 %


Isothermal crystallization study of a polypropylene for fiber spinning

Here, an isothermal crystallization study of a polypropylene homopolymerwith a meltindex of 18 g/10 min was required for the modeling of an industrial fiber spinningprocess. The study was carried out within an interval between 120 ◦C and 128 ◦C.The samples were measured by DSC running a heating program from 40 ◦C up

to 250 ◦C at a constant heating rate of 10 K/minute under nitrogen atmosphere. Af-terwards an isotherm was run at 250 ◦C during 5 min and finally a cooling programproceeded at a constant rate of 30 K/minute until the predefined isothermal crystal-lization temperature was reached. The results are presented in Fig. 4.44 [23].


Figure 4.44: Isothermal crystallization of polypropylene

The heats of crystallization (areas under the exothermal peaks) at different crystal-lization temperatures were obtained and are presented in Table 4.13.

Table 4.13: Heats of crystallization of polypropylene at various temperatures

Crystallization Temperature (◦C) Heat of Crystallization (J/g)

120.18 45.99

122.28 52.89

124.29 62.62

126.57 67.29

128.27 79.87

From the thermogrampresented in Fig. 4.44, the degree of crystallization as a func-tion of time and temperature was obtained. This function was modeled by Nakamuraand Avrami theories. This crystallization model was integrated to the correspondingtransport phenomena equations to successfully predict the fiber diameter as a functionof the length in an air quench chamber of a spinning process. Figure 4.45 shows thegood agreement between themeasured and predictedfiber diameter using a Newtonianand a non-Newtonian model [23].


Figure 4.45: Measured and calculated fiber diameter versus length in an air quench chamber

4.7.2 Thermogravimetry (TGA)

Thermogravimetric analysis (TGA) is a thermal analysis technique that measures the weightchanges of a sample under a certain temperature-time program working on the principle ofa beam balance. By using TGA, it is possible to evaluate weight changes caused by the fol-lowing thermal events: volatilization of moisture, volatilization of additives, decompositionof polymers and additives, decomposition of organic pigments, and decomposition of somemineral fillers (i.e., calcium carbonate, CaCO3). This measurement technique is typicallyused for thermal stability. The testing chamber can be heated (up to approximately 1,200 ◦C)and rinsed with gases (inert or reactive).Table 4.14 presents the standardized test ASTM E1131 that describes a method for com-

positional analysis of a compound using thermogravimetry.

Table 4.14: Standard test method for compositional analysis by thermogravimetry


Abstract This test method provides a general technique incorporating thermo-gravimetry to determine the composition of a sample, including theamount of highly volatile matter, medium volatile matter, combustiblematerial, and ash content of compounds.

Specimen Mixture or blends (solids and liquids)Continued on next page



Apparatus A thermobalance composed of a furnace, a temperature sensor, an elec-trobalance and a means of sustaining the specimen and container. Tem-perature controller, recording device and gas flow control device.

Test procedures This test method is an empirical technique using thermogravimetry inwhich the mass of a substance, heated at a controlled rate in an appro-priate environment, is recorded as a function of time or temperature.Mass loss over specific temperature ranges and in specific atmosphereprovide a compositional analysis of that substance. Furthermore, therate of mass change as a function of temperature can be used to pinpointdegradation temperatures

Values and Units Temperature range (◦C), purge gas, flow rate (mL/min) and composition(%), preanalysis purge time (min), number of determinations and weightpercent volatile matter

Table 4.15: Peak decomposition temperatures obtained by TGA for different elastomersat 10◦C/min and N2 50ml/min [4, 8, 9]

Elastomer Td1◦C Td2

◦C

Natural rubber (NR) 370 -

Synthetic polyisoprene (IR) 378 -

Butadiene rubber (cis BR) 388 460

Styrene butadiene rubber (SBR 23.5 %) 389 438

Styrene butadiene rubber (SBR 1712) 310 444

Styrene butadiene rubber (SBR 1778) 286 443

Ethylene propylene terpolymer (EPDM) - 422 to 459

Polychloroprene rubber (CR) 368 448

Nitrile rubber (NBR 18 % acryl nitrile) 391 445 to 462

Nitrile rubber (NBR 28 % acryl nitrile) - 453



Silicone - 488 to 500

Polyacrylate rubber (ACM ) - 401

Chlorinated polyethylene (CPE) 337 to 341 464 to 466

Butyl rubber (IIR) 374 -

Ethyl vinyl acetate rubber (EVA) 340 to 355 434 to 443


Decomposition temperatures of elastomers: Table 4.15 illustrates the typical peakdecomposition temperatures, Td, for different elastomers. Some elastomers show two de-composition temperatures (Td1 and Td2). Thermogravimetry is often used to identify thecomponents in a rubber compound or a blend based on the thermal stability of each compo-nent.

Decomposition temperatures of thermoplastics: Table 4.16 shows the typical peakdecomposition temperatures for several polymers. A thermogravimetric analyzer can detectweight changes of less than 10 μg as a function of temperature and time.

Decomposition temperatures of additives: Some of the typical components in arubber or PVC compound are processing aids, plasticizers, or mineral fillers such as carbonblack or calcium carbonate, among others. As an example, a flexible PVC sample measuredby TGA can show several transitions representing the decomposition of volatile components,the decomposition of the plasticizer, the formation of HCl, the carbon-carbon scission, andthe forming of CO2.

Table 4.16: Peak decomposition temperatures obtained by TGA for various polymers[4]

Polymer 10 ◦C/min and 20 ◦C/min and 30 ◦C/min andN2 50 ml/min N2 50 ml/min N2 50 ml/min

Td1 (◦C) Td2 (◦C) Td1 (◦C) Td2 (◦C) Td1 (◦C) Td2 (◦C)

PVC - - 333 466 280 460

LDPE - - - 487 - 480

PP - - - - - 480

PS - - - 443 - -

ABS - 420 to 425 - - - -

PA 66 - - - 430 to 473 - -

POM - 315 370 - -


Elastomer formulation analysisHere, an unknown rubber compound based on NR and SBR rubber was analyzed

to determine weight percentages of the different components in the formulation.A typical TGA of an elastomer formulation presents volatiles decomposition below

350 ◦C and elastomer and resin decompositions between 350 ◦C and 500 ◦C. Withregard to the fillers in the formulation,carbon black decomposition takes place between550 ◦C and 650 ◦C, calcium carbonate between 550 ◦C and 650 ◦C, and finally, otherinorganic materials above 800 ◦C.


Table 4.17: Peak decomposition temperatures obtained by TGA for various additivesat 10 ◦C/min and N2 50 ml/min [9]

Additive Td1 (◦C )

Aromatic oil 306 to 240

Paraffinic oil 265 to 298

Naftenic oil 216 to 293

Mineral oil 245

DBP plasticizer 206

DOP plasticizer 259

DIDP plasticizer 289

DOA plasticizer 241

DOM plasticizer 217

Stearic acid 221

Carbon black N 550 648

Carbon black N 375 689

Calcium carbonate 754

Erucamide 280

Oleamide 240

A 15 mg sample was measured by TGA under a heating program at a constant rateof 50 K/minute under nitrogen atmosphere up to 500 ◦C and afterwards under oxygenatmosphere up to 900 ◦C. Figure 4.46 shows the obtained results.

Figure 4.46: TGA of an elastomer formulation


Table 4.18: Composition by TGA of an elastomer

Sample composition Percentage Weight Formulateddifference (%) percentage (%) value (%)

Low molecular weight volatiles 99.96 - 87.34 12.62 13.55

Elastomeric material 87.34 - 28.35 58.99 59.49

Carbon black 28.35 - 3.13 25.22 23.8

Other inorganic material 3.133

Total 100 %


Analysis of an EVA-based Rubber

Here, an unknown black foamed product was analyzed to determine its composition(weight percentages of the main components). Prior to the TGA, an FTIR analysisdiscovered that the material was an EVA-based rubber (ethyl vinyl acetate).

Figure 4.47: TGA of an EVA-based rubber

A 15 mg sample was measured by TGA under a heating program at a constant rateof 50 K/minute. Figure 4.47 presents the obtained results.


Table 4.19: Composition by TGA of an EVA-based rubber

Sample composition Decomposition tempera-ture ranges, (◦C)

Weight percentage, (%)

Low molecular weight volatiles < 334.47 2.01

Polymeric material 338.47 - 599.32 58.36

CO2 from calcium carbonate 599.32 - 654.23 12.23

CaO ashes from calcium carbonate 654.23 - 838.33 9.33 ( equivalent to 21.2 cal-cium carbonate)

Other inorganic materials � 838.33 18.07

Total 100 %

According to Table 4.19, the total weight percentage of fillers in this EVA-basedrubber was 39.3 % by weight, where 21.2 % corresponded to calcium carbonate and18.07 % corresponded to other inorganic materials.


Characterization of filler content in a polypropylene resin

In this case, pellets from a polypropylene resin containing an inorganic filler wereanalyzed to determine weight percentage of the fillers in the resin. This case was alsopresented in industrial application 2.5 focused on the FTIR analysis to determine thefiller type.A 16 mg sample was measured by TGA under a heating program at a constant rate

of 50 K/minute. Figure 4.48 shows the obtained results.The figure presents clear decomposition temperature (T d) ranges for each compo-

nent in the sample. The results are summarized in Table 4.20.

Table 4.20: Composition by TGA of a PP resin containing a filler

Sample composition Decomposition tempera-ture ranges, (◦C)

Weight percentage, (%)

Low molecular weight volatiles < 338.47 0.27

Polymeric material 338.47 - 636.46 92.3

CO2 from Calcium Carbonate 710.91 3.09 (equivalent to 7.03 ofcalcium carbonate)

CaO ashes from calcium carbonate � 801.18 3.94

Other inorganic material � 801.18 0.4

Total 100 %


Figure 4.48: TGA of a PP resin containing a filler

According to Table 4.20, the total weight percentage of the fillers in the polypropy-lene resin was 7.43 % by weight, where 7.03 % corresponded to calcium carbonateand 0.4 % corresponded to other inorganic materials.

References

1. A. Naranjo. Status of the development of a new method to determine the thermal diffusivity ofthermoplastics under processing conditions. 1st ICIPC Colloquium, 2003.

2. A. Naranjo. Bestimmung der Temperaturleitfahigkeit von Thermoplasten unter Verarbeitungsbe-dingungen. PhD thesis, Institut fur Kunststoffverarbeitung. RWTH, Aachen, Germany, 2004.

3. W.Michaeli, A.Naranjo, andO.Lingk. BestimmungundModellierungderTemperaturleitfahigkeitvon thermoplastischen Kunststoffen unter realen Verarbeitungsbedingungen. Institut fur Kunst-stoffverarbeitunganderRWTH,Abschlussbericht zumvonderVW-Stiftung gefordertenForschungsvorhaben,I/79 205, 2006.

4. S. Knappe, E. Kaisersberger, and H. Mohler. Netzsch annual for science and industry. 2, 1993.

5. W. F. Hemminger and H. K. Cammenga. Methoden der thermischen Analyse. 1988.

6. M. De Greiff, N. Castano, and A. Naranjo. Applied Rubber Technology (Plastics Pocket Power).Hanser Publishers. 2001.

7. J. Sierra. Development of biconstituent fibers of polypropylene and polyamide 6 for high speedfiber spinning. PhD thesis, University of the Vasc Country, Spain, 2005.

8. Dupont. DIK, TGA - thermal analysis information.

9. ICIPC. Rubber and plastic institute for training and research - ICIPC. ICIPC Library of TGAAnalyses, 1993-2007.

127

CHAPTER 5

MELT RHEOLOGY

Rheology is the field of science that studies fluid behavior during flow-induced deformation.From the variety of materials that rheologists study, polymers have been found to be themost interesting and complex. Polymer melts are shear thinning, viscoelastic, and their flowproperties are temperature dependent. Viscosity is the most widely used material parameterwhen determining the behavior of polymers during processing. Since the majority of poly-mer processes are shear-rate dominated, the viscosity of the melt is commonly measuredusing shear deformation measurement devices. However, there are polymer processes, suchas blow molding, thermoforming, and fiber spinning, that are dominated by either elonga-tional deformation or by a combination of shear and elongational deformation. In addition,some polymer melts exhibit significant elastic effects during deformation. Rheometry is theaspect of rheology that measures by means of analytical techniques the rheological proper-ties required for process layout and assessment. Furthermore, rheological characterizationis an important tool for studying the molecular weight distribution of polymers, as wellas for troubleshooting, optimizing, and designing processing equipment. Some industrialapplications and applications are discussed later in this chapter.

128 5 Melt Rheology

5.1 BASIC CONCEPTS AND TERMINOLOGY

This section summarizes the basic concepts and terminology commonly used in the field ofrheology.

Stress: Stress, τ , is the amount of force applied in a particular area. Depending of thetype of flow, it is common to define the following stresses: shear stress and normal stress.

Strain: Strain, γ, quantifies the deformation imposed on a material element. Dependingof the type of flow, we distinguish between shear strains and elongational strains.

Strain rate: The strain strain rate, γ, is sometimes also referred to as a rate of deformation:or shear rate. The natural response of a solid is a finite strain; however, for a liquid, thenatural response is a strain rate rather than a finite strain.

Viscosity: Viscosity, η, is the rheological property that relates the stress to the strain rate.In a Newtonian fluid, the deviatoric stresses that occur during deformation, τ , are directlyproportional to the rate of deformation tensor, γ,

τ = μγ. (5.1)

For Newtonian liquids, the viscosity, μ, is considered to be only dependent on tem-perature. However, the viscosity of most polymer melts is shear thinning in addition tobeing temperature dependent. The shear thinning effect is the reduction in viscosity at highrates of deformation. This phenomenon occurs because, at high rates of deformation, themolecules are stretched out and disentangled, enabling them to slide past each other withmore ease, hence lowering the bulk viscosity of the melt. To take into consideration thesenon-Newtonian effects, it is common to use a viscosity which is a function of the strain rateand temperature to calculate the stress tensor in Eq. 5.1

τ = η(γ, T )γ, (5.2)

where η is the non-Newtonian viscosity and γ the magnitude of strain rate or rate of defor-mation tensor defined by

γ =

√12II, (5.3)

where II is the second invariant of the strain rate tensor defined by

II =∑

i

∑j

γij γji. (5.4)

The strain rate tensor components in Eq. 5.4 are defined by

γij =∂ui

∂xj+

∂uj

∂xi. (5.5)

The temperature dependence of the polymer’s viscosity is normally factored out as

η(γ, T ) = f(T )η(γ), (5.6)


Figure 5.1: Viscosity curve for a polypropylene

10

100

1000

10000

10 100 1000 10000 100000

Fiber spinningInjection moldingExtrusionCompression molding

Calendering

Shear rate

220oC

ABS

260oC

300oCPC

340oC260oC

300oC

PA6

γ

101

102

103

104

Figure 5.2: Viscosity curves for a selected number of thermoplastics

where for small variations in temperature, f(T ) can be approximated using an exponentialfunction such as

f(T ) = e-a(T -T0). (5.7)

Figure 5.1 illustrates the typical viscosity curve of a polymericmelt at three different temper-atures. As presented in this figure, the viscosity curve is best presented in double-log graphs.Figures 5.2 through 5.6 show the shear thinning behavior and temperature dependence ofthe viscosity for a selected number of thermoplastics.

Elongational viscosity: In polymer processes such as fiber spinning, blow molding,thermoforming, foaming, certain extrusion die flows, and compression molding with spe-cific processing conditions, the major mode of deformation is elongational. To illustrateelongational flows, consider the fiber-spinning process shown in Fig. 5.7.

130 5 Melt Rheology

10

100

1000

10000

100000

1 10 100 1000 10000 100000

PE-HD

Low MFI (230 oC)Pa•s

s-1

PE-HD

High MFI (230 oC)

PP

High MFI (230 oC)

PP

Low MFI (230 oC)

Rate of deformation

Figure 5.3: Viscosity curves for PE-HD and PP with low and high MFI at 230 ◦C

1

10

100

1000

10000

1 10 100 1000 10000 100000

SAN (250 oC)

ABS (250 oC)

PS (250 oC)

PBT (250 oC)

PA6 (250 oC)

Pa•s

s-1

Rate of deformation

Figure 5.4: Viscosity curves for a selected number of thermoplastics at 250 ◦C


1

10

100

1000

10000

1 10 100 1000 10000 100000

ASA (240 oC)

PES (340 oC)

PA66 (290 oC)

SB (240 oC)

Pa•s

s-1

Rate of deformation

Figure 5.5: Viscosity curves for selected thermoplastics

1

10

100

1000

10000

100000

1 10 100 1000 10000 100000

PMMA

Low MFI (200 oC)

PMMA

High MFI (200 oC)

PMMAHigh MFI

(220 oC)

LCP (340 oC)

PAEK

(400 oC)PMMA Low MFI

(240 oC)

Pa•s

s-1

Rate of deformation

Figure 5.6: Viscosity curves for PMMA, PAEK, and LCP

F

Figure 5.7: Schematic diagram of a fiber-spinning process

132 5 Melt Rheology

A simple elongational flow is developed as the filament is stretched with the followingcomponents of the rate of deformation:

γ11 = -ε

γ22 = -ε

γ33 = 2ε

(5.8)

where ε is the elongation rate, and the off-diagonal terms of γ ij are all zero. The diagonalterms of the total stress tensor can be written as

σ11 = -p-ηε

σ22 = -p-ηε

σ33 = -p+2ηε

(5.9)

Since the only outside forces acting on the fiber are in the axial or 3-direction, for theNewtonian case, σ11 and σ22 must be zero. Hence,

p = -ηε (5.10)

andσ33 = 3ηε = ηε, (5.11)

which is known as elongational viscosity or Trouton viscosity [1]. This is analogous toelasticity where the following relation between elastic modulus, E, and shear modulus, G,can be written

E

G= 2(1+ν), (5.12)

where ν is Poisson’s ratio. For the incompressibility case, where ν = 0.5, Eq. 5.12 reducesto

E

G= 3. (5.13)

102 5•102 103 104 105 5•105106

5•106

107

108

5•108

5•107

Stress, τ, σ

μo = 1.6•108 Pa-s

μo = 1.7•108 Pa-s

ηo = 5.5•107 Pa-s

ηo = 5•107 Pa-s

(Pa)

T = 140 °C

Polystyrene IPolystyrene II

Elongational test

Shear test

Vis

cosi

ty (

Pa-s

)

Figure 5.8: Shear and elongational viscosity curves for two types of polystyrene


LDPE

Ethylene-propylene copolymer

PMMA

POM

PA66

6

5

4

3

2 3 4 5 6

Tensile stress, log σ (Pa)

Log

(Vis

cosi

ty)

(Pa-

s)

Figure 5.9: Elongational viscosity curves as a function of tensile stress for several thermoplastics

0.0

0.1

0.2

0.3

0.5

0.4

0.6

0.7

0.8

10-1 100 101 102Cure time (min)

60 °C

50 °C

40 °C

Deg

ree

of c

ure

, c

Figure 5.10: Degree of cure as a function of time for a vinyl ester at various isothermal curetemperatures

Figure 5.8 [2] shows shear and elongational viscosities for two types of polystyrene. Inthe region of the Newtonian plateau, the limit of 3, shown in Eq. 5.11, can be seen.Figure 5.9 presents plots of elongational viscosities as a function of stress for various

thermoplastics at common processing conditions. It should be emphasized that measuringelongational or extensional viscosity is an extremely difficult task. For example, to maintaina constant strain rate, the specimen must be deformed both uniformly and exponentially.In addition, a molten polymer must be tested completely submerged in a heated, neutrallybuoyant liquid at a constant temperature.

134 5 Melt Rheology

0 0.1 0.2 0.3 0.4 0.6 0.5 0.710-1

Degree of cure, c

40 °C

50 °C60 °C

Vis

cosi

ty (

Pa-

s)

100

10

Figure 5.11: Viscosity as a function of degree of cure for a vinyl ester at various isothermal curetemperatures

Curing effects of viscosity A curing thermoset polymer has a conversion or cure de-pendent viscosity that increases as the molecular weight of the reacting polymer increases.For vinyl ester, whose curing history is shown in Fig. 5.10 [3], the viscosity behaves as shownin Fig. 5.11 [3].Hence, a complete model for viscosity of a reacting polymer must contain the effects of

strain rate, γ, temperature, T , and degree of cure, c, such as

η = η(γ, T, c). (5.14)

There are no generalized models that include all these variables for thermosetting polymers.However, extensive work has been done on the viscosity of polyurethanes [4, 5] used in thereaction injection molding process. An empirical relation that models the viscosity of thesemixing-activated polymers, given as a function of temperature and degree of cure, is writtenas

η = η0eE/RT

(cg

cg − c

)c1+c2c

(5.15)

where E is the activation energy of the polymer, R is the ideal gas constant, T is thetemperature, cg is the gel point1, c the degree of cure, and c1 and c2 are constants that fit theexperimental data. Figure 5.12 shows the viscosity as a function of time and temperature fora 47% MDI-BDO P(PO-EO) polyurethane.

1At the gel point, the cross-linking creates a closed network, at which point it is said that the molecular weight goesto infinity.


90 °C50 °C30 °C

0.01

0.1

1

10

100

0.1 1.0 10 100Time (min)

Vis

cosi

ty (

Pa-

s)

Figure 5.12: Viscosity as a function of time for a 47%MDI-BDOP(PO-EO) polyurethane at variousisothermal cure temperatures

Suspension rheology: Particles suspended in a material, such as in filled or reinforcedpolymers, have a direct effect on the properties of the final article and on the viscosity duringprocessing. Numerous models have been proposed to estimate the viscosity of filled liquids[6, 7, 8, 9, 10]. Most models proposed are a power series of the form

ηf

η= 1+a1φ+a2φ

2+a3φ3+..... (5.16)

The linear term in Eq. 5.16 represents the narrowing of the flow passage caused by the fillerthat is passively entrained by the fluid and sustains no deformation as shown in Fig. 5.13. For

γ. κγ.

v(z) v (z)f

V V

z

Particles

Figure 5.13: Schematic diagram of strain rate increase in a filled system

instance, Einstein’s model, which only includes the linear term with a 1 = 2.5, was derivedbased on a viscous dissipation balance. The quadratic term in the equation represents thefirst-order effects of interaction between the filler particles. Geisbusch suggested a modelwith a yield stress and where the strain rate of the melt increases by a factor κ as

ηf =τ0

γ+ κη0(κγ). (5.17)

136 5 Melt Rheology

1

2

3

4

5

6

7

0 10 20 30 40 50Volume fraction of filler (%)

Experimental dataa = 2.5, a = 14.1 (Guth, 1938)21

η /η f

Figure 5.14: Viscosity increase as a function of volume fraction of filler for polystyrene and low-density polyethylene containing spherical glass particles with diameters ranging between 36 μm and99.8 μm

For high deformation stresses, which are typical in polymer processing, the yield stress inthe filled polymer melt can be neglected. Figure 5.14 compares Geisbusch’s experimentaldata to Eq. 5.16 using the coefficients derived by Guth [9]. The data and Guth’s model seemto agree well. A comprehensive survey on particulate suspensions was recently given byGupta [11] and on short-fiber suspensions by Milliken and Powell [12].

Complex modulus: The complexmodulusG∗ is the overall resistance to deformation ofa material, regardless of whether that deformation is recoverable (elastic) or non-recoverable(viscous).

Complex viscosity: The complex viscosity is a ratio of complex modulus to angularfrequency, usually denoted by the symbol η ∗.

Dynamic storage modulus: The dynamic storagemodulus is the contribution of elastic(solid-like) behavior to the complex modulus, usually denoted by the symbolG ′.

Dynamic loss modulus: The dynamic loss modulus is the component of the complexmodulus that is out of face, usually denoted by the symbolG ′′.

Compliance: The compliance, J , is the ratio of strain to stress.

Viscoelastic memory effects: When a polymer melt is deformed, either by stretching,shearing, or often by a combination of the above, the polymer molecules are stretched anduntangled. In time, the molecules try to recover their initial shape, in essence getting used totheir new state of deformation. If the deformation is maintained for a short period of time,the molecules may go back to their initial position, and the shape of the melt is fully restoredto its initial shape. Here, it is said that the molecules remembered their initial position.


However, if the shearing or stretching goes on for an extended period of time, the polymercannot recover its starting shape, in essence forgetting the initial positions of the molecules.The time it takes for a molecule to fully relax and get used to its new state of deformationis referred to as the relaxation time, λ. A useful parameter often used to estimate the elasticeffects during flow is the Deborah number2,De. The Deborah number is defined by

De =λ

tprocess, (5.18)

where tprocess is a characteristic process time. For example, in an extrusion die,a characteristicprocess time can be defined by the ratio of characteristic die dimension in the flow directionand average speed through the die. A Deborah number of zero represents a viscous fluidand a Deborah number of ∞ an elastic solid. As the Deborah number becomes > 1,the polymer does not have enough time to relax during the process, resulting in possibleextrudate dimension deviations or irregularities such as extrudate swell, shark skin, or evenmelt fracture.

Melt fracture: This phenomenon appears in the form of waves in the extrudate when thepolymer is extruded at high speeds and is not allowed to relax.

a)

b)

c)

d)

Figure 5.15: Various shapes of extrudates under melt fracture [14]

This phenomenon is sometimes referred to as shark skin and is shown for a high-densitypolyethylene in Fig. 5.15a [13]. It is possible to extrude at such high speeds that an intermit-tent separation of melt and inner die walls occurs, as shown in Fig. 5.15b. This phenomenonis often referred to as the stick-slip effect or spurt flow and is attributed to high shear stressesbetween the polymer and the die wall. This phenomenon occurs when the shear stress isnear the critical value. If the speed is further increased, a helical geometry is extruded as

2From the Song of Deborah, Judges 5:5 – "The mountains flowed before the Lord."M. Rainer is credited for namingthe Deborah number; Physics Today, 1, (1964).

138 5 Melt Rheology

shown for a polypropylene extrudate in Fig. 5.15c. Eventually, the speeds are so high that achaotic pattern develops, such as the one shown in Fig. 5.15d. This well-knownphenomenonis called melt fracture. The shark skin effect is frequently absent, and spurt flow seems tooccur only with linear polymers.Table 5.1 presents estimated critical melt fracture stresses for various polymers.

Table 5.1: Critical shear stress for flow instabilities prediction for some polymers

Material Critical shear stress, (MPa)

HDPE 0.145

LLDPE 0.145

LDPE 0.130

PP 0.130

PS 0.130

Normal stresses: The tendency of polymer molecules to curl up while they are beingstretched in shear flow results in normal stresses in the fluid. For example, shear flows exhibita deviatoric stress defined by

τxy = η(γ)γxy. (5.19)

Measurable normal stress differences, N1 = τxx-τyy and N2 = τyy-τzz are referred to asthe first and second normal stress differences.

Reduced shear rate, log aT γo (s-1)

-4 -3 -2 -1 0 1 2 3 4

1

2

3

4

5

6

7

115 oC130 oC

150 oC170 oC190 oC

210 oC

.

T

Red

uce

d fi

rst

no

rmal

str

ess

diff

eren

ce

Lo

g(ψ

/a

) (P

a-s

)2

2

Experiments done between 115 and 210oC

Figure 5.16: Reduced first normal stress difference coefficient for a low-density polyethylene meltat a reference temperature of 150 ◦C

The first and second normal stress differences are material dependent and are defined by

N1 = τxx-τyy = -Ψ1γ2xy (5.20)

N2 = τyy-τzz = -Ψ2γ2xy. (5.21)


Reduced shear rate, log aT γo (s-1)

-4 -3 -2 -1 0 1 2 3 4

1

2

3

4

5

6

7

115 oC130 oC

150 oC170 oC190 oC

210 oC

.

Red

uce

d v

isco

sity

, Lo

g(η

/a )

(Pa-

s)T

Figure 5.17: Reduced viscosity for a low-density polyethylene melt at a reference temperature of150 ◦C

The material functions, Ψ1 and Ψ2, are called the primary and secondary normal stresscoefficients, and are also functions of themagnitude of the strain rate tensor and temperature.The first and second normal stress differences do not change in sign when the direction ofthe strain rate changes. This is reflected in Eqs. 5.20 and 5.21. Figure 5.16 presents the firstnormal stress difference coefficient for the low density polyethylene melt of Fig. 5.17 at areference temperature of 150 ◦C. The second normal stress difference is much smaller thanthe first normal stress difference and is therefore difficult to measure.

Material data banks: The rheological behavior of molten polymers are found inmaterialdata banks, such as CAMPUS�, and are presented in graphs such as shown in Figs. 5.16and 5.17.

Surface tension: Surface tension plays a significant role in the deformation of polymersduringflow, especially in dispersivemixing of polymer blends. Surface tension,σ S , betweentwo materials appears as a result of different intermolecular interactions. In a liquid-liquidsystem, surface tension manifests itself as a force that tends to maintain the surface betweenthe two materials to a minimum. Thus, the equilibrium shape of a droplet inside a matrix,which is at rest, is a sphere. When three phases touch, such as liquid, gas, and solid, we getdifferent contact angles depending on the surface tension between the three phases.Figure 5.18 schematically depicts three different cases. In case 1, the liquid perfectly

wets the surface with a continuous spread, leading to a wetting angle of zero. Case 2, withmoderate surface tension effects, shows a liquid that has a tendency to flow over the surfacewith a contact angle between zero and π/2. Case 3, with a high surface tension effect, iswhere the liquid does not wet the surface, which results in a contact angle greater than π/2.In Fig. 5.18, σS denotes the surface tension between the gas and the solid, σ l the surfacetension between the liquid and the gas, and σsl the surface tension between the solid andliquid.The wetting angle can be measured using simple techniques such as a projector, as shown

schematically in Fig. 5.19. This technique, originally developed by Zisman, can be used in

140 5 Melt Rheology

Case 1

φσs,l

σl

σsCase 2

Case 3

Figure 5.18: Schematic diagram of contact between liquids and solids with various surface tensioneffects

φ

Micrometer

Syringe

Drop

Magnifying apparatus

xy-translator

Optical bench

Figure 5.19: Schematic diagram of apparatus to measure contact angle between liquids and solids

1.0

0.5

0 σc σl

cosφ

Figure 5.20: Contact angle as a function of surface tension

the ASTMD2578 standard test. Here, surface tension, σ l is applied to a film. The measuredvalues of cosφ are plotted as a function of surface tension σ l, as shown in Fig. 5.20, andextrapolated to find the critical surface tension, σc, required for wetting.For liquids of low-viscosity, a useful measurement technique is the tensiometer, schemat-

ically represented in Fig. 5.21. Here, the surface tension is related to the force it takes to pulla platinum ring from a solution. Surface tension for selected polymers are listed in Table 5.2,for some solvents in Table 5.3, and between polymer-polymer systems in Table 5.4.There are many areas in polymer processing and in engineering design with polymers

where surface tension plays a significant role. These areas are the mixing of polymer blends,adhesion, treatment of surfaces to make them non-adhesive, and sintering. During manufac-turing, it is often necessary to coat and crosslink a surface with a liquid adhesive or bonding


material. To enhance adhesion it is often necessary to raise surface tension by oxidizing thesurface, by creating COOH-groups, using flames, etching, or releasing electrical discharges.

Table 5.2: Typical surface tension values of selected polymers at 180 ◦C

Polymer σs (N/m) ∂σs/∂T(N/m/K)

Polyamide resins (290 ◦C) 0.0290 -

Polyethylene (linear) 0.035 -5.7 × 10-5

Polyethylene teraphthalate (290 ◦C) 0.045 -6.5 × 10-5

Polyisobutylene 0.0234 -6 × 10-5

Polymethyl methacrylate 0.0289 -7.6 × 10-5

Polypropylene 0.030 -5.8 × 10-5

Polystyrene 0.0292 -7.2 × 10-5

Polytetrafluoroethylene 0.0094 -6.2 × 10-5

Force measuringdevice

Level

Fluid

Ring

Figure 5.21: Schematic diagram of a tensiometer used to measure surface tension of liquids

Table 5.3: Surface tension for several solvents

Solvent Surface tension - σs (N/m)

n-Hexane 0.0184

Formamide 0.0582

Glycerin 0.0634

Water 0.0728

142 5 Melt Rheology

Table 5.4: Surface tension between polymers

Polymers σs (N/m) ∂σs/∂T (N/m/K) T (◦C)

PE-PP 0.0011 - 140

PE-PS 0.0051 2.0×10-5 180

PE-PMMA 0.0090 1.8 × 10-5 180

PP-PS 0.0051 - 140

PS-PMMA 0.0016 1.3 × 10-5 140

This is also the case when enhancing the adhesion properties of a surface before painting.On the other hand, it is often necessary to reduce adhesiveness of a surface, such as requiredwhen releasing a product from the mold cavity or when coating a pan to give it nonstickproperties. A material often used for this purpose is polytetrafluoroethylene (PTFE), mostlyknown by its tradename Teflon.

5.2 CONSTITUTIVE MODELS

A constitutivemodel is a mathematical expression that relates stress, strain, stress rate, strainrate, pressure, and temperature, just to name a few. The most common constitutive modelrelates stress to strain rate and temperature. The relationship between stress and strain rateis a viscosity function that typically incorporates the dependence of other factors, such astemperature, pressure, and time. It can be stated that the viscosity is a complex function thatdepends on factors including:

• Macromolecular characteristic of the polymer, such as chain branches and rigidity• Molecular weight distribution• Shear rate• Temperature• Pressure• Time• Voltage in the case of electro-rheological fluids• Magnetic field in case of magneto-rheological fluids

Although several viscosity functions are presented in the literature, in this book the New-tonian model, the Power law and Bird-Carreau-Yasuda model were selected because theycan be easily related to most polymer flows that involve shear. For non-isothermal and non-isobaric problems, models that relate the viscosity to temperature and pressure were alsoincluded. Finally, for complex flows, such as those that involve viscoelastic and elonga-tional effects, the Phan-Thien and Tanner multimode model is presented.


5.2.1 Newtonian Model

TheNewtonianmodelwas developedbyNewton in 1687 andpredicts a viscosity independentof the shear rate (i.e., the shear stress is a linear relationship of shear rate). Although thismodel is easy to apply, it can be used only for the beginning of the viscosity curve at lowshear rates. Mathematically, the Newtonian model can be expressed as

μ =τ

γ, (5.22)

where μ is the shear viscosity (Pa· s), γ is the shear rate (s-1), and τ is the stress (Pa). Notethat for Newtonian fluids the viscosity is represented by μ.

5.2.2 Power Law Model

This model, also known as the Ostwald and deWaale model, is easy to use and can representthe pseudoplastic behavior of polymer melts. The term pseudoplastic was introduced byWilliamson and Ostwald in 1925 to describe the behavior of the fluids that suffer a reduc-tion of viscosity with an increase of shear rate. It can be applied for the pseudoplastic orshear thinning region because for low shear rates the prediction of viscosity is very high.Mathematically, the Power law model can be expressed as

η = m · γn-1, (5.23)

where η is the shear viscosity (Pa·s), γ is the shear rate (s-1), m is the consistency factor(Pa · sn), and n is the Power law index. For polymers the Power law index n is typicallybetween 0.2 and 0.9. The deviation of n from the unity is taken as a measurement of thenon-Newtonian behavior. For values of n > 1, the fluid behaves as a dilatant, or shearthickening fluid. Table 5.5 presents a list of typical Power law and consistency indices forcommon thermoplastics.

Table 5.5: Power law and consistency indices for common thermoplastics

Polymer m (Pa· sn) n T (◦C)

High-density polyethylene 2.0 × 104 0.41 180

Low-density polyethylene 6.0 × 103 0.39 160

Polyamide 66 6.0 × 102 0.66 290

Polycarbonate 6.0 × 102 0.98 300

Polypropylene 7.5 × 103 0.38 200

Polystyrene 2.8 × 104 0.28 170

Polyvinyl chloride 1.7 × 104 0.26 180

The temperature dependence of the Power-law viscosity can be built into the consistency as

m = m0e-a(T -Tref ) (5.24)

144 5 Melt Rheology

or by introducing a time-temperature superposition shift factor,

η = k · aT · (aT · γ)n-1, (5.25)

where for amorphous polymers, the shift factor is best defined using the Williams, Landel,and Ferry model3 given by

aT = 10-

C1(T -Tref )C2+(T -Tref ) , (5.26)

where C1, C2 are empirical constants obtained by statistical regression of viscosity curve atdifferent temperatures and selecting a particular value of reference temperature (C 1 = 17.44and C2 = 51.6 when Tref = Tg . If Tref = Tg+45K ,C1 = 8.86 and C2 = 101.6), T is thetemperature (K), and Tref is the reference temperature (K).

A shift commonly used for semicrystalline polymers is the Arrhenius shift, which iswritten as

Ln(aT ) =E0

R

(1T-

1T0

), (5.27)

where E0 is the activation energy (J· mol-1) (this constant can be obtained by statisticalregression of the viscosity curve at different temperatures and selecting a particular valueof reference temperature), T0 is the reference temperature (K), and R is the universal gasconstant (8.314 J· mol-1· K-1).

5.2.3 Bird-Carreau-Yasuda Model

The Bird-Carreau-Yasuda model is more complex and has the advantage of predicting boththe Newtonian and the pseudoplastic behavior of polymers, as well as the transition region.Mathematically, the Bird-Carreau-Yasuda model can be expressed as follows

η − η0

η0 − η∞= [1+|λγ|a](n-1)/a, (5.28)

where η is the shear viscosity (Pa·s), η0 is the zero-shear-rate viscosity (Pa·s), η∞ is theinfinite-shear-rate viscosity (Pa·s), λ is the time constant , γ is the shear rate, (s -1), and n isthe Power law index.

In the original Bird-Carreaumodel, the constant a = 2. In many cases, the infinite-shear-rate viscosity is negligible, reducing Eq. 5.28 to a three parameter model. Equation 5.28 wasmodified by Menges, Wortberg, and Michaeli to include a temperature dependence using aWLF relation. The modified model, which is used in commercial polymer data banks, iswritten as:

η =A · aT

[1+BγaT ]C, (5.29)

3Often referred to as WLF equation.


where aT is the temperature shift factor (A) is the viscosity constant (Pa·s-C), B is thetime constant (s), and C is the shear thinning index. The shift aT , for the best-fit referencetemperature, Tref , is given by4

Log(aT ) =8.86(Tref -Tg)101.6+Tref -Tg

− 8.86(T -Tg)101.6+T -Tg

, (5.30)

where aT is the temperature shift factor, Tg is the glass transition temperature (K), and Tref

is the reference temperature (Tref = Tg + 45K). Table 5.6 presents constants for Carreau-WLF (amorphous) and Carreau-Arrhenius models (semi-crystalline) for various commonthermoplastics.

Table 5.6: Constants for Carreau-WLF (amorphous) and Ccarreau-arrhenius (semi-crystalline) models for various common thermoplastics

Polymer A B C Tref Tg T0 E0

(Pa·s) (s) (◦C) (◦C) (◦C) (J/mol)

High-density polyethylene 24,198 1.38 0.60 - - 200 22,272

Low-density polyethylene 317 0.015 0.61 - - 189 43,694

Polyamide 66 44 0.00059 0.40 - - 300 123,058

Polycarbonate 305 0.00046 0.48 320 153 - -

Polypropylene 1,386 0.091 0.68 - - 220 427,198

Polystyrene 1,777 0.064 0.73 200 123 - -

Polyvinyl chloride 1,786 0.054 0.73 185 88 - -

5.2.4 Pressure Dependence of Viscosity

The viscosity of a polymer melt is also dependent on the pressure, which is particularlyimportant in injection molding processes of thin parts where the pressure levels are thehighest. The pressure dependence of viscosity can be modeled by using:

• Pressure Coefficient – The viscosity at a certain pressure can be predicted based ona viscosity data at another pressure if the coefficient of pressure is known,

η(P ) = η(Po) · eφ·P , (5.31)

whereη(P ) is the viscosity at a pressurep (Pa· s),φ is the pressure coefficient atm-1, andη(Po) is the viscosity at a pressure po (Pa· s). The pressure coeffcient can be obtainedby statistical regression of viscosity data at various pressures. Very little informationon the coefficient of pressure has been published so far. Table 5.7 presents the reporteddata for some particular polymers.

4This shift should be used for amorphous polymers.

146 5 Melt Rheology

Table 5.7: Coefficient of pressure for some particular polymers

Polymer Temperature, ◦C φ, 10-3atm

PVC for injection molding 180 6.00190 4.00200 3.00

Linear low-density Polyethylene (LLDPE) - 2.31

• Modified WLF model – In addition to the temperature shift, Menges, Wortberg, andMichaeli measured a pressure dependence of the viscosity and proposed the followingmodel, which includes both temperature and pressure viscosity shifts:

log η(T, p) − log η0 =8.86(T -T0)101.6+T -T0

− 8.86(T -T0+0.02p)101.6+(T -T0+0.02p)

, (5.32)

where η is the pressure dependent viscosity, η0 is the reference viscosity, and p is thepressure in bar (the constant 0.02 represents a 2 ◦C shift per bar).

5.2.5 Phan-Thien and Tanner Multimode Model

A great variety of viscoelastic models have been used to describe the viscoelastic behaviorof polymer melts, including the model independently developed by Phan-Thien and Tanner(PTT) [15] and by Acierno et al. [16]. The multimode Phan-Thien and Tanner model hasbeen successfully used for modeling the shear, elongational, and oscillatory shear behaviorof polymers, as well as for modeling the processing of viscoelastic polymers. Mathemat-ically, the multimode Phan-Thien and Tanner (PTT) 2D viscoelastic model in cylindricalcoordinates, can be expressed as

exp(εiλi

ηi(τzzi+2τrri))τzzi+λiV

dτzzi

dz− 2λi(1 − ξi)τzzi

dV

dz= 2ηi

dV

dz(5.33)

exp(εiλi

ηi(τzzi+2τrri))τrri+λiV

dτrri

dz+λi(1 − ξi)τrri

dV

dz= −ηi

dV

dz(5.34)

τzz =N∑

i=1

τzzi τrr =N∑

i=1

τrri (5.35)

where τzz is the z component of the elongational stress, τrr is the r component of theelongational stress, V is the velocity in z direction, ηi is the elongational viscosity parameterfor PTT model, λi is the relaxation time parameter for PTT model, ε i is the parameter forPTT model, and ξi is the parameter for PTT model.

5.3 Rheometry 147

5.3 RHEOMETRY

There are variousways to qualify and quantify the properties of the polymermelt in industry.The techniques range from simple analyses for checking the consistency of the material atcertain conditions to more complex measurements that evaluate viscosity and normal stressdifferences. This section includes three such techniques to give the reader a general idea ofcurrent measuring methods.

5.3.1 The Melt Flow Indexer

Themelt flow indexer is often used in industry to characterize a polymermelt and as a simpleand quickmeans of quality control. It takes a single pointmeasurement using standard testingconditions specific to each polymer class on a ram-type extruder or extrusion plastometer asshown in Fig. 5.22.

Weight

Thermometer

Capillary

Polymer

Figure 5.22: Schematic diagram of an extrusion plastometer used to measure the melt flow index

The standard procedure for testing the flow rate of thermoplastics using an extrusionplastometer is described in the ASTM D1238 test as presented in Table 5.8. During thetest, a sample is heated in the barrel and extruded from a short cylindrical die using a pistonactuated by a weight. The weight of the polymer in grams extruded during the 10-minutetest is the melt flow index (MFI) of the polymer.

148 5 Melt Rheology

Table 5.8: Standardmethods ofmeasuringmelt flow index (MFI):melt flow rate (MFR),melt volume rate (MVR), and flow rate ratio (FRR)(after Shastri)

Standard ISO 1133 ASTM D1238 - 98

Specimen Powder, pellets, granules, orstrips of films

Powder, pellets, granules,strips of films, or molded slugs

Conditioning In accordance with the mate-rial standard, if necessary

Check the applicable materialspecification for any condition-ing requirements before usingthis test. See practice D618 forappropriate conditioning prac-tices.

Apparatus Extrusion plastometer with asteel cylinder (115 – 180) mm(L) x 9.55 ±0.025 mm (D),and a die with an orifice of8.000 ±0.025 mm (L) x 2.095±0.005 mm (D)

Extrusion plastometer with asteel cylinder 162 mm (L)x 9.55 ±0. 008 mm (D),and a die with an orifice of8.000 ±0.025 mm (L) x 2.0955±0.0051 mm (D)

Test procedures Test temperature and test loadas specified in Part 2 ofthe material designation stan-dards, or as listed in ISO1133. Some examples are:PC (300 ◦C /1.2 kg)ABS (220 ◦C /10 kg)PS (200 ◦C /5 kg)PS-HI (200 ◦C /5 kg)SAN (220 ◦C /10 kg)PP (230 ◦C /2.16 kg)PE (190 ◦C / 2.16 kg)POM (190 ◦C /2.16 kg)PMMA (230 ◦C /3.8 kg)Charge⇒ within 1 minPreheat⇒ 4 minTest time ⇒ last measure-ment not to exceed 25 minfrom charging.Procedure A – manual oper-ation using the mass and cut-time intervals shown in thefollowing:

Test temperature and test loadas specified in the applicablematerial specification, or aslisted in D1238. Some exam-ples are:PC (300 ◦C /1.2 kg)ABS (230 ◦C /10 kg)PS (200 ◦C /5 kg)PS-HI (200 ◦C /5 kg)SAN (220 ◦C /10 kg)PP (230 ◦C /2.16 kg)PE (190 ◦C / 2.16 kg)POM (190 ◦C /2.16 kg)Acrylics (230 ◦C /3.8 kg)Charge⇒ within 1 minPreheat⇒ 6.5 minTest time⇒ 7.0 ±0.5 min frominitial charging.Procedure A – manual oper-ation using the mass and cut-time intervals shown in the fol-lowing:


5.3 Rheometry 149

Standard ISO 1133 ASTM D1238 - 98

MFR; Mass; Time0.1 to 0.5g/10min; 3–5g ;4min >0.5 to 1g/10min; 4–5g;2min >1 to 3.5g/10min; 4–5g;1min >3.5 to 10 g/10 min 6–8g; 30s > 10g/10min; 6–8g;5-15sProcedure B – automatedtime or travel indicator is usedto calculate the MFR (MVR)using the mass as specifiedabove in Procedure A for thepredicted MFR

MFR; Mass; Time0.15 to 1g/10min; 2.5–3g; 6min >1 to 3.5g/10min; 3–5g; 3min >3.5 to 10g/10min; 4–8g;1 min >10 to 25g/10min; 4–8g;30s > 25g/10min; 4–8g; 15sProcedure B – MFR (MVR)is calculated from automatedtime measurement based onspecified travel distances,< 10 MFR⇒ 6.35 ±0.25 mm.> 10 MFR⇒ 25.4 ±0.25 mm.and using the mass as specifiedabove for the predicted MFR

Values and units MFR⇒g/10minMVR⇒cm3/10min

MFR⇒ g/10minMVR⇒ cm3/10minFRR ⇒ Ratio of the MFR(190/10) by MFR (190/2.16)(used specifically for PE)


Industrial Application of Weathering of an Exterior Polyethylene Application

A failed polyethylene component exposed to the elements was analyzed to determinethe cause of failure (Figure 5.23). Most likely, the cause of failure was degradationdue to UV radiation. UV rays can lead to molecular chain sission, often leading to asignificant reduction in molecular weight.

Figure 5.23: Failed polyethylene part

150 5 Melt Rheology

Polyethylene

Part core

Part surface

5001000200030004000

Abs

Abs

Abs

0.2

0.4

0.6

Wavelength (cm )-1

Figure 5.24: FTIR Spectrums of the surface of the failed part (top), inner core (center) and referencepolyethylene (bottom)

A common test performed to detect a loss in molecularweight is measuring changesin melt flow index. For the failed parts the melt flow index was measured to beabove 150 g/10 minutes. The material specified for this application was an HDPEwith a melt flow index of 15 g/10 minutes. This large difference between specifiedand tested MFI is due to a significant loss in molecular weight as a result of UVdegradation. Another analytical test that can be performed to detect UV degradation isa Fourier Transform Infrared Spectroscopy (FTIR). FTIR spectroscopywas performedat the surface and core of the HDPE sample, and is shown in Fig. 5.24. The FTIRshows the typical spectral results expected for polyethylene. However, the spectrumshows two additional absorption bands (one between 1750 cm -1 and 1700 cm-1, andanother between 1300 cm-1 and 1100 cm-1) that indicate the formation of carbonylsand byproducts associated with oxidation, a result of UV degradation. The FTIRperformed at the surface of the part shows stronger absorption bands compared to theFTIR at the core. Therefore, as expected, the level of oxidation at the surface is muchhigher than the oxidation at the core of the part. If the reduction in properties hadbeen caused by oxidation during processing the part would have exhibited uniformdegradation throughout the thickness of the part.

5.3.2 Capillary Viscometer

The most common and simplest device for measuring viscosity is the capillary viscometer.Its main component is a straight tube or capillary, and it was first used to measure theviscosity of water by Hagen and Poiseuille. A capillary viscometer has a pressure drivenflow for which the velocity gradient or strain rate and also the shear rate will be maximumat the wall and zero at the center of the flow, making it a non-homogeneous flow. Since

5.3 Rheometry 151

pressure driven viscometers employ non-homogeneous flows, they can only measure steadyshear functions such as viscosity, η(γ). However, they are widely used because they arerelatively inexpensive to build and simple to operate. Despite their simplicity, long capillaryviscometers provide the most accurate viscosity data available. Another major advantageis that the capillary viscometer has no free surfaces in the test region, unlike other typesof rheometers, such as the cone and plate rheometers, which we will discuss in the nextsection. When the strain rate dependent viscosity of polymer melts is measured, capillaryviscometers may provide the only satisfactory method of obtaining such data at shear rates>10 s-1. This is important for processes with higher rates of deformation such as mixing,extrusion, and injection molding. Other advantages of the capillary viscometer include.

• Capillary flows and geometries are very similar to those encountered in real processingequipment.

• A capillary viscometer can be adapted to on-line measurement.• The system allows the study of flow anomalies such as extrudate swell, melt fracture,or stick-slip conditions.

• A capillary viscometer can be used to study the pressure dependence of viscosity

Pressuretransducer

L

R

Polymersample

InsulationHeater

Extrudate

Figure 5.25: Schematic diagram of a capillary viscometer

As shown in Fig. 5.25, in a capillary viscometer the material is fed into a cylinder wherethe temperature is maintained within a very narrow range (about T ±0.5 ◦C). Once the mate-rial is molten, the piston traveling at a well controlled speed pushes the material through thecapillary. The pressure is measured at the inlet of the circular capillary, and for rectangularcapillaries the pressure can be measured inside of the capillary. Using the piston speed,the dimensions of the piston, and the capillary, the apparent shear rate can be calculated;and using the pressure and the dimensions of the capillary, the apparent shear stress canbe computed. With the apparent shear rate and shear stress, the apparent viscosity can becomputed. Tests at different piston speeds and temperatures can be carried out to obtain anapparent viscosity curve. Subsequent corrections on shear rate and shear stress allow theprediction of the actual viscosity curve. The capillary extrudate can be collected to observethe range of flow anomalies when they occur.

152 5 Melt Rheology

The capillary viscometer includes the following instrumentation:

• A piston and its speed control• A cylinder with temperature control• An auxiliary extruder and purge valve (optional)• A capillary set

There are three types of capillaries in use today:

• Circular capillary – This capillary works best for higher shear rates, so it is usefulto define the pseudoplastic behavior of polymer melts. The geometrical parametersrequired to obtain the viscosity data are the inside diameter D (or radius R) and thelength L.

• Rectangular capillary – This capillary is used for lower shear rates, so it is useful tomeasure the Newtonian plateau of a polymer melt. This capillary has the advantagethat the pressure can bemeasured directly inside the capillary. Therefore, inlet pressurecorrection, such as Bagley corrections, are not required. This type of capillary is easierto clean up. The required geometrical parameters to obtain the viscosity data are theinternal heighth, thewidth b, and the lengthL. Tominimize the entrance effects, a b/hratio of 15:1 is normally used. To obtain a complete viscosity curve, measurementswith circular and rectangular capillaries are usually done.

• Annular capillary – This capillary allows the alteration of the length and the radius bychangingonly the core and does not have entrance effects. Themain disadvantages arethat it is difficult to control the temperature of the core and that a considerably higheramount of polymer melt is required. The required geometrical parameters to obtainthe viscosity data are the inside diameterDi (or inside radiusRi), the outside diameterDo (or outside radiusRo), and the length L. Annular capillaries are fabricated with adiameter of 20 mm and ratioDi/(Do − Di) higher than 20.

For accurate measurements a piston displacement control is needed. Three possible pistondisplacement controls exist. These are:

• Constant speed control – This control provides a constant piston speed, if the sealbetween piston and cylinder is adequate. In this alternative the displacement of thepiston is controlled while the pressure is registered. Two possible constant speedcontrollers can be used:

– Mechanical – This controller uses a screw that moves axially at a constant linearspeed

– Hydraulic – This controller uses a very precise hydraulic system to push thepiston at a carefully controlled speed

• Constant pressure control – Here, pressurized gas pushes the piston. With the help ofa pressure sensor located at the inlet (or inside) of the capillary, a constant pressurecan be obtained and the volumetric flow can be measured.

• Constant volume control – this technology uses a gear pump or an extruder to controlthe flow of melt while the pressure is measured. Although this alternative nears actualprocessing conditions, controlling a constant flow is difficult to attain.

5.3 Rheometry 153

The extruder is often a desirable and recommendedcomponent of the capillary viscometerto avoid air entrapment and to obtain thermal homogeneity in the melt. A manual load ofthe cylinder can be done. The extruder delivers the molten polymer to be fed to the cylinderby means of a three-way valve.

Corrections: Because of geometrical constraints, the pressure sensor cannot be placedinside the circular capillary. The deformation at the inlet of the capillary leads to pressurelosses that require a correction of the shear stress. The correction of the inlet pressure lossis normally called the Ryder-Bagley correction. In the calculation of the shear rate, New-tonian equations are used, so it is necessary to correct for the non-Newtonian behavior ofpolymer melts. The correction of the non-Newtonian behavior is called the Weissenberg-Rabinowitsch correction.

Ryder-Bagley Correction: For the Ryder-Bagley correction, measurements of pressure forseveral capillary lengths must be done. At least three capillary lengths are normally used.When the sensor pressures plotted as a function of the capillary lengths at each shear rate,straight lines (or parabolic lines for higher shear rates) are obtained (see Fig. 5.26). Theintercept with the y-axis is the Ryder-Bagley correction and has to be deducted from themeasured pressure to obtain the real shear stress. The corrected shear stress for a circularcapillary can be calculated using

τ =(ΔP − ΔPBagley) · R

2 · L , (5.36)

where τ is the corrected shear stress (Pa),ΔP is the measured pressure (Pa),ΔPBagley is theRyder-Bagley correction (Pa),R is the capillary internal radius (mm), and L is the capillarylength (mm).

Figure 5.26: Ryder-Bagley correction for polypropylene at different shear rates

154 5 Melt Rheology

Table 5.9: Coefficient of pressure for some particular polymers

Circular capillary Rectangular capillary

Shear rate for a Newtonian fluid Shear rate for a Newtonian fluidγap = 4·V

π·R3 γap = 6·Vb·h2

Weissenberg-Rabinowitsch correction Weissenber-Rabinowitsch correction

First point (i = 1) First point (i = 1)

γw1 = 34γwap1+

14τwap1

γwap2τwap2

γw1 = 23γwap1+

13τwap1

γwap2τw2

Intermediate point Intermediate point

γw1 = 34γwapi+

14τw1

γwapi+1−γwapi-1τwi+1−τwi-1

γw1 = 23γwapi+

13τw1

γwapi+1−γwapi-1τwi+1 -τwi-1

Last point (i = n) Last point (i = n)

γwn = γwnVn

Vn-1γwn = γwn

Vn

Vn-1

Weissenberg-RabinowitschCorrection: Asmentioned earlier, Newtonian equations are usedin the calculation of the shear rate. Because polymer melts are non-Newtonian, a correctionmust be done that takes into account the shear thinning behavior. This correction is the so-called Weissenberg-Rabinowitsch correction. Table 5.9 presents the equations to calculatethe shear rate for Newtonian fluids and theWeissenberg-Rabinowitsch correction for circularand rectangular capillaries.The standardized techniques used to measure rheological properties of polymeric materi-

als by means of a capillary viscometer are the ISO 11443 and the ASTM D3835 tests. Bothtests are presented in Table 5.10. TheASTMD5099 test is used tomeasure rheological prop-erties of rubber materials using capillary viscometry. The ASTM D5099 test is presented inTable 5.11.

Table 5.10: Standard test method for determination of properties of polymeric materialsby means of a capillary viscometer

Standard ISO 11443:1995 ASTM D3835-02

Abstract ISO 11443:2005 specifiesmethods for determining thefluidity of polymer melts sub-jected to shear stresses atrates and temperatures ap-proximating to those arisingin plastics processing.

This test method covers mea-surement of the rheologicalproperties of polymeric materi-als at various temperatures andshear rates common to process-ing equipment.


5.3 Rheometry 155

Standard ISO 11443:1995 ASTM D3835-02

Specimen Plastic melt forced through acapillary or slit die of knowndimensions. A small repre-sentative sample is taken fromthe product to be tested.

The test specimen may be inany form that can be introducedinto the bore of the cylindersuch as powder, beads, pellets,strips of film, or molded slugs.In some cases it may be desir-able to preform or pelletize apowder.

Apparatus A heatable barrel, the bore ofwhich is closed at the bottomend by an exchangeable cap-illary or slit die. The test pres-sure shall be exerted on themelt contained in this barrelby a piston, a screw or gaspressure

A capillary viscometer, the bar-rel, the capillary with a smoothstraight bore, and the piston.

Test procedures The polymer is introducedin the barrel preheated andforced through the capillaryat a predetermined piston ve-locity. The pressure observedis registered with a pressuretransducer. The pressure reg-istered and the geometry ofthe capillary is used to calcu-late the shear stress (see equa-tions in Table 5.9).

The polymer is introduced inthe barrel preheated and forcedto the capillary at a predeter-mined piston velocity. Thepressure observed is registeredwith a pressure transducer. Thepressure registered and the ge-ometry of the capillary is usedto calculate the shear stress.

The piston velocity andgeometry of the barrel andcapillary are used to calcu-late shear rate. For circularcapillaries two correctionsare performed, the Ryder-Bagley and the Weissenberg-Rabinowitsch. For rectan-gular capillaries only theWeissenberg-Rabinowitschcorrection is performed.

The piston velocity and geom-etry of the barrel and capillaryare used to calculate the shearrate. For circular capillariestwo correction are performed,the Ryder-Bagley and theWeissenberg-Rabinowitsch.For rectangular capillaries onlythe Weissenberg-Rabinowitschcorrection is performed.

Values and Units Shear stress (Pa), Shear rate(s-1),Viscosity (Pa·s)

Shear stress, (Pa),Shear rate(s-1), Viscosity (Pa·s)

156 5 Melt Rheology

Table 5.11: Standard test methods for rubber-measurement of processing propertiesusing capillary rheometry


Scope This test methods describes how capillary rheometry may be used tomeasure the rheological characteristics of rubber. Two methods arecovered, Method A, which uses a piston type capillary viscometer, andMethod B, which uses a screw extrusion type capillary viscometer. Thetwo methods have important differences, as outlined by the test.The test methods cover the use of a capillary viscometer for the measure-ment of the flow properties of thermoplastic elastomers, unvulcanizedrubber, and rubber compounds. These material properties are related tofactory processing.Since the piston type capillary viscometers impart only a small amountof shearing energy to the sample, these measurements directly relateto the state of the compound at the time of sampling. Piston capillaryviscometer measurements will usually differ from measurements witha screw extrusion type rheometer, which imparts shearing energy justbefore the rheological measurement.The capillary viscometer measurements for plastics are described in testmethod ASTM D3835.

Specimen Massed specimen of raw or compounded unvulcsanized rubber for testmethod A -Piston extrusion capillary viscometer. Raw rubber or unvul-canized elastomeric compound formed into sheets on a two-roll mill fortest method B - Screw extrusion capillary viscometer

Apparatus A piston type capillary viscometer for test method AA screw extrusion capillary viscometer for test method B

Test procedures Test method A - Piston extrusion capillary viscometerUnvulcanized rubber compound is placed in a temperature controlledcylinder fitted at one end with a conical transition section and a standardcapillary die. The sample is driven through the die with the help ofthe piston while measuring or controlling the rate of extrusion and thepressure on the sample at the entrance of the die.Test method B - Screw extrusion capillary viscometerUnvulcanized rubber compound compound is formed into sheets on atwo-roll mill. Strips cut from these sheets are fed to the extruder whosebarrel is equipped with a temperature control. The end of the extruder isequipped with a transition conical section and a capillary die. A pressuretransducer and temperature measuring device are placed in the chamberbefore the die. The rate of extrusion is calculated from the amountof extrudate collected over a timed interval. The rate of extrusion iscontrolled by adjusting the drive speed.


5.3 Rheometry 157


Values and Units Viscosity curve (apparent and corrected) in log-log graphCorrected shear stress at 500 s-1

Corrected shear stress at 1000 s-1

Corrected viscosity at 500 s-1,Corrected viscosity at 1000 s-1

Shear sensitivity, NEntrance effect, E

5.3.3 Rotational Rheometry

A rotational rheometer is a particular type of rheometer in which the shear is produced by adrag flow between a moving part and a fixed one, including the following geometries: plate-plate, cone-plate, and concentric cylinders. The main features of a rotational rheometer arethe following:

• The rotational rheometer canmeasure rheological properties under transient and steadystate conditions.

• It can reach the lowest shear rates of all rheometers. With this equipment it is pos-sible to obtain shear rates typically from 10 -6 to 2.5 · 102 s-1, so it is useful formacromolecular characterization (molecular weight distribution, relaxation spectra,and chain branching).

• It can be used to measure the normal force in a polymer melt.• It offers a high degree of versatility because the following type of tests can be carriedout: dynamic test (oscillation), flow test (rotation), static test, temperature sweep,torque sweep, frequency sweep, and time sweep.

• It is used in conjunction with the capillary viscometer to obtain the complete viscositycurve.

Rotational rheometers are used when more complex properties, such as normal stresses,are sought. There are twomain types of rotational rheometers: the controlled rate rheometer(CRR), in which the strain or the shear strain is imposed and the stress is measured and thecontrolled stress rheometer (CSR), in which the stress is imposed and the strain or the shearrate is measured. Advances in rotational rheometer instrumentation have made it possibleto have systems where both controlled rate and controlled stress can be programmed.Rotational rheometers include a temperature controller (which can be electrical heated

plates, a Peltier system or an environmental test chamber), a test geometry (being the mostcommon – plate-plate, cone-plate and concentric cylinders), a magnetic induction motor(being the most common a drag cup motor), an angular displacement measurement device(being the most typical an optical encoder), an electronic system to measure or control thetorque, a mechanical frame, and a computer-based data acquisition and processing unit [17].

Parallel-plate rheometer: Aparallel plate rheometer, schematicallydepicted inFig. 5.27,is the geometrically simplest rotational rheometer, but mathematically it is more complex toanalyze than its counterpart, the cone-and-plate rheometer.

158 5 Melt Rheology

Force

Torque

Ω

R

θ

h

Figure 5.27: Schematic diagram of a parallel-plate rheometer

The plate-plate rheometer is sometimes the preferred system because of the followingadvantages:

• Easy sample preparation of viscous materials and soft solids.• The shear rate can be easily changed by programming different rotational speeds orby adjusting the gap between plates or by changing the frequency.

• Higher shear rates can be obtained before edge effects appear.• In conjunction with cone-plate geometry, the normal stress can be measured.• This geometry is preferred for viscous melts when small shear rates are required.

The following equations are normally used in the flow mode:

γR = MΩ (5.37)

γR = Mϕ (5.38)

where M is the geometric factor (R/h), h is the gap (mm), R is the external radius of theplate (mm), and ϕ is the deflection angle.

Ω =2π · N

60(5.39)

where Ω is the angular speed (s-1) andN is the rotor speed (rpm).

τ = Md · A · (3 + n

4) (5.40)

where Md is the torque (N· m), A is the geometric factor 2/R3 (m-3), and n is the Powerlaw exponent (Weissenberg correction).

N1-N2 = (2Fn

πR2)(1+

12

dlnFn

dlnγR) (5.41)

whereN1-N2 is the second normal stress difference (Pa), and Fn is the normal force (N).

5.3 Rheometry 159

Cone-plate geometry: The cone-plate rheometer is sometimes the preferred systembecause of the following advantages:

• This rheometer allows the measurement of normal stresses.• Homogeneous strain and simple equations.• Useful for measurement of linear viscoelasticity,G(t, γ).• Normally used for intermediate viscosity ranges. High-viscosity measurements arelimited by the elastic problems in the borders and low-viscosity measurements arelimited by inertial effects and sample loss in the borders.

Torque

Force

φ θ

Ω

θo

Fixed platePressure transducers

R

Figure 5.28: Schematic diagram of a cone-plate rheometer

The following equations are used in the flow mode:

γR =Ωβ

(5.42)

γR =ϕ

β(5.43)

where Ω is the angular speed (s-1), β is the cone angle, and ϕ the deflection angle.

τ =3Md

2πR3(5.44)

where τ is the shear stress (τΦΘ component) (Pa), andMd is the torque (N· m).

τ = Md · A · (3 + n

4) (5.45)

where Md is the torque (N· m), A is the geometric factor 2/R3, (m-3), and n is the Powerlaw exponent (Weissenberg correction).

N1 = (2Fn

πR2) (5.46)

whereN1-N2 is the second normal stress difference (τΦΦ-τΘΘ component), (Pa), and Fn isthe normal force (N).

160 5 Melt Rheology

Concentric cylinders geometry The concentric cylinders rheometer (also called theCouette rheometer) has the following characteristics:

• Better for low-viscosity samples (under 100 (Pa·s))• Useful in high shear rates• Gravity settling of a suspension has less effect than in a cone and plate rheometer• Normal stress is difficult to measure

Polymer

Ω, T

RoRi

L

Figure 5.29: Schematic diagram of a Couette rheometer.

The following equations are used in the flow mode:

γ = ϕΘ(Ro+Ri)2(Ro − Ri)

(5.47)

γ(Ri) =2Ω

(1 − ( Ri

Ro)2)

forRi

Ro> 0.99 (5.48)

γ(Ri) =2Ω

n(1 − ( Ri

Ro)

2n )

for 0.50 <Ri

Ro< 0.99 (5.49)

n =dlnMd

d(lnΩ)(5.50)

where Ω is the angular speed (s-1), Ro is the outside radius (mm), Ri is the internal radius(mm), ϕ is the deflection angle, n is the Power law index (Weissenberg correction), andM d

is the torque (N·m).

τ =Md

2πR2i L

(5.51)

5.3 Rheometry 161

where τ is the shear stress (τΦΘ component) (Pa),Md is the torque (N·m),Ri is the internalradius (mm), and L is the length of inside cylinder (mm).

Temperature controllers: Because all rheological properties depend on temperature,the success of a rheologicalmeasurement startswith a very precise control of the temperature.Modern rheometers include the following types of temperature controls:

• Fluid circulators – Fluid circulators use a thermostatic bath that precisely controlsthe temperature and circulates the fluid in the plates of the rheometer. Typically thiscontrol has a temperature range between -40 ◦C and 250 ◦C.

• Peltier plate – This is the most common temperature control in rheometers and ituses the thermo-electric phenomenon called Peltier effect. The main limitation for apolymer analysis is the temperature range of -20 ◦C to 200 ◦C. The Peltier plate is avery accurate control, with a tolerance of about±0.1 ◦C, and has typical heating ratesup to 20 ◦C/min.

• Electrical heated plates – In this temperature control, one plate is electrically heated.Typically, this control has a temperature range of -130 ◦C up to 400 ◦C. The lowtemperatures could be obtained with a special cooling device.

• Thermal chamber – This is an oven that operates by convection and radiation. Themain advantage of this system is the possibility of higher temperatures (typically fromroom temperature up to 1000 ◦C, with the possibility of starting from -160 ◦C usinga special liquid (nitrogen) cooling device). Typical heating rates are up to 60 ◦C/min.

0.5

-0.5

Figure 5.30: Description of the dynamic test in a rotational rheometer

Operation modes: One of the advantages of the rotational rheometer is the versatilitythat allows different operation modes and tests. Rotational rheometry operation modes arepresented in the following.

Dynamic Test: These tests are done while subjecting one of the plates to oscillatory motionand by varying the frequency and the amplitude of the oscillation at isothermal conditions(see Fig. 5.30). This operation test can be used to obtain the complex viscosity curve, and itscomponents, as a function of frequency. According to the Cox-Merz rule, in order to have a

162 5 Melt Rheology

complete viscosity curve, the complex viscosity curve can be superimposed with the viscos-ity curve obtained from a flow test and a capillary viscometer. This operation test obtainsimportant viscoelastic functions, such as dynamic storage modulusG ′(ω) and dynamic lossmodulusG′′(ω).

Flow Test: In this test, one of the plates is subjected to a continuous rotational motion,enabling viscosity measurements as a function of the shear rate under realistic continuousflow. The main limitations are the centrifugal forces and border effects.

Creep Test: The creep test, also called retardation, is a special test where thefluid is subjectedto a stress step (stress controlled mode), and the strain variation during a period of time isregistered. Eventually, the stress is released again and the strain recovery is registered. Thisexperiment reflects viscoelastic behavior and the macromolecular characteristics of polymermelt, such as relaxation times.

Relaxation Test: In the relaxation test, the fluid is subjected to a strain step (strain-controlledmode), and after some period of time the stress variation as a function of time, is registered.The relaxation test provides important information about the viscoelastic behavior and themacromolecular characteristics of polymer melts, such as stress overshoot.

Torque Sweep: This test is useful in identifying the linear viscoelasticity region, whichis the region where the compliance curves at different stresses can be super-imposed in amaster curve independent of the applied stress. As a rule, the majority of rheological char-acterizations of a polymeric fluid are done in the linear viscoelastic region, so it is firstrecommended to determine the stress that limits this region.

Frequency Sweep: This is a special dynamic test used to obtain the viscosity curve andimportant information about the viscoelastic behavior of a polymer melt. A sweep of fre-quency is normally done from very low to higher possible values without any border effectand under isothermal conditions.

Temperature Sweep: In this test, the polymer sample is evaluated at a certain fixed frequencyunder a temperature program. The temperature sweep is particularly useful to determinesome transition temperatures, such as glass transition and curing rate of thermosets and rub-bers. The temperature sweep is also used to study curing of thermosets and degradation ofpolymers.

Time Sweep: In this test, the polymer sample is evaluated at a given frequency during aperiod of time, and the change in the viscosity as a function of time is recorded. This par-ticular test is useful in characterizing the thixotropic and rheopexic fluids. The thixotropicmaterials are fluids where the viscosity decreases with the time at a fixed shear rate, whilerheopexic materials are fluids where the viscosity increases with time at a fixed shear rate.The standardized test to measure complex properties using parallel plate as well as cone-and-plate rheometers are the ISO 6721 and ASTM D4440 tests presented in Table 5.12.

5.3 Rheometry 163

Table 5.12: Dynamic mechanical properties - complex shear viscosity using a parallel-plate oscillatory rheometer

Standard ISO 6721-10:1999 ASTM D4440-01

Abstract/Scope Determination of dynamicmechanical properties, suchas complex shear viscosity asa function of frequency, strainamplitude, temperature, andtime, using a parallel-plateoscillatory rheometer. Thispart specifies the general prin-ciples of a method for de-termining the dynamic rheo-logical properties of polymermelts at angular frequenciestypically in the range 0.01 -10 Hz by means of an oscilla-tory rheometer with a parallelplate test geometry. Frequen-cies outside this range can beused if edge distortions andanomalies are not observed.

Dynamic mechanical test tomeasure rheological propertiesof thermoplastic resins, such ascomplex viscosity, tan δ andsignificant viscoelastic charac-teristics as a function of fre-quency, strain amplitude, tem-perature, and time. This testmethod is valid for awide rangeof frequencies, typically from0.01 to 100 Hz.

The method is used to de-termine values of the dy-namic rheological properties:complex shear viscosity h∗,dynamic shear viscosity h’,the out-of-phase componentof the complex shear viscos-ity h", complex shear mod-ulus G∗, shear loss modulusG" and shear storage modu-lus G".

This test method is intendedfor homogenous and heteroge-neous molten polymeric sys-tems and composite formula-tions containing chemical ad-ditives, including fillers, rein-forcements, stabilizers, plasti-cizers, flame retardants, impactmodifiers, processing aids, andother important chemical ad-ditives often incorporated intoa polymeric system for spe-cific functional properties, andwhich could affect the process-ability and functional perfor-mance. Apparent discrepan-cies may arise in results ob-tained under differing experi-mental conditions.


164 5 Melt Rheology


It is suitable for measuringcomplex shear viscosity val-ues typically up to approxi-mately10MPa.s.Test dataob-tained by this test method arerelevant and appropriate foruse in engineering design.

Without changing the observeddata, reporting in full (as de-scribed in this test method)the conditions under which thedata were obtained will enableapparent differences observedin another study to be recon-ciled. Test data obtained by thistestmethod are relevant and ap-propriate for use in engineeringdesign.

Specimen In the form of a disc whenproduced by injection or com-pression molding or by cut-ting from sheet. Also, pelletsor molten polymer.

A known amount of thermo-plastic resin (molten powder orpellet, or solid preform disk)Molten polymer should be bothhomogeneous and representa-tive.

Apparatus Two concentric, rigid, cir-cular parallel plates betweenwhich the specimen is placed.One of these plates oscil-lates at a constant angular fre-quency while the other re-mains at rest. An angular dis-placement and a torque mea-suring device record the strainand the stress during the test.

An apparatus to hold a moltenpolymer of known volume anddimensions so that the mate-rial acts as the elastic and dis-sipative element in a mechani-cally driven oscillatory system.The apparatus consists of thetest fixtures (polished cone andplate, or parallel plates havingeither smooth, polished, or ser-rated surface), oscillatory de-formation device, detectors (todetermine stress, strain, fre-quency, and temperature), tem-perature controller and oven,Nitrogen, or other gas supplyfor purging purposes.

Test procedures The specimen is held betweenthe parallel plates and sub-jected to either a sinusoidaltorque (controlled-stressmode) or sinusoidal angulardisplacement (controlled-strain mode).

Specimen is held between par-allel plates or cone and plateand subjected to either a sinu-soidal torque (controlled-stressmode) or sinusoidal angu-lar displacement (controlled-strain mode).


5.3 Rheometry 165


In the controlled-stress modethe resultant displacementand the phase shift betweentorque and displacement areregistered. In the controlled-strain mode the resultanttorque and the phase shift be-tween torque and displace-ment are registered. Theequipment is able to measureimportant viscoelastic func-tions of the polymer melts.

In the controlled-stress modethe resultant displacement andthe phase shift between torqueand displacement are regis-tered. In the controlled-strainmode the resultant torque andthe phase shift between torqueand displacement are regis-tered. The equipment is able tomeasure important viscoelasticfunctions for the polymer meltunder consideration.

Values and Units Torque, angular displace-ment, angular frequency,shear stress, shear strain,shear storage modulus, shearloss modulus, complex shearmodulus, dynamic shearviscosity, out-of-phase com-ponent of the complex shearviscosity, complex shearviscosity, and phase shift orloss angle all in SI units.

Dynamic moduli, complex vis-cosity, and tan δ as a functionof the dynamic oscillation (fre-quency), percent strain, tem-perature, or time, all given inthe standard SI units.

5.3.4 Extensional or Elongational Rheometry

It should be emphasized that the shear behavior of polymers measured with the equipmentdescribed in the previous sections cannot be used to deduce the extensional behavior ofpolymermelts. Extensional rheometry is the least understoodfield of rheology. Elongationalor extensional properties are important when analyzing and understanding fiber spinning,thermoforming,filmblowing, film casting, blowmolding, and foaming. Several elongationalrheometers have been designed to measure the elongational viscosity (or elongational stress)as a function of the elongational rate of deformation at different temperatures. However,the main challenges are how to obtain higher elongational rates, as well as simplifying themeasurements, and making them reproducible. When measuring extensional viscosities, wecan divide the techniques into direct and indirect methods.

Direct measurement of elongational viscosity The following rheometers and elon-gational techniques, which fall under direct measuring techniques, have been proposed andused in the past [18].

• Extensional methods – These methods are more direct ways to measure the elonga-tional behavior of polymers. Several types of extensional rheometers have been used,the following being the most common:

166 5 Melt Rheology

– Uniaxial extension– In this particular technique, thepolymeric sample is stretchedin one direction, and the elongational stress is measured under a defined elonga-tion rate. Some examples of this type of rheometer are the Meissner rheometer[18], the vertical buoyancy bath [18], and the Sentmanat extensional rheometer(SER) [19, 20]. A schematic of Meissner’s extensional rheometer incorporatingrotary clamps is shown in Fig. 5.31.

Lo

Drive motor

Spring

Displacementsensor

Sample

LR

LA

εr = ln LA/LR

Figure 5.31: Schematic diagram of an extensional rheometer

– Lubricated compression – Another setup that can be used to measure extensionalproperties without clamping problems andwithout generating orientation duringthe measurement is the lubricating squeezing flow, which generates an equibi-axial deformation. To lubricate the material, the plates are usually coated withpolydimethylsiloxane (silicone oil). A schematic of this apparatus is shown inFig. 5.32.

Figure 5.32: Schematic diagram of squeezing flow

– Biaxial and multiaxial extension – For high-viscosity polymers and rubber, itis possible to use a special rheometer with translating clamps that move in theorthogonal axis [18]. Rheometers have been built in the past that are able tomovethe sample in all directions, generating an equibiaxial extension of the sample.

5.3 Rheometry 167

– Bubble blowing – With this system, a sheet is clamped between two plates withcircular holes and a pressure differential is introduced to deform it and blowthe bubble into a test fluid. The pressure applied and deformation of the sheetare monitored over time and related to extensional properties of the material.The radius of the bubble allows the measurement of the extensional rate and theextensional strain, and the pressure difference and the interfacial tension allowone to determine the elongational stress [18]. The bubble blowing system isschematically depicted in Fig. 5.33. This test has been successfully used tomeasure extensional properties of polymer membranes for blow molding andthermoforming applications.

Rα

h

Figure 5.33: Schematic diagram of sheet inflation

– Fiber spinning – This method is particularly useful for low-viscosity samples,where the polymer is continuously extruded and stretched by a rotating wheel.The diameter of the fiber as a function of the axial distance can be measuredphotographically and the forcemeasuredby thewheelwith a loadcell [18, 23, 24].

Figure 5.34: Schematic diagram of a Rheotens extensional rheometer

168 5 Melt Rheology

– Rheotens – This technique was developed by the company Gottfert and consistsof a tandem pulley system in which the melt that comes out from the circularcapillary is pulled off between two sets of counter-rotating pulleys. A Rheotensrheometer is schematically depicted in Fig. 5.34. One of the pulleys is used tomeasure the torque [21]. The elongation viscosity as a function of the elonga-tional rate can be determinedwith the help of software developed byWagner andcoworkers at the IKT, University of Stuttgart, Germany [22].

Indirect measurement of elongational viscosity Indirect methods for measuringelongational viscosity have been reported in the literature. The most popular method usesthe pressure drop in sudden flow contraction and the stagnation flow.

• Flow stagnation – This technique uses the principle that steady extensional deforma-tions can be created by impinging two liquid streams, such as depicted in Fig. 5.35[18]. Although with stagnation flows it is only possible to measure steady extensionalviscosity, there is great interest in this technique because high elongational rates andlow-viscosity samples can be studied.

Stagnant region

Figure 5.35: Schematic diagram of an impinging flow

• Entrance flows – This method is based on the pressure losses in sudden flow contrac-tions and can be considered as a special case of a flow stagnation technique. The mostcommon methods are the following:

– Cogswell’s method – According to the theory developed by Cogswell, the elon-gational viscosity is obtained from the pressure drop in a sudden flow contrac-tion, such as a capillary with an inlet angle of 90◦, as schematically depicted inFig. 5.36 [18, 23, 24, 25]. According to Cogswell, the elongational rate and theelongational viscosity can be estimated by using the following equations:

5.3 Rheometry 169

Recirculation or vortex zone

Pressure transducer

Entrance pressure drop

Figure 5.36: Schematic diagram of the Cogswell method

ε =4ηγ2

ap

3(n + 1)ΔPe(5.52)

ηe =9(n + 1)2

32η

(ΔPe

γap

)(5.53)

γap =4Q

πR3(5.54)

where ε is the elongational rate, ηe is the elongational viscosity, η is the viscosity,γap is the power law index,ΔPe is the pressure drop at capillary inlet (obtainedfrom Bagley correction extrapolation at L/D = 0) , and n is the apparent shearrate

– Binding’s method – This method is based in the theory developed by Cogswell,but it is a more accurate method since Binding does not neglect theWeissenberg-Rabinowitsch correction. However, this leads to more complex calculations[26, 27]. To model the shear viscosity, and the elongational viscosity Bindingarbitrarily assumes a Power law model.

– Semihyperbolically converging die – In this technique, schematically depictedin Fig. 5.37, the polymer flows through a cylindrical, converging die whosesemihyperbolic shape leads to a shear-free flow within the die, assuming wallslip conditions. From the analysis of the relevant flow equations in the die, theuse of a numerical method (typically the finite element method (FEM)) and theuse of a constitutive equation, the elongational viscosity can be measured [28].

170 5 Melt Rheology

Figure 5.37: Schematic diagram of a semihyperbolically converging extensional rheometer


Molecular Weight Distribution Comparison Using Rheometry Characterization

Here, wewill performan analysis ofmolecularweight distributions of three differentpolypropylenes using storage modulus,G ′, and loss modulus,G′′, measurements as afunction of the frequency. These measurements are presented in Table 5.13.

Table 5.13: Dynamic modulus for three different polypropylenes

PP - A PP - B PP - CFrequency G′ G" Frequency G′ G" Frequency G′ G’"(rad/s) (Pa) (Pa) (rad/s) (Pa) (Pa) (rad/s) (Pa) (Pa)

0.1000 585 1340 0.0300 585 1340 0.0300 1170 2680

0.2150 1190 2130 0.0646 1190 2130 0.0646 2380 4250

0.4640 2200 3330 0.1390 2200 3330 0.1390 4410 6650

1 3900 5010 0.3000 3900 5010 0.3000 7790 10000

2.1500 6480 7340 0.6460 6480 7340 0.6460 13000 14700

4.6400 10200 10300 1.3900 10200 10300 1.3900 20500 20500

10 15600 14200 3 15600 14200 3 31100 28400

21.5000 23000 19400 6.4600 23000 19400 6.4600 45900 38700

46.4000 32900 25900 13.9000 32900 25900 13.9000 65700 51700100 45000 33700 30 45000 33700 30 90100 67300

5.3 Rheometry 171

Using the crossover5 of storagemodulusG′ and lossmodulusG′′, themolecularweightdistribution (MWD) of the different polypropylenes was compared.Figure 5.38 illustrates the relation between the crossover of G ′ and G′′ and the

molecular weight distribution. As shown in the figure, as the molecular weight in-creases, the crossovermodulus,Gc, shifts to a lower frequency; and asMWD narrows,the crossover modulus shifts to a higher value.

Figure 5.38: Correlation between the molecular weight distribution and the crossover modulus

Figure 5.39 presents plots of the dynamic modulus presented in Table 5.13. Thecrossovermodulus allows the comparisonof themolecularweight distribution (MWD)of the three polypropylenes.

Figure 5.39: Comparison of the crossover modulus for the three different polypropylenes

Conclusions: When comparing the crossovermodulus for the three polypropylenes,the following conclusions could be obtained:

5The crossover point is where G′/G" = 1.

172 5 Melt Rheology

– The molecular weight for the three polypropylenes isMWC > MWB > MWA,because the order of the crossover on the frequency axis was G cA > GcB > GcC .– Themolecularweight distribution of polypropyleneC was narrower than polypropy-lenes A and B, because the order of the crossover on the modulus axis was G cC >GcA = GcB .– Because polypropylene C exhibited the higher molecular weight and the narrowerMWD, it will more easily result in flow instabilities and can exhibit higher elasticeffects in the molten state.– The shear viscosity curve can also be used to interpret molecular weight distribu-tions. The smaller Newtonian plateau and the more gradual pseudoplastic decrease ofviscosity exhibited by a polymer reflect a wider molecular weight distribution. Thehigher zero viscosity (the viscosity value in the Newtonian plateau) exhibited by thepolymer reflects a higher average molecular weight of the polymer melt. To illustratethe correlation, Fig. 5.40 compares the viscosity curves for two different polymers atthe same temperature. When looking at the figure, one can deduce that polymer Bhas the wider MWD because of its narrow Newtonian plateau and its more gradualpseudoplastic decrease of viscosity.

Figure 5.40: Correlation between MWD and the viscosity curves for two polypropylene melts atthe same temperature


Flow Instabilities Study in a Thermoplastic Polymer

In this case study, a mass flow of 70 kg/h of polypropylene was extruded througha rectangular die of 50 cm width, 10 cm length and 0.2 cm height, at 220 ◦C. Theparticular PP to be extruded had the following rheological information based on aBird-Carreau-Yasuda model: A = 4254 (Pa· s), B = 0.22 (s) , C = 0.63 , Tref = 243(◦C) , and U = 46015 (J/mol). The density of polypropylene at 220 ◦C is 0.75 g/cm3.The estimated pressure drop and the prediction of flow instabilities at the exit of thedie were required under the specified conditions.

5.3 Rheometry 173

The volumetric flow was calculated as follows

V =m

ρ=

70 · kg · h · 1000 · g · cm3

h · 3600 · s · kg · 0.75 · g = 25.93cm3

s. (5.55)

The shear rate for a non-Newtonian polymer was calculated with the followingapproximated equation:

γ =6 · V

W · h2=

0.772 · 6 · 25.93 · cm3

s · 50 · cm · 0.22 · cm2= 60.04 · s-1. (5.56)

The shear viscosity can be calculated using

aT = exp

(U

R(1T

− 1Tref

))

= exp

(46015 · J ·mol · Kmol · 8.3141 · J (

1(220+273.15)K

− 1(243+273.15)K

))

= 1.65

(5.57)

η =A · aT

(1+B · aT γ)c=

4254Pa · s · 1.65(1+0.22 · s · 1.65 · 64.04

s )0.63= 979 · Pa · s. (5.58)

The pressure drop can be estimated using

ΔP =12 · V · η · L

W · h3=

12 · 25.93 · cm3 · 979 · Pa · s · 10 · cms · 50 · cm · (0.2)3 · cm3

= 7614111 · Pa (5.59)

ΔP =7614111 · Pa · bar

105Pa= 76.14 · bar. (5.60)

The shear stress can now be computed using

τ = η · γ = 979 · Pa · s60.04s

· MPa106 · Pa = 0.06 ·MPa. (5.61)

Conclusions: An estimated pressure drop of 76.14 bar was predicted for the par-ticular die and the given extrusion conditions. Because the calculated shear stress wasbelow the critical shear stress for flow instabilities of polypropylene (0.13 MPa, seeTable 5.1), flow instabilities were not predicted under the conditions stated in this case.


Modeling the Shear Viscosity Curves of a Polypropylene

Here, a Bird-Carreau-Yasuda model was used to fit the data for a polypropylenepolymer melt.

174 5 Melt Rheology

Table 5.14: Capillary rheometry data for a polypropylene

Temperature, (◦C) 200 210 220shear rate, (s-1) Viscosity, (Pa· s) Viscosity,(Pa· s) Viscosity, (Pa· s)

10 591 501 429

20 575 490 420

50 532 458 396

70 508 440 382

100 475 415 363

200 395 351 313

500 270 248 227

700 227 210 194

1000 185 172 161

2000 120 113 106

5000 64 61 58

7000 50 48 46

10000 39 37 35

The curve was obtained using a capillary viscometer, and the data was correctedaccording to the Ryder-Bagley and Weissenberg-Rabinowitsch correction. The dataare presented in Table 5.14.

– The parameters of the Bird-Carreau-Yasuda model were obtained by fitting theexperimental viscosity values and the calculated viscosities. Since polypropyleneis a semicrystalline polymer, the best model to correlate the temperature dependenceof viscosity is the Arrhenius model

aT = exp

(U

R(1T

− 1Tref

))

(5.62)

η =A · aT

(1+B · aT γ)c(5.63)

– The values of A, B, and C were obtained by minimization of the error betweenexperimental data and the calculated data for the different shear rates and temperatures,according to the following error metrics

Error =M∑i=1

(ηcalc − ηexptal) (5.64)

–Whenfitting the parameters of theBird-Carreau-Yasudamodelwith the experimentaldata, a non-linear optimizationwas doneusinga commercial equation solving software.

5.3 Rheometry 175

Because of the non-linearity of the model, the initial guess values were very importantfor the convergence of the optimization. It was necessary to impose some limits to theA, B, and C values, as follows:

• A is greater than zero

• B is greater than zero

• C is within the range of 0 to 1 (typically between 0.3 and 0.7)

It was also important to limit the activation energy,U , to be greater than zero.

Table 5.15 presents the optimized parameters of the Bird-Carreau-Yasuda modelfor the given polypropylene data. Figure 5.41 shows a comparison between the exper-imental data and the model.

Figure 5.41: Experimental data (symbols) and the model prediction (lines) for the viscosity of apolypropylene polymer melt

Table 5.15: Parameters of the Bird-Carreau-Yasuda model for a polypropylene

Parameter Value

A, (Pa · s) 608.758667

B,(s) 0.003946

C 0.744911

U , (J/mol) 32052.3943

Tref , (◦C) 200

Conclusions: The obtained parameters of the Bird-Carreau-Yasuda model repro-duced with good precision the experimental viscosity data for all three temperatures.

176 5 Melt Rheology


Regression Analysis of Rheological Data to Obtain the Phan-Thien and TannerMultimode Model Parameters

The parameters of the Phan-Thien and Tanner multimode model for a particularpolypropylene to be used for fiber spinning applications were obtained by fitting thefollowing rheological data:

– Material – Homopolymer polypropylene with a MFI 16 g/10 m at 230 ◦C/2.16 kg

– Shear viscosity and Cogswell’s elongational viscosity – These data were measuredin a capillary viscometer using a 1 mm circular capillary with 10, 20, 30, and 40 mmlengths.

– Elongational viscosity –Measured at low elongational rates (in the Newtonian range,below 0.1 s-1) and computed using the Trouton viscosity equation. This relationshipstates that the elongational viscosity at very low elongational rates is equal to 3 timesthe shear viscosity.

– Shear viscosity and complex modulus – These data was measured in a rotationalrheometer with a 25 mm diameter plate-plate, 1 mm gap, 1% deformation (in the lin-ear viscoelasticity range), and frequency within the range from 0.005 and 100 rad/s.

The rheological data are presented in Fig. 5.42. The unfilled circles in the figurecorrespond to the shear viscosity obtained by capillary rheometry, and the filled circlescorrespond to the shear viscosity obtained by rotational rheometry and by applyingthe Cox-Merz principle of complex viscosity. The unfilled triangles in the figurecorrespond to loss modulusG′′ obtained by rotational rheometry; the unfilled squarescorrespond to storagemodulusG ′ obtained by rotational rheometry; the unfilled rhom-boids correspond to the elongational viscosity estimated by the Cogswell’s method;and the filled rhomboids correspond to the elongational viscosity estimated with theTrouton relationship.

The parameters of the model were obtained by fitting the rheological data, accord-ing to the following procedure:

– The values of λi and Gi were obtained by fitting the storage and loss modulus,according to the equations

G′ =N∑

i=1

Gi(λiω)2

1+(λiω)2G′′ =

N∑i=1

Giλiω

1+(λiω)2(5.65)

5.3 Rheometry 177

Figure 5.42: Dynamic test in a rotational rheometer [23, 24]

and the restriction

ηo =N∑

i=1

Giλi. (5.66)

– The values of ξi were obtained by fitting shear viscosity according to

η =N∑

i=1

Giλi

1+ξi(2 − ξi)(λiω)2. (5.67)

– The λi, Gi and ξi values were obtained by minimization of the error between ex-perimental data and the calculated data using the previous equations for the differentfrequencies, using the error metrics

Error =M∑i=1

(G

′calci

G′exptali

− 1

)2

+M∑i=1

(G

′calci

G′′exptali

− 1

)2

+M∑i=1

(η∗calc

η∗exptal− 1

)2

.

(5.68)

– The values of εiwere obtained by fitting the Trouton viscosity at low elongationalrates and the Cogswell’s elongational viscosity. To fit the elongational viscosity, itwas necessary to solve by iteration the non-linear equation resulting from applyingthe Phan-Thien and Tanner equations to an elongational, uniaxial, and uniform flowat steady state:

178 5 Melt Rheology

exp

(εi

Gi(τzzi+2τrri)

)τzzi − 2λi(1 − ξi)τzzi ε = 2λiGiε, (5.69)

exp

(εi

Gi(τzzi+2τrri)

)τrri − 2λi(1 − ξi)τrri ε = 2λiGiε, (5.70)

τzz =N∑

i=1

τzzi τrr =N∑

i=1

τrri η =τzz − τrr

ε. (5.71)

– The ξi values were obtained by minimization of the error between experimentaldata and the calculated data using the above equations for the different frequencies,according to the error metrics

Error =M∑i=1

(ηcalc

e

ηexptale

− 1)2

. (5.72)

Table 5.16: Parameters for Phan-Thien and Tanner model (PP PROPILCO 18H86 at230 ◦C)

i λi εi ξi Gi

1 2.51E-04 1.00E+00 8.60E-02 1.22E+05

2 1.66E-03 1.00E+00 3.06E-01 4.02E+04

3 5.94E-03 8.00E-01 9.43E-01 1.53E+04

4 2.07E-02 2.00E-01 5.89E-01 6.39E+03

5 9.00E-02 3.50E-02 8.30E-02 2.88E+03

6 4.86E-01 3.00E-02 2.62E-01 3.62E+02

7 2.71E+00 3.00E-02 9.99E-01 3.44E+01

When fitting the parameters of the Phan-Thien and Tanner multimode model with theexperimental data, a non-linear optimization was done using a commercial equation-solving software. Table 5.16 shows the parameters of the Phan-Thien and Tannermultimodemodel for the given polypropylene. The solid lines of Fig. 5.42 correspondto the Phan-Thien and Tanner multimode model predictions.

Conclusions: The Phan-Thien and Tanner multimode model agreed very well withthe given experimental data. Small oscillations are visible because of the discretizationof the relaxation spectra.

5.3 Rheometry 179


Modeling the Shear Viscosity Curves and Their Application in InjectionMolding

In this case study, the cold runners and gates of a six-cavity mold presented inFig. 5.43 needed to be rheologically balanced, such that every cavity filled at the sametime. The polymer melt data is given by,

– Material – Injection molding grade polyamide 6

– Rheological data – The rheological properties were modeled at the injection temper-ature using the Bird-Carreau-Yasudamodel with parameters, A = 373 (Pa· s), B = 0.12s and C = 0.35. The details of the regression procedure to obtain the Bird-Carreau-Yasuda model parameters were presented in in a case study above.

– Processing conditions and properties – The following injection molding conditionswere set: part weight 20 g, total length of channel 250mm, density at melt temperature1.1 g/cm3, injection molding speed 100 mm/s and thickness 2.5 mm.

– Geometry of gates and runners – The dimensions of the runners and gate system arepresented in Table 5.17. The diameters of channels 1 and 3 were used for balancingthe runners and gate system. The values presented are the final values obtained afterthe iteration process.

Table 5.17: Dimensions of the runners and gate system of the six-cavity mold

Diameter (mm) Length (mm) Number of channels

Channel 1 5.11 100 2

Channel 2 7 150 2

Channel 3 4.88 100 4

Gate I 1 1 2

Gate II 2 1 4

The first step is to calculate the total volume of the part, runners, and gates of thegiven mold system. The total volume was calculated by adding the volume of the sixparts (calculated with the weight of the part and the melt density), the volume of thedifferent channels and volume of the different types of runners (calculated with thegiven geometry),

VTot =N∑

i=1

Wparti

ρmelt− 1+

M∑j=1

Vchannelj+P∑

k=1

Vgatesk. (5.73)

180 5 Melt Rheology

Figure 5.43: Six-cavity mold to be rheologically balanced

The injection time was calculated by dividing the injection molding speed by thechannel length,

t =Vinj

L. (5.74)

The volumetric flow was calculated by dividing total volume by the injection time,

V =VTot

t. (5.75)

Table 5.18: Calculations for balancing the runners and gate system of the six-cavitymold

Diameter Length # of Flow rate Shear Viscosity Pressure(mm) (mm) Channels (cm3/s) Rate (1/s) (Pa· s) drop (Bar)

Channel 1 5.11 100 2 8.8 547.4 85.8 45.1

Channel 2 7 150 2 17.6 426.7 93.4 41.9

Channel 3 4.88 100 4 8.8 629.3 81.7 51.7

Gate I 1 1 2 8.8 73186.6 15.5 55.8

Gate II 2 1 4 8.8 9148.3 32.2 7.2

Total 52.8

The volumetric flow of channels 1 and 3 was calculated as the total volume dividedby 6. The volumetric flow of channels 2 was calculated as the total volume divided by3. The shear rate for each channel and gate was approximated using

γ = 0.815 · 4 · Vπ · R3

. (5.76)

The viscosity was calculatedwith the Bird-Carreau-Yasudamodel, and the pressuredrop for each channel and gate was obtained with the expression

η =A

(1+B · γ)c, (5.77)

ΔP =8 · V · η · L

π · R4. (5.78)

5.3 Rheometry 181

Using an iterative scheme with the diameters of channels 1 and 3 and with thediameter of channel 2 fixed, the runners and gate system were obtained. Because therunners and gate system were balanced, the pressure drop through every channel wasthe same and equal to 100.9 bar. The maximum recommended shear rates for gatesare presented in Table 5.19. For a PA6 a maximum shear rate of 60000 1/s is recom-mended. According to the calculations, the higher shear rate 73186.6 1/s was obtained.

Table 5.19: Maximum shear stress and shear rates for various polymers [29, 30]

Polymer Max. shear stress, (Pa) Max. shear rate, (1/s)

PP 250,000 100,000

HDPE 200,000 40,000

LDPE 100,000 40,000

Flexible PVC 150,000 20,000

Rigid PVC 200,000 20,000

PS 250,000 40,000

HIPS 300,000 40,000

SAN 300,000 40,000

ABS 300,000 50,000

PA6 500,000 60,000

PA66 500,000 60,000

PET 500,000 6,000

PBT 400,000 50,000

PC 500,000 40,000

PMMA 400,000 40,000

PPS 345,000 50,000

PSU 500,000 50,000

PUR 250,000 40,000

Conclusions: Although the cold runners and gates system of the six-cavity moldwas balanced, a shear rate at gate 1 exceeded themaximum recommendedvalue;hence,a redesign of this gate must be done.


Dispersion of a Polymer Blend Using a Single-Screw Extruder

In this case study a 50% PP and 50% LDPE polymer blend was supposed to beprocessed in a 45-mm single-screw extruder. It was necessary to predict beforehandwhich polymer could be used as the dispersed phase to guarantee the required product

182 5 Melt Rheology

quality. The intendedoperating conditions of the extruder and the barrier gapgeometryof the screw in the metering zone were:

Temperature of the melt is 210 ◦CScrew rotational speed, N = 45 rpm = 0.8 rev/sBarrier gap, δ = 0.3 mm

The first step is to estimate the viscosities of both polymeric materials at the extru-sion shear rate (γ) within by the 45-mm screw. The shear rate was calculated by theexpression

γ =π · D · N

δ=

π · 45 mm · 0.8rev/s0.3 mm

= 377s-1. (5.79)

Figures 5.44 and 5.45 present the viscosity curves of LDPE and PP as a function ofshear rate and temperature of the melt.

Figure 5.44: Viscosity curve of LDPE

The viscosity values of the polymer melts shown in Eq. 5.80 can be obtained fromthe curves in Fig. 5.44 and 5.45.

Figure 5.45: Viscosity curve of PP

5.3 References 183

Figure 5.46: Grace diagram [1]

ηLDPE = 80(Pa · s)ηPP = 250(Pa · s) (5.80)

The viscosity ratios were also calculated to predict the dispersed phase reading inthe Grace diagram and are shown in Eq. 5.81.

ηLDPE

ηPP=

80250

= 0.32

ηPP

ηLDPE=

25080

= 3.12(5.81)

From the Grace diagram in Fig. 5.46, it was clear that PP cannot be employed in thedispersed phase because the viscosity ratio ηPP over ηLDPE was near the 3.8 limit.Because the ratio ηLDPE over ηPP was the lowest, for LDPE it is likely to be selectedfor the dispersed phase.

Conclusion: The predicted dispersed phase for the physical blend of 50% PP and50% LDPE at the given operating conditions was LDPE, and the matrix or continuousphase was PP.

References

1. F.T. Trouton. Proc. Roy. Soc. A, 77, 1906.

2. H. Muenstedt. Rheol. Acta, 14:1077, 1975.

3. C.D. Han and K.W. Len. J. Appl. Polym. Sci., 29:1879, 1984.

4. J.M. Castro and C.W. Macosko. AIChE J., 28:250, 1982.

5. J.M. Castro, S.J. Perry, and C.W. Macosko. Polym. Comm., 25:82, 1984.

6. G.K. Batchelor. Annu. Rev. Fluid Mech., 6:227, 1974.

184 5 Melt Rheology

7. A. Einstein. Ann. Physik, 19:549, 1906.

8. P. Geisbusch. PhD thesis, IKV-RWTH-Aachen, Germany, 1980.

9. E. Guth and R. Simha. Kolloid-Zeitschrift, 74:266, 1936.

10. E. Guth. Phys. Rev., 53:321, 1938.

11. R.K. Gupta. Flow and rheology in polymer composites manufacturing. Elsevier, Amsterdam,1994.

12. W.J. Milliken and R.L. Powell. Flow and rheology in polymer composites manufacturing. Else-vier, Amsterdam, 1994.

13. J.F. Agassant, P. Avenas, J.-Ph. Sergent, and P.J. Carreau. Polymer Processing - Principles andModeling. Hanser Publishers, Munich, 1991.

14. J. P. Sergent J. F. Agassant, P. Avenas and P. J. Carreau. Polymer processing: principles andmodelling. Hanser Publishers, Munich, 1991.

15. R. I. Tanner, N. Phan-Thien. J. Now-Newt Fluid Mech, 2:353, 1977.

16. D. Acierno, F. P. La Mantia, G. Marrucci, and G. Titomanlio. J. Now-Newt Fluid Mech, 1:125–147, 1977.

17. H. A. Barnes and D. Bell. Controlled-stress rotational rheometry: A historical review. Korea-Australia Rheol. J, 15(4):285–336, 2003.

18. C.W. Macosko. RIM Fundamentals of reaction injection molding. Hanser Publishers, Munich,1989.

19. B. N. Wang, M. Sentmanat. and G. H. McKinley. Measuring the transient extensional rheologyof a LDPE melt using the SER universal testing platform. J. Rheol, pages 1–29, 2004.

20. M. Sentmanat. Miniature universal testing platform: from extensional melt rheology to solid-statedeformation behavior. Rheol Acta, 43:657–669, 2004.

21. RHEOTENS 71.97. The New Tensile Tester for Polymer Melts. Gottfert, Germany.

22. A. Bernnat. Polymer Melt Rheology and the Rheotens Test. PhD thesis, Institut fur Kunststoffver-arbeitung, 2001.

23. J. Sierra. Development of biconstituent fibers of polypropylene and polyamide 6 for high speedfiber spinning. PhD thesis, University of the Vasc Country, Spain, 2005.

24. M. P. Noriega, J. D. Sierra, I. D. Lopez, and I. Katime. Biconstituent fibers from polypropyleneand polyamide 6: fiber spinning modeling and properties. WAKKunststoffetechnik, 2:1–28, 2006.

25. F. N. Cogswell. Polymer melt rheology: A guide for industrial practice. John Wiley & Sons,1981.

26. D. Binding. An approximate analysis for contraction and converging flows. J. Non-NewtonianFluid Mech, 27:173–189, 1988.

27. M. Gupta. Effect of elongational viscosity on axisymmetric entrance flow of polymers. Polym.Eng. Sci., 40, 23, 2000.

28. K. Feigl, F.X. Tanner, B.J. Edwards, and J.R. Collier. A numerical study of the measurement ofelongational viscosity of polymeric fluids in a semihyperbolically converging die. To appear inJournal of Non-Newtonian Fluid Mechanics.

29. H. Rees. Mold Engineering. 2nd edition Hanser Publishers, Munich, 2002.

30. J. P. Beaumont. Runner and Gating Design Handbook: Tools for Successful Injection Molding.2nd edition Hanser Publishers, Munich, 2007.

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185

CHAPTER 6

MECHANICAL PROPERTIES

6.1 MECHANICAL PROPERTIES

Polymericmaterials are implemented into various designs because of their low cost, process-ability, and desirable material properties. Of interest to the design engineer are the short- andlong-term responses of a loaded component. Properties for short-term responses are usu-ally acquired through short-term tensile tests and impact tests, whereas long-term responsesdepend on properties measured using techniques such as the creep and the dynamic tests.

6.1.1 The Short-Term Tensile Test

The most commonly used mechanical test is the short-term stress-strain tensile test. Stress-strain curves for selected polymers are displayed in Fig. 6.1 [1].The next two sections discuss the short-term tensile test for elastomers and thermoplastic

polymers separately. The main reason for identifying two separate topics is that the defor-mation of a cross-linked elastomer and an uncross-linked thermoplastic vary greatly. Thedeformation in a cross-linked polymer is in general reversible, whereas the deformation intypical uncross-linked polymers is associated with molecular chain relaxation, which makesthe process time-dependent and is sometimes irreversible.

186 6 Mechanical Properties

0

10

20

30

40

50

60

70

80

90

100

20 120 220 320 420 520 620 720 820 92020 100 200 300 400 500 600 700 800 900 1000

PA6

PC

PUR Elastomer

PP

PE-LD

PE-HD

Strain (%) ε

0

100

200

300

400

0 1 2 3 4

UP-GF 60

PA-Dry

Phenolic

%ε

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20

PMMA

PA6

PC

ABS

PP

PE-HD

PUR Elastomer

PE-LD

T= 22 oC

Figure 6.1: Tensile stress-strain curves for several materials

Rubber elasticity: The main feature of elastomeric materials is that they can undergovery large and reversible deformations. This is because the curled-up polymer chains stretchduring deformation but are hindered from sliding past each other by the cross-links betweenthe molecules. Once a load is released, most of the molecules return to their coiled shape.As an elastomeric polymer component is deformed, the slope of the stress-strain curve dropssignificantly as the uncurled molecules provide less resistance and entanglement, allowingthem to move more freely. Eventually, at deformations of about 400%, the slope starts toincrease because the polymer chains are fully stretched. This is followed by polymer chainbreakage or crystallization that ends with the fracture of the component. Stress-deformationcurves for natural rubber (NR) [2] and a rubber compound [3] composed of 70 parts ofstyrene-butadiene-rubber (SBR) and 30 parts of natural rubber are presented in Fig. 6.2.Because of the large deformations, typically several hundred percent, the stress-strain dataare usually expressed in terms of extension ratio, λ defined by

λ =L

L0, (6.1)

where L represents the instantaneous length and L0 the initial length of the specimen.Finally, it should be noted that the stiffness and strength of rubber is increased by filling

with carbon black. The most common expression for describing the effect of carbon blackcontent on the modulus of rubber was originally derived by Guth and Simha [4] for theviscosity of particle suspensions, and later used by Guth [5] to predict the modulus of filledpolymers. The Guth equation can be written as

Gf

G0= 1 + 2.5φ + 14.1φ2, (6.2)

whereGf is the shear modulus of the filled material,G0 is the shear modulus of the unfilledmaterial, and φ the volume fraction of particulate filler. The above expression is comparedto experiments [6, 7] in Fig. 6.3.


Figure 6.2: Experimental stress-extension curves for NR and a SBR/NR compound

Figure 6.3: Effect of filler on modulus of natural rubber

The tensile test and thermoplastic polymers: Of all the mechanical tests done onthermoplastic polymers, the tensile test is the least understood, and the results are oftenmisinterpreted and misused. Because the test was inherited from other materials that havelinear elastic stress-strain responses, it is often inappropriate for testing polymers. However,standardized tests such as DIN 53457 and ASTM D638 are available to evaluate the stress-strain behavior of polymeric materials. The DIN 53457, for example, is performed at aconstant elongational strain rate of 1%perminute,and the resulting data are used to determinethe short-termmodulus. The ASTMD638 test also uses one rate of deformation per materialto measure the modulus; a slow speed for brittle materials and a fast speed for ductile ones.However, these tests do not reflect the actual rate of deformation experienced by the narrow


portion of the test specimen, making it difficult to maintain a constant speedwithin the regionof interest. The standard tests ASTM D638 and ISO 527-1 are presented in Table 6.1.

h=4 ± 0.2 mm

b2=20 ± 0.2 mm

b1=10 ± 0.2 mm

L1=80 ± 2 mm

L2=104 to 113 mm

L3 ≥ 150 mm

r= 20 to 25 mm

Figure 6.4: Standard ISO-3167 tensile bar

T=3.2 ± 0.4 mm

WO=19 (+6.4, 0) mm

W=13 ± 0.5 mm

L=57 ± 0.5 mm

D=115 ± 5 mm

LO = 165 mm

R= 76 ± 1 mm

G=50 ± 0.25 mm

Figure 6.5: Standard ASTM-D638 tensile bar

Table 6.1: Standard methods of measuring tensile properties (Shastri)

Standard ISO 527-1:93 and 527-2:93 D638-98

Specimen ISO 3167 (Type A or B*) multipurposetest specimens (Figure 6.4). * TypeA is recommended for directly moldedspecimens, so the 80 mm x 10 mm x4 mm specimens required for most testsin ISO 10350-1 can be cut from the cen-ter of these specimens. Type B is rec-ommended for machined specimens.

For rigid/semirigid plastics: D638Type I specimens (Figure 6.5) arethe preferred specimen and shall beused when sufficient material hav-ing a thickness of 7 mm or less isavailable.




Dimensions for ISO 3167 specimensare:Overall Length⇒ >150 mmWidth⇒ 10 mmThickness⇒ 4 mmFillet radius ⇒ 20-25 mm (Type A) or>60 mm (Type B)

Dimensions for D638 Type Ispecimens are:Overall Length⇒ 165 mmWidth⇒ 12.7 mmThickness⇒ 3.2 mmFillet radius⇒ 76 mmLength of parallel narrow section⇒57 mmLength of parallel narrow section⇒80 mm (Type A) or 60 mm (Type B)

Conditioning Specimen conditioning, including anypost molding treatment, shall be carriedout at 23 ◦C ±2 ◦C and 50 ±5%R.H. foraminimum length of timeof 88 h, exceptwhere special conditioning is requiredas specified by the appropriate materialstandard.

At 23 ±2 ◦C and 50 ±5% rela-tive humidity for no less than 40 hprior to testing in accordance withD618 Procedure A for those testswhere conditioning is required. Forhygroscopic materials, the materialspecification takes precedence overthe above routine preconditioningrequirements.

Test procedures A minimum of five specimens shall beprepared in accordance with the relevantmaterial standard. When none exists,or unless otherwise specified specimensshall be directly compression or injec-tion molded in accordance with ISO 293or ISO294-1. Test speed for ductile fail-ure (defined as yielding or with a strainat break >10%) is 50 mm/min and for abrittle failure (defined as rupture with-out yielding or strain at break < 10%) is5 mm/min. For modulus determinationsthe test speed is not specified in ISO10350; however, in ISO 527-2 it is spec-ified for molding and extrusion plasticsthat the test speed is 1 mm/min. Ex-tensometers are required for determin-ing strain at yield and tensile modulus.

A minimum of five test specimensshall be prepared by machining op-erations or die cutting the materi-als in sheet, plate, slab or similarform. Specimens can also be pre-pared by injection or compressionmolding the material to be tested.Test speed is specified in the specifi-cation for the material being tested.If no speed is specified, then use thelowest speed (5, 50, or 500mm/min)which gives rupture within 0.5 to5.0 minutes. Modulus testing maybe conducted at the same speed asthe other tensile properties providedthat recorder response and resolu-tion are adequate. Extensometersare required for determining strainat yield and tensile modulus.




The specified initial gauge length is50 mm. The extensometer shall be es-sentially free of inertia lag at the speci-fied speed of testing and capable ofmea-suring the change in gauge with an accu-racy of 1%of the relevant value or better.This corresponds to ±1 micrometer forthe measurement of modulus on a gaugelength of 50 mm.

The specified initial gauge lengthis 50 mm. For modulus deter-minations, an extensometer whichmeets Class B-2 (Practice E-38) isrequired, for low extensions (<20%)the extensometer must at least meetClass C (Practice E38) require-ments, for high extensions (>20%)any measurement technique whichhas an error no greater than ±10%can be used.

The reported tensile modulus is achord modulus determined by drawinga straight line that connects the stressat 0.05% strain and the stress at 0.25%strain. There is no requirement fortoe compensation in determining a cor-rected zero point, if necessary.

Tangent modulus is determined bydrawing a tangent to the steepest ini-tial straight line portion of the load-deflection curve and then dividingthe difference in stress on any sec-tion of this line by the correspondingdifference in strain. Secant modulusis the ratio of stress to correspond-ing strain at any given point on thestress-strain curve, or the slope ofthe straight line that joins the zeropoint or corrected zero point and theselected point corresponding to thestrain selected on the actual stress-strain curve. Toe compensation, ifapplicable as defined, is mandatory.

Values and units For ductile materials: For ductile materials:Stress at yield⇒MPaStrain at yield⇒%Stress at 50% strain*⇒MPaNominal strain at break**⇒%Tensile modulus⇒MPa* If the material does not yield before50% strain, report stress at 50% strain.**Nominal strain at break based on ini-tial and final grip separations, if ruptureoccurs above 50% nominal strain onecan either report the strain at break orsimply > 50%.

Stress at yield⇒MPaStrain at yield⇒ %Stress at break⇒MPaStrain at break⇒%Tangent modulus or⇒MPaSecant modulus⇒MPa

Stress at break⇒MPaStrain at break⇒ %Chord modulus (0.5–0.25% strain) ⇒MPa

Stress at break⇒MPaStrain at break⇒%Modulus⇒MPa


Figure 6.6: Stress-strain behavior of PMMA at various strain rates

0

100

200

300

400

0 200 400 600 800 1000 1200

Strain

Strain rate = 1 10 100 mm/minNormalized work = 1 0.75 0.55N/mm 2

%

Strain rate= 100 mm/min

10

1

Figure 6.7: Stress-strain behavior of PE at various rates of deformation

However, the rate of deformation has a great impact on the measured results. A typicaltest performed on PMMA at various strain rates at room temperature is shown in Fig. 6.6.The increased curvature in the results with slow elongational speeds suggests that stressrelaxation plays a significant role during the test.Similarly, Fig. 6.7 reflects the effect of rate of deformation on the stress-strain behavior of

a typical semicrystalline polymer. The ultimate strength is also affected by the deformationrate, and the trend depends on the polymer, as depicted in Fig. 6.8. Again, the effect is causedby the relaxation behavior of the polymer. The relaxation behavior and memory effects of


20

30

40

50

60

70

80

90

100

110

0.01 0.1 1 10 100 1000 10000 100000

AMMA

PMMA

PA 6 (2.1% H 20)

PVC

PC

CAB

ABS

PE

Cross - Linked PUR elastomerShore - hardness A= 70

Strain rate

22 oC

%/s

σ B

N/mm 2

10-2 10-1 100 101 102 103 104 105

Figure 6.8: Rate of deformation dependence of strength for various thermoplastics

polymers are illustrated in Fig. 6.9, which shows the strain one minute after the specimenfailed for tests performed at different rates of deformation.

0

10

20

30

40

50

60

70

80

90

100

0.01 0.1 1 10 100 1000 10000 100000

%

PA 6(2.1 % H 20)

AMMA PC

PE CAB

ABSPVC

Rate of deformation

10-2 10-1 100 101 102 103 104 105%/s

Figure 6.9: Residual strain in the test specimen as a function of strain rate for various thermoplastics

It can be shown that for small strains the secant modulus, described by

Es =σ

ε, (6.3)


Figure 6.10: Schematic of the stress-strain behavior of a viscoelastic material at two rates ofdeformation

and the tangent modulus, defined by

Et =dσ

dε, (6.4)

are independent of strain rate and are functions only of time and temperature. This isschematically shown in Fig. 6.10 [8].The figure shows two stress-strain responses: one at a slow elongational strain rate, ε 1,

and one at twice the speed, defined by ε2. The tangent modulus at ε1 in the curve with ε1 isidentical to the tangent modulus at ε2 in the curve with ε2, where ε1 and ε2 occurred at thesame time. For small strains the tangent modulus,Et, is identical to the relaxation modulus,Er, measured with a stress relaxation test. This is important because the complex stressrelaxation test can be replaced by the relatively simple short-term tensile test by plotting thetangent modulus versus time.Generic stress-strain curves and stiffness and compliance plots for amorphous and semicrys-talline thermoplastics are shown in Fig. 6.11 [9]. The stress-strain behavior for thermoplasticpolymers can be written in a general form as

σ = E0ε1 − D1ε

1 + D2ε, (6.5)

whereE0,D1 andD2 are time- and temperature-dependentmaterial properties. The constantD1 = 0 for semi-crystaline polymers andD2 = 0 for amorphous plastics.Figure 6.12 shows E0 and D2 for a high-density polyethylene at 23 ◦C as a function of

strain rate. The values of E0, D1 and D2 can be easily calculated for each strain rate fromthe stress-strain diagram [10]. The modulus E0 simply corresponds to the tangent modulusat small deformations where

σ = E0ε (6.6)

Assuming that for amorphous thermoplastics D2 ≈ 0 when T � Tg and for semicrys-talline thermoplasticsD1 ≈ 0 when T � Tg, we can computeD1 from

D1 =σ2ε1 − σ1ε2σ2ε21 − σ1ε22

(6.7)


Figure 6.11: Schematic of the stress-strain response, modulus, and compliance of amorphous andsemicrystalline thermoplastics at constant rates of deformation

Figure 6.12: Coefficients E0 and D2 for a high-density polyethylene at 23 ◦C


Figure 6.13: Poisson’s ratio as a function of rate of deformation for PMMA

0.3

0.35

0.4

0.45

0.5

20 40 60 80 100 120 140 160

PE-LD

PE-HD

PA610

PMMA

PP

PS

PVC-P

Temperature

oC

-50oC

Figure 6.14: Poisson’s ratio as a function of temperature for various temperatures

andD2 from

D2 =σ1ε2 − σ2ε1

ε1ε2 (σ2 − σ1). (6.8)

Depending on the time scale of the experiment, a property that also varies considerablyduring testing is Poisson’s ratio, ν. Figure 6.13 [9] shows Poisson’s ratio for PMMA de-formed at rates (%/h) between 10−2 (creep) and 103 (impact). Temperature affects Poisson’sratio in a similar way, as depicted in Fig. 6.14 for several thermoplastics. The limits are ν=0.5(fluid) for high temperatures or very slow deformation speeds and ν=0.33 (solid) at low tem-peratures or high deformation speeds. In fiber filled plastics, Poisson’s ratio is affected by the


0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60 70 80

ψFiber fraction (weight)

a)

b)

EP, unidirectional

UP, matt

EP, unidirectional

a) Loading parallel to fibersb) Loading perpendicular to fibers

%

Figure 6.15: Poisson’s ratio as a function of fiber content for fiber-filled thermosets

fiber content and the orientation of the reinforcing fibers. This is demonstrated in Fig. 6.15for fiber-filled thermosets.

Flexular test: The flexural test is widely accepted in the plastics industry because itaccurately portrays bending load cases, which often reflect realistic situations. However,because of the combined tensile and compressive stresses encountered in bending, it is a testthat renders properties that should be regardedwith caution. The test is summarized for ISOand ASTM standards in Table 6.2.

Table 6.2: Standard methods of measuring flexural properties (Shastri)

Standard ISO 178 D790 - 98

Specimen 80mmx 10mmx4mmcut from thecenter of an ISO 3167 Type A speci-men. In any one specimen the thick-ness within the central one-third oflength shall not deviate bymore than0.08 mm from its mean value, andthe corresponding allowable devia-tion in the width is 0.3 mm from itsmean value.

Specimens may be cut from sheets,plates, molded shapes or moldedto the desired finished dimensions.The recommended specimen formolding materials is 127 mm x12.7 mm x 3.2 mm.




Conditioning Specimen conditioning, includingany post molding treatment, shall becarried out at 23 ◦C ±2 ◦C and 50±5% R.H. for a minimum length oftime of 88 h, except where specialconditioning is required as speci-fied by the appropriatematerial stan-dard.

At 23 ±2 ◦C and 50 ±5% relative hu-midity for not less than 40h prior totesting in accordance with to D618Procedure A for those tests whereconditioning is required. For hygro-scopic materials, the material spec-ification takes precedence over theabove routine preconditioning re-quirements.

Apparatus Support and loading nose radius 5.0±0.1 mm (Fig. 6.16)

Support and loading nose radius 5.0±0.1 mm (Fig. 6.17)

Parallel alignment of the supportand loading nose must be less thanor equal to 0.02 mm.

Parallel alignment of the supportand loading noses may be checkedby means of a jig with parallelgrooves into which the loading noseand supports will fit if properlyaligned.

ISO/IEC (see ISO 10350 - 1) ASTMMethodsSupport span length 60 - 68 mm(Adjust the length of the span towithin 0.5%, which is 0.3 mm forthe span length specified above)Support span to specimen depth ra-tio 16 ±1; 1 mm/mm

Support span length* 49.5–50.5 mm(Measure the span accurately to thenearest 0.1 mm for spans less than63 mm. Use the measured spanlength for all calculations).

Support span to specimen depth ra-tio 16 (+ 4, -1); 1 mm/mm (speci-mens with a thickness exceeding thetolerance of ±0.5%).

Test procedures Testing conditions indicated in ma-terial specifications take prece-dence; therefore, it is advisable torefer to thematerial specification be-fore using the following procedures.

Test speed⇒ mm/min Procedure A crosshead speed* ⇒1.3 mm/minProcedure B crosshead speed* ⇒13 mm/min * Procedure A must beused for modulus determinations,Procedure B may be used for flex-ural strength determination only




A minimum of five specimensshall be prepared in accordancewith the relevant material standard.When none exists, or unless oth-erwise specified, specimens shallbe directly compression or injectionmolded in accordance with ISO 293or ISO 294-1.

A minimum of five test specimensare required. No specimen prepara-tion conditions are given.

Test specimens that rupture outsidethe central one-third of the spanlength shall be discarded and newspecimen shall be tested in theirplace.Measure the width of the test spec-imen to the nearest 0.1 mm and thethickness to the nearest 0.01 mm inthe center of the test specimen.

Measure the width and depth of thetest specimen to the nearest 0.03mmat the center of the support span.

The reported flexural modulus is achord modulus determined by draw-ing a straight line that connects thestress at 0.05% strain and the stressat 0.25% strain. There is no require-ment for toe compensation in deter-mining a corrected zero point, if nec-essary.

Tangent modulus is determined bydrawing a tangent to the steepest ini-tial straight line portion of the load-deflection curve and then dividingthe difference in stress on any sec-tion of this line by the correspondingdifference in strain.

Secant modulus is the ratio of stressto corresponding strain at any givenpoint on the stress-strain curve, orthe slope of the straight line thatjoins the zero point and a selectedpoint on the actual stress-straincurve. Toe compensation, if appli-cable, as defined is mandatory.

Values and units Flexural modulus⇒MPaFlexural strength, at rupture⇒MPaFlexural strength, at maximumstrain*⇒MPa*At conventional deflection which is1.5 x height: therefore 4 mm speci-mens would have a maximum strainat 3.5%.

Tangent modulus or⇒MPaSecant modulus⇒MPaFlexural strength, (at rupture*) ⇒MPaFlexural yield strength**⇒MPa* Maximum allowable strain in theouter fibers is 0.05 mm/mm**The point where the load does notincrease with increased deflection,provided it occurs before the maxi-mum strain rate*


R1= 5 ± 0.1mm

R2= 5 ± 0.1mm d = 4 ± 0.2mm

5o

Test specimen

Loading nose

F

Support

L = 60-68mm

l = 80 ± 2mm

Figure 6.16: Test specimen and fixture for the ISO 178 flexural test

R = 5 ± 0.1mm

L = 49.5-50.5 mm

R = 5 ± 0.1mm

Figure 6.17: Test specimen and fixture for the ASTM D790 flexural test


6.1.2 Impact Strength

In practice, nearly all polymer components are subjected to impact loads. Since manypolymers are tough and ductile, they are often well suited for this type of loading. However,under specific conditions even the most ductile materials, such as polypropylene, can failin a brittle manner at very low strains. These types of failure are prone to occur at lowtemperatures and at very high deformation rates. As the rate of deformation increases, thepolymer has less time to relax. The limiting point is when the test is so fast that the polymerbehaves as a linear elastic material. At this point, fracture occurs at a minimum value ofstrain, εmin, and its corresponding stress, σmax. During impact, one should always assumethat if this minimum strain value is exceeded at any point in the component, initial fracturehas already occurred. Table 6.3 presents minimum elongations at break and correspondingstresses for selected thermoplastics during impact loading.

Table 6.3: Minimum elongation at break and corresponding stress on impact loading

Polymers εmin (%) σmax (MPa)

HMW-PMMA 2.2 135

PA6+25% SFR 1.8 175

PVC-U 2.0 125

POM 4.0 >130

PC+20% SFR 4.0 >110

PC 6.0 >70

Figure 6.18 summarizes the stress-strain and fracture behavior of a HMW-PMMA testedat various rates of deformation. The area under the stress-strain curves represents the volume-specific energy to fracture (w). For impact, the elongation at break of 2.2% and the stressat break of 135 MPa represent a minimum of volume-specific energy because the stressincreases with higher rates of deformation, but the elongation at break remains constant.Hence, if we assume a linear behavior, the minimum volume-specific energy absorption upto fracture can be calculated using

wmin =12σmaxεmin. (6.9)

The impact strength of a copolymer and polymer blend of the same materials can be quitedifferent, as shown in Fig. 6.19. From the figure it is clear that the propylene-ethylenecopolymer, which is an elastomer, has a much higher impact resistance than the basicpolypropylene-polyethylene blend. It should be pointed out here that elastomers usuallyfail by ripping. The ripping or tear strength of elastomers can be tested using the ASTMD1004, ASTM D1938, or DIN 53507 test methods. The latter two methods make use ofrectangular test specimens with clean slits cut along the center. The tear strength of elas-tomers can be increased by introducing certain types of particulate fillers. For example,a well-dispersed carbon black filler can double the ripping strength of a typical elastomer.


Figure 6.18: Stress-strain behavior of HMW-PMMA at various rates of deformation

Figure 6.19: Impact strength of a propylene-ethylene copolymer and a polypropylene-polyethylenepolymer blend

Figure 6.20 shows the effect that different types of fillers have on the ripping strength of apolychloroprene elastomer.In general, one can say if the filler particles arewell-dispersed and have diameters between

20 nm and 80 nm, they will reinforce the matrix. Larger particles will act as microscopicstress concentrators and will lower the strength of the polymer component. A case where


Figure 6.20: Ripping strength of a polychloroprene elastomer as a function of filler content fordifferent types of fillers (Menges)

Figure 6.21: Tensile strength of PVC as a function of calcium carbonate content (Menges)

the filler adversely affects the polymer matrix is presented in Fig. 6.21, where the strengthof PVC is lowered with the addition of a calcium carbonate powder.

Impact test: The most common impact tests used to evaluate the strength of polymers arethe Izod and the Charpy tests.The Charpy test evaluates the bending impact strength of a small notched or unnotched

simply supported specimen that is struck by a swinging hammer. There are notched andunnotched Charpy impact tests. The standard unnotched Charpy impact test is given by theISO 179 test; however, ASTM does not offer such a test. The ISO 179 test is presented inTable 6.4. The notchedCharpy test is done such that the notch faces away from the swinginghammer creating tensile stresses within the notch, as shown in Fig. 6.22. The standard ISO

(MP

a)


179 also describes the notched Charpy test, as well as the ASTMD256 andDIN 53453 tests.The standard Charpy notched tests ISO 179 and ASTM D256 are presented in Table 6.5.

Figure 6.22: Schematic of the clamp, specimen, and striking hammer in a Charpy impact test

Table 6.4: Standard methods of measuring unnotched charpy impact strength (Shastri)

Standard ISO 179 - 1 and ISO 179 - 2

Specimen 80 mm x 10 mm x 4 mm cut from the center of an ISO 3167 Type Aspecimen, also referred to as an ISO 179/1eU specimen

Conditioning Specimen conditioning, including any post molding treatment, shall becarried out at 23 ◦C ±2 ◦C and 50 ±5% R.H. for a minimum length oftime of 88 h, except where special conditioning is required as specifiedby the appropriate material standard.

Apparatus The machine shall be securely fixed to a foundation having a mass atleast 20 times that of the heaviest pendulum in use and be capable ofbeing leveled.


0.0025



Apparatus Striking edge of the hardened steel pendulums is to be tapered to anincluded angle of 30 ±1◦ and rounded to a radius of 2.0 ±0.5 mm Thestriking edge of the pendulum shall pass midway, to within ± 0.2 mm,between the specimen supports. The line of contact shall be within ±2◦

of perpendicular to the longitudinal axis of the test specimen. Pendulumswith specified nominal energies shall be used: 0.5, 1.0 2.0, 4.0, 5.0, 7.5,15.0, 25.0, and 50.0 J. Velocity at impact is 2.9 + 10% m/s for the 0.5 to5.0 J pendulums and 3.8 ±10% m/s for pendulums with energies from7.5 to 50.0 J. The support anvil’s line of contact with the specimen shallbe 62.0 (+0.5, -0.0) mm.

Test procedures A minimum of ten specimens shall be prepared in accordance with therelevant material standard. When none exists, or unless otherwise spec-ified, specimens shall be directly compression or injection molded inaccordance with ISO 293 or ISO 294-1. Edgewise impact is specified.Consumed energy is 10 to 80% of the pendulum energy, at the cor-responding specified velocity of impact. If more than one pendulumsatisfies these conditions, the pendulum having the highest energy isused.(It is not advisable to compare results obtained using different pendu-lums). Maximum permissible frictional loss without specimen:

0.02% for 0.5 to 5.0 J pendulum

0.04% for 7.5 J pendulum



0.20% for 50.0 J pendulumPermissible error after correction with specimen: 0.01 J for 0.5, 1.0, and2.0 J pendulums. No correction applicable for pendulums with energies> 2.0 J.Four types of failure are defined as:

C – Complete break; specimen separates into one or more pieces.

H – Hinge break; an incomplete break such that both parts of the spec-imen are only held together by a thin peripheral layer in the form of ahinge.

P – Partial break; an incomplete break which does meet the definitionfor a hinge break.

NB – Non-break; in the case of the non-break, the specimen is only bentand passed through, possibly combined with stress whitening.




Values and units The measured values of complete and hinged breaks can be used for acommon mean value with remark. If in the case of partial breaks a valueis required, it shall be assigned with the letter P. In case of non-breaks,no figures are to be reported. (If within one sample the test specimensshow different types of failures, the mean value for each failure typeshall be reported).Unnotched Charpy impact strength⇒ kJ/m2.

Table 6.5: Standard methods of measuring notched charpy impact strength (Shastri)

Standard ISO 179 - 1 and ISO 179 - 2 D256 - 97

Specimen 80 mm x 10 mm x 4 mm cut fromthe center of an ISO 3167 Type Aspecimen with a single notch A, alsoreferred to as an ISO 179/1eA spec-imen. (see Figure 6.23). Notch Ahas a 45◦ ±1◦ included angle with anotch base radius of 0.25 ±0.05 mm.The notch should be at a right an-gle to the principal axis of the speci-men. The specimens shall have a re-maining width of 8.0 ±0.2 mm afternotching. These machined notchesshall be prepared in accordance withISO 2818.

124.5 to 127 mm x 12.7 mm x(*)mmspecimen, *Thewidth of thespecimens shall be between 3.0 and12.7 mm as specified in the materialspecification, or as agreed upon asrepresentative of the crosssection inwhich the particularmaterialmay beused. (Figure 6.24). A single notchwith 45◦ ±1◦ included angle with aradius of curvature at the apex 0.25±0.05 mm. The plane bisecting thenotch angle shall be perpendicular tothe face of the test specimen within2◦ The depth of the plastic mate-rial remaining in the bar under thenotch shall be 10.16 ±0.05 mm. Thenotches are to be machined.

Conditioning Specimen conditioning, includingany post molding treatment, shall becarried out at 23◦C ±2◦C and 50±5% R.H. for a minimum length oftime of 88 h, except where specialconditioning is required as speci-fied by the appropriatematerial stan-dard.

At 23◦C ±2 ◦C and 50 ±5% rela-tive humidity for not less than 40hprior to testing in accordance withD618 Procedure A for those testswhere conditioning is required. Forhygroscopic materials, the materialspecification takes precedence overthe above routine preconditioningrequirements.




Apparatus The machine shall be securely fixedto a foundation having a mass atleast 20 times that of the heaviestpendulum in use and be capable ofbeing leveled.

The machine shall consist of a mas-sive base.

Striking edge of the hardened steelpendulums is to be tapered to anincluded angle of 30◦ ±1◦ androunded to a radius of 2.0 ±0.5 mm.

Striking edge of hardened steelpendulums is to be tapered toan included angle of 45◦ ±2◦

and rounded to a radius of 3.17±0.12 mm.

Pendulums with the specified nom-inal energies shall be used: 0.5, 1.0,2.0, 4.0, 5.0, 7.5, 15.0, 25.0, and50.0 J.

Pendulum with an energy of 2.710±0.135 J is specified for all spec-imens that extract up to 85% ofthis energy. Heavier pendulums areto be used for specimens that re-quiremore energy; however, no spe-cific levels of energy pendulums arespecified.

Velocity at impact is 2.9 ±10% m/sfor the 0.5 to 5.0 J pendulums and3.8 ±10% m/s for pendulums withenergies from 7.5 to 50.0 J. Thesupport anvils line of contact withthe specimen shall be 62.0 (+0.5, -0.0) mm.

Velocity at impact is approximately3.46 m/s, based on the verticalheight of fall of the striking nosespecified at 610 + 2 mm. The anvilsline of contact with the specimenshall be 101.6 ±0.5 mm.

Test procedures A minimum of ten specimensshall be prepared in accordancewith the relevant material standard.When none exists, or unless oth-erwise specified, specimens shallbe directly compression or injectionmolded in accordance with ISO 293or ISO 294-1. Edgewise impact isspecified (Figure 6.23).

At least five, preferably 10 speci-mens shall be prepared from sheets,composites (not recommended), ormolded specimen. Specific speci-men preparations are not given orreferenced. Edgewise impact isspecified (Figs. 6.22 and 6.26).

Consumed energy is 10 to 80% ofthe pendulum energy, at the corre-sponding specified velocity of im-pact. If more than one pendulumsatisfies these conditions, the pen-dulum having the highest energy isused. (It is not advisable to com-pare results obtained using differentpendulum)




Maximum permissible frictionalloss without specimen:0.02% for 0.5 to 5.0 J pendulum0.04% for 7.5 J pendulum0.05% for 15.0 J pendulum0.10% for 25.0 J pendulum0.20% for 50.0 J pendulumPermissible error after correctionwith specimen: 0.01 J for 0.5, 1.0,and 2.0 J pendulums. No correctionapplicable for pendulums with ener-gies > 2.0 J.

Windage and friction correction arenot mandatory; however, a methodof determining these values is given.

Four types of failure are defined as:C – Complete break; specimen sep-arates into two or more pieces.H – Hinge break; an incompletebreak such that both parts of thespecimen are only held together bya thin peripheral layer in the form ofa hinge.P – Partial break; an incompletebreak which does not meet the defi-nition for a hinge break.NB – Non-break; in the case of thenon-break, the specimen is only bentand passed through, possibly com-bined with stress whitening.

Four types of failure are specified:C – Complete break; specimen sep-arates into two or more pieces.H – Hinge break; an incompletebreak such that one part of the spec-imen cannot support itself above thehorizontal when the other part isheld vertically (less than 90◦ in-cluded angle).P – Partial break; an incompletebreak which does not meet the defi-nition for a hinge break, but has frac-tured at least 90% of the distance be-tween the vertex of the notch and theopposite side.NB – Non-break; an incompletebreak where the fracture extendsless than 90% of the distance be-tween the vertex of the notch andthe opposite side.

Values and units The measured values of completeand hinged breaks can be used fora common mean value with remark.If in the case of partial breaks a valueis required, it shall be signed withthe letter P. (If within one sample thetest specimens show different typesof failures, the mean value for eachfailure type shall be reported.)Notched Charpy impact strength⇒kJ/m

Only measured values for completebreaks can be reported. (If morethan one type of failure is observedfor a samplematerial, then report theaverage impact value for the com-plete breaks, followed by the num-ber and percent of the specimen fail-ing in that manner suffixed by theletter code.)Notched Charpy impact strength⇒J/m


bN = 8 ± 0.2mm

b = 10 ± 0.2mm

b = 4 ± 0.2mm45o ± 1o

L = 80 ± 2mm

R = 0.25 ± 0.05mm (Type A notch)

Direction of impact

5o 5o

30o ± 1o

R = 1 ± 0.1mm

Figure 6.23: Dimensions of Charpy impact test with support and striking edge for ISO 179

A = 10.16 ± 0.05mmE = 12.7 ± 0.15mm

45o ± 1o

C = 60.3-63.5mm

R = 0.25 ± 0.05mm

Figure 6.24: Dimensions of Charpy impact test specimen ASTM D256

The Izod test evaluates the impact resistance of a cantilevered, notched bending specimenas it is struck by a swinging hammer. Figure 6.25 shows a typical Izod-type impact machine,and Fig. 6.26 shows a detailed view of the specimen, the clamp, and the striking hammer.The standard test method that describes the Izod impact test is also the ASTM-D 256 test.The Izod and Charpy impact tests impose bending loads on the test specimens. For tensile

impact loading one uses the standard tensile impact tests prescribed by tests ISO 8256 andASTM D1822 presented in Table 6.6.


Figure 6.25: Cantilever beam Izod impact machine

Figure 6.26: Schematic of the clamp, specimen, and striking hammer in an Izod impact test


x = 6 ± 0.2mm

b = 10 ± 0.5mm

45o ± 1o

L = 80 ± 2mm

R = 0.25 ± 0.05mm (Type A notch)

Le = 30 ± 2mm

Figure 6.27: Tensile impact specimen (Type 1) for ISO 8256

25.4mm19.05mm

3.18 ± 0.03mm

R=12.7 ± 0.08mm

9.35 or 12.71mm

63.50mm

3.18 ± 0.03mm9.35 or 12.71mm

3.2mm

3.2mm

9.53 ± 0.08mm

27.0mm

R=12.7 ± 0.08mm

Type S

Type L

Figure 6.28: Type S and L tensile impact test specimens (ASTM D1822)

Table 6.6: Standard methods of measuring impact strength (Shastri)

Standard ISO 8256 : 90 D1822 - 93

Specimen 80 mm x 10 mm x 4 mm, cut fromthe center of an ISO 3167 TypeA specimen, with a double notch.Also referred to as an ISO8256Type1 specimen (Fig. 6.27). Type Sor L specimen as specified by thisstandard (Fig. 6.28). 63.50 mmlength x 9.53 or 12.71 mm tab widthx 3.2 mm (preferred thickness).

Type S has a non-linear narrow por-tion width of 3.18 mm, whereasType L has a 9.53 mm length linearnarrow portion width of 3.18 mm.



Standard ISO 8256 : 90 D1822 - 93


At 23 ±2 ◦C and 50 ±5% relative hu-midity for not less than 40h, prior totesting in accordance with PracticeD618, procedure A. Material spec-ification conditioning requirementstake precedence.

Apparatus The machine shall be securely fixedto a foundation having a mass atleast 20 times that of the heaviestpendulum in use and be capable ofbeing leveled.

The base and suspending frame shallbe of sufficiently rigid and massiveconstruction to prevent or minimizeenergy losses to or through the baseand frame.

Pendulums with the specified initialpotential energies shall be used: 2.0,4.0, 7.5, 15.0, 25.0, and 50.0 J.

No pendulums specified

Velocity at impact is 2.6 to 3.2 m/sfor the 2.0 to 4.0 J pendulums and3.4 to 4.1 m/s for pendulums withenergies from 7.5 to 50.0 J.

Velocity at impact is approximately3.444 m/s, based on the verticalheight of fall of the striking nosespecified at 610 ±2 mm.

Free length between grips is 30±2 mm.

Jaw separation is 25.4 mm.

The edges of the serrated grips inclose proximity to the test regionshall have a radius such that they cutacross the edges of the first serra-tions.

The edge of the serrated jaws inclose proximity to the test regionshall have a 0.40 mm radius to breakthe edge of the first serrations.

Unless otherwise specified in therelevant material standard, a mini-mum of ten specimens shall be pre-pared in accordance with that samematerial standard.

Material specification testing condi-tions take precedence; therefore, itis advisable to refer to the materialspecification before using the fol-lowing procedures.

When none exists, or unless oth-erwise specified, specimens shallbe directly compression or injectionmolded in accordance with ISO 293or ISO 294-1.

At least five, preferably 10, sanded,machined, die cut or molded in amold with the dimensions specifiedfor Type S and L specimen.

Test procedures Notches shall be machined in ac-cordance with ISO 2818. The ra-dius of the notch base shall be 1.0±0.02mm, with an angle of 45◦ ±1◦.

Specimens are unnotched.



Standard ISO 8256 : 90 D1822 - 93

Test procedures The two notches shall be at right an-gles to its principal axis on oppo-site sides with a distance betweenthe two notches of 6 ±0.2 mm. Thetwo lines drawn perpendicular tothe length direction of the specimenthrough the apex of each notch shallbe within 0.02 mm of each other.The selected pendulum shall con-sume at least 20%, but notmore than80% of its stored energy in break-ing the specimens. If more than onependulum satisfies these conditions,the pendulum having highest energyis used.

Use the lowest capacity pendulumavailable, unless the impact valuesgo beyond the 85% scale reading.If this occurs, use a higher capacitypendulum.

Run three blank tests to calculatethe mean frictional loss. The lossshould not exceed 1%for a 2.0 J pen-dulum and 0.5% for those specifiedpendulums with a 4.0 J or greaterenergy pendulum.

A friction and windage correc-tion may be applied. A non-mandatory appendix provides thenecessary calculations to determinethe amount of this type of correction.

Determine the energy correction,using Method A or B, before onecan determine the notched tensileimpact strength, En. Method A-Energy correction due to the plas-tic deformation and kinetic energyof the crosshead, Eq Method B-Crosshead-bounce energy, Eb.

The bounce correction factor maybe applied. A non-mandatory ap-pendix provides the necessary cal-culations to determine the amount ofthis correction factor. (A curvemustbe calculated for the cross head andpendulum used before applying inbounce correction factors).

Calculate the notched tensile impactstrength, En by dividing the the cor-rected energy (Method A or B) bythe cross sectional area between thetwo notches.

Calculate the corrected impact en-ergy to break by subtracting the fric-tion and windage correction and/orthe bounce correction factor fromthe scale reading of energy to break.

Values and units Notched tensile impact strength, En

⇒ kJ/m2Tensile-impact energy⇒ J.

Depending on the type of material, the notch tip radius may significantly influence theimpact resistance of the specimen. Figure 6.29 presents impact strengths for various ther-moplastics as a function of notch tip radius. As expected, impact strength is significantlyreducedwith decreasing notch radius. Another factor that influences the impact resistance ofpolymeric materials is the temperature. This is clearly demonstrated in Fig. 6.30, in whichPVC specimens with several notch radii are tested at various temperatures. In addition, theimpact test sometimes brings out brittle failure in materials that undergo a ductile breakagein a short-term tensile test.


Figure 6.29: Impact strength as a function of notch tip radius for various polymers (Kinloch andYoung) [1]

Figure 6.30: Impact strength of PVC as a function of temperature and notch tip radii (Kinloch andYoung) [1]

Similar to a small notch radius, brittle behavior is sometimes developed by lowering thetemperature of the specimen. Figure 6.31 shows the brittle to ductile behavior regimes as afunction of temperature for several thermoplastic polymers.Finally, processing conditions, such as barrel temperature during injection molding or

extrusion and residence time inside the barrel, can also affect the impact properties of aplastic component. Higher processing temperatures as well as longer residence times willhave an adverse effect on impact properties, as depicted for a PA blend in Fig. 6.32.


Figure 6.31: Brittle to ductile behavior regimes as a function of temperature for several thermoplasticpolymers (Crawford) [12]

0

10

20

30

40

50

60

70

80

90

100

-60 -40 -20 0 20 40 60

Test temperature

kJ/m 2

PA- Blend

Ductile

280oC 290oC 300oC 290oC

6 min 6 min 6 min 12 min

Mass temperature

Residence time in barrrel

Brittle fracture

oC

Figure 6.32: Notched impact strength of a PA blend as a function of test temperature, barreltemperature, and barrel residence time

Another impact test worth mentioning is the falling dart test. This test, described by theASTM 3029 andDIN 53 453 standardmethods, is well suited for specimens that are too thinor flexible to be tested using the Charpy and Izod tests, and when the fracture toughness ofa finished product with large surfaces is sought. Figure 6.33 shows a schematic of a typicalfalling dart test set-up.


Figure 6.33: Schematic of a drop weight impact tester


PVC Plastic Pipe Failure

To illustrate impact failure, an analysis was performed on a failed PVC pipe, shownin Fig. 6.34.

Figure 6.34: Photo of a PVC plastic pipe failure


To determine the cause of failure, a variety of standard procedureswere used. Theseare:

• Visual inspection of the failed part• Material evaluation• Structural finite element analysisA visual inspection of the part indicates that this was a brittle failure. Brittle failures,such as this one, occur rapidly,while ductile failures occur over a longer period of time.In this case study, the pipe was in a cold environment when it failed, at a temperaturebelow -5.0◦C. This temperature is low enough that the impact strength is significantlylowered. Any external force or water hammer effect could have caused the pipe to failcatastrophically.Depending on the quantity or type of plasticizer used, the characteristics of PVC

can be dramatically altered to have high impact strength with relatively low hardnessand rigidity. Unplasticized PVC pipes are quite rigid with high strength and goodchemical resistance. These properties make it attractive for use in above or belowground plumbing applications. However, at reduced temperatures the impact strengthof PVC drastically decreases. This means that at low temperatures the ability of PVCto dissipate the energy from a sudden impact is limited and may result in part failure.Figure 6.30 clearly demonstrates how the impact strength of PVC drastically drops atreduced temperatures.One can improve this situation by using a plasticizer that moves the curves in

Fig. 6.30 to the left and gives the part a high impact strength at a much lower tem-perature. However, the gain in one property usually means a compromise of otherproperties, in this case, a loss in stiffness. One additive that is often used to reducecost is calcium carbonate, unfortunately, at a significant reduction of impact strength.A reduction in the calcium carbonate added to the base material will significatly im-prove the impact strength of the PVC pipe.One additive that is often used to reduce cost is calcium carbonate, unfortunately, at

a significant reduction of impact strength. A reduction in the calcium carbonate addedto the base material will significantly improve the impact strength of the PVC pipe.

Figure 6.35: Numerical simulation of the PVC pipe failure

Using PVC properties of the used materials, under the given conditions, a finiteelement analysis was performed. For the analysis the failure of a pipe was simulated


Figure 6.36: Cross section view of the numerical simulation

using an extreme internal pressure as a condition. The simulated failure of the PVCpipe is presented in the Figs. 6.35 and 6.36.


Failure of a Polycarbonate Bottle

In this application, the screw-top of a polycarbonate bottle failed by cracking. Thecrack’s initiation site is an important indicator for the root cause of failure, such as:

• high-stress region or stress concentration point• presence of impurities, air entrapment or voids caused during manufacturing• presence of a knit-line or weld line• indication that the plastic was in contact with a corrosive chemical environment thatmay have led to environmental stress cracking

Analyzing how the crack propagated during failure can help define the mode offailure and consequently the cause of failure:

• brittle or ductile failures• fast or slow crack growth• identification of crack growth direction fatigue crackingSEM (Scanning Electron Microscopy) is used first to perform an in-depth analysis

of the fractured surfaces. This analysis is also known as fractography. A fractographyallows one to locate the initiation site of the crack as well as details about how thecrack propagated during failure.The image presented in Fig. 6.37 is a cross-sectional view of the bottle’s threaded

region taken with an optical stereomicroscope at a magnification of 10. The failed


Figure 6.37: PC bottle threaded region with a magnification of 10

Figure 6.38: SEM of threaded region with a magnification of 50

surface was gold sputter coated to increase the resolution of the fractographyunder theSEM. Figure 6.38 presents a magnification of 50 taken under the SEM. Here, multiplecrackorigins are observed along the inner diameter of the threads. Thematerial exhibitssmooth features typical of brittle fracture. Within the mid-wall there is a significantamount of secondary cracking. At high magnification, presented in Fig. 6.39. witha magnification of 900, the crack surfaces show a significant degree of ondulations.These ondulations are the result of absorption or solvation of constituents from thebottle’s fluid into the part. This fractography analysis points to environmental stresscracking (ESC) failure. The extensive secondary cracking and the evidence of chemicalabsorption suggest that someof the ingredients in thefluidmaybe inherently aggressiveto PC. Contributing factors to the failure are the inherent stress concentration regionsat the root of the threads, and usage of a low molecular weight resin to manufacturethe bottles. It is very likely that the material grade was substituted during productionfor one with a higher melt flow index. A possible reason for substitution is an effort ofthe molder to reduce cost by using a high melt flow index grade that results in lowerpressures and shorter cycles. Lower molecular weight PC grade is more susceptibleto environmental stress cracking, chemical attack and has lower impact properties. Aswe continue the trend of outsourcing,material substitution issues will become a mayorfactor in part and material quality.


Figure 6.39: SEM of threaded region with a magnification of 900

10 40 13010070 160Temperature ( C)o

Dim

ensi

on c

hang

e (

μm)

0

50

-50

Figure 6.40: Thermomechanical analysis (TMA) results

To determine possible contributions of residual stresses in the ESC failure, thermo-mechanical analysis (TMA) tests were conducted on samples in the threaded regionof the bottle. There is always a possibility that an important contributor of stress atthreaded regions are residual stresses that result from themanufacturingprocess. TMAmeasures dimensional change as a function of temperature. High levels of residualstress can appear in the formof an anomalous expansion and contractionof thematerialaround the glass transition temperature. The threaded regions were heated from roomtemperature to 165◦C. A typical TMA is presented in Fig. 6.40. The samples showeda contraction onset near the glass transition temperature with a secondary expansionbefore the final contraction. This secondary expansion is evidence of low level residualstresses. These levels are not sufficient to be amajor contributing factor in the observed


failures. This suggests that some combination of the chemicals and tightening stressesare the more important factors that give rise to the cracking in the threaded region ofthe bottles.


Stress Failure of a Filter Housing

A water filter housing was inspected for failure analysis. The filter’s housing failed atthe bottom, as depicted in Fig. 6.41. The failure appears as a circumferential crackthat separated the bottom of the housing from the rest of the part. The failure led toextensive water damage in the property where it was installed.

Failure

Figure 6.41: Water filter failure

When analyzing the stresses and forces on the filter’s housing during operation, twomain sources of stresses were identified: (1) a stress originating at the threads of thehousing caused by tightening the filter housing to the base, and (2) a stress caused bythe internal water pressure.The later was most likely the cause of failure. A finite element structural analysis

was performed to determine which areas were exposed to high stress due to internal


water pressure. As Fig. 6.42 reveals, the maximum stresses occur at the inner cornerof the bottom cap, the region where the crack originated.

Maximum stress

Figure 6.42: Simulated stress fields in the water filter housing

The situation was further aggravated by processing defects in the part. Furtherinspection of the housing revealed thereweremolding defects andpoormaterialmixingin the region of highest stress. Themolding defects were generated duringmold fillingand they are a source of stress concentrations that can lead to crack initiation. Poormixing during processing leads to material inhomogeneities that weaken the areas ofstress concentrations. The processing defects identified here are contributing factorsthat led to failure of the filter housing

Molding defects

Poor mixing

Figure 6.43: Cross-section of the water filter housing


Analysis of impact data: Although the most common interpretation of impact tests isqualitative, it is possible to use linear elastic fracture mechanics to quantitatively evaluateimpact test results. Using LEFM, it is common to compute the material’s fracture toughnessGIC from impact test results. Obviously, LEFM is only valid if the Izod or Charpy testspecimen is assumed to follow linear elastic behavior and contains a sharp notch.

Ue

(J)

Figure 6.44: Elastic energy absorbed at impact fracture as a function of test specimen cross-sectionalgeometry for a medium-density polyethylene (Plati and Williams) [1]

The Izod or Charpy test specimen absorbs a certain amount of energy,U e, during impact.This energy can be related to the fracture toughness using

Ue = GICtwa, (6.10)

where t and w are the specimens thickness and width, respectively. The parameter a is ageometric crack factor found in Table 6.7 for various Charpy impact test specimens and inTable 6.8 for various Izod impact test specimens. The elastic energy absorbed by the testspecimen during fracture can be represented with energy lost by the pendulum during thetest. This allows the test engineer to relate impact test results with the fracture toughnessof a material. Figure 6.44 contains both Charpy and Izod test result data for a medium-density polyethylene as plots ofUe versus twa with kinetic energy corrections. The fracturetoughness is the slope of the curve.Figure 6.45 compares plots of impact-absorbed energy as a function of twa for unfilled

epoxy and epoxies filled with irregular-shaped silica with weight percents of 55% and 64%.


twã (10-5m2)

GIC=0.44(kJ/m2)

GIC=0.37(kJ/m2)

GIC=0.24(kJ/m2)

filled

Figure 6.45: Impact absorbed energy as a function of specimen size for unfilled epoxy and epoxiesfilled with irregular-shaped silica with weight percents of 55% and 64%

Table 6.7: Charpy impact test geometric crack factors ea2L/w = 4 2L/w = 6 2L/w = 8 2L/w = 10 2L/w = 12

a/w ea0.04 1.681 2.456 3.197 3.904 4.580

0.06 1.183 1.715 2..220 2.700 3.155

0.08 0.933 1.340 1.725 2.089 2.432

0.10 0.781 1.112 1.423 1.716 1.990

0.12 0.680 0.957 1.217 1.461 1.688

0.14 0.605 0.844 1.067 1.274 1.467

0.16 0.550 0.757 0.950 1.130 1.297

0.18 0.505 0.688 0.858 1.015 1.161

0.20 0.468 0.631 0.781 0.921 1.050

0.22 0.438 0.584 0.718 0.842 0.956

0.24 0.413 0.543 0.664 0.775 0.877

0.26 0.391 0.508 0.616 0.716 0.808

0.28 0.371 0.477 0.575 0.665 0.748

0.30 0.354 0.450 0.538 0.619 0.694

0.32 0.339 0.425 0.505 0.578 0.647

0.34 0.324 0.403 0.475 0.542 0.603

0.36 0.311 0.382 0.447 0.508 0.564

0.38 0.299 0.363 0.422 0.477 0.527

0.42 0.276 0.328 0.376 0.421 0.462



2L/w = 4 2L/w = 6 2L/w = 8 2L/w = 10 2L/w = 12a/w ea0.44 0.265 0.311 0.355 0.395 0.433

0.46 0.254 0.296 0.335 0.371 0.405

0.48 0.244 0.281 0.316 0.349 0.379

0.50 0.233 0.267 0.298 0.327 0.355

0.52 0.224 0.253 0.281 0.307 0.332

0.54 0.214 0.240 0.265 0.88 0.310

0.56 0.205 0.228 0.249 0.270 0.290

0.58 0.196 0.216 0.235 0.253 0.271

0.60 0.187 0.205 0.222 0.238 0.253

Table 6.8: Izod impact test geometric crack factors ea2L/w = 4 2L/w = 6 2L/w = 8 2L/w = 10 2L/w = 12

a/w ea0.06 1.540 1.744 1.850 2.040 -

0.08 1.273 1.400 1.485 1.675 1.906

0.10 1.060 1.165 1.230 1.360 1.570

0.12 0.911 1.008 1.056 1.153 1.294

0.14 0.795 0.890 0.932 1.010 1.114

0.16 0.708 0.788 0.830 0.900 0.990

0.18 0.650 0.706 0.741 0.809 0.890

0.20 0.600 0.642 0.670 0.730 0.810

0.22 0.560 0.595 0.614 0.669 0.750

0.24 0.529 0.555 0.572 0.617 0.697

0.26 0.500 0.525 0.538 0.577 0.656

0.28 0.473 0.500 0.510 0.545 0.618

0.30 0.452 0.480 0.489 0.519 0.587

0.32 0.434 0.463 0.470 0.500 0.561

0.34 0.420 0.446 0.454 0.481 0.538

0.36 0.410 0.432 0.440 0.468 0.514

0.38 0.397 0.420 0.430 0.454 0.494

0.40 0.387 0.410 0.420 0.441 0.478

0.42 0.380 0.400 0.411 0.431 0.460

0.44 0.375 0.396 0.402 0.423 0.454



2L/w = 4 2L/w = 6 2L/w = 8 2L/w = 10 2L/w = 12a/w ea0.46 0.369 0.390 0.395 0.415 0.434

0.48 0.364 0.385 0.390 0.408 0.422

0.50 0.360 0.379 0.385 0.399 0.411

Table 6.9 presents values for stress intensity factor and fracture toughness for severalplastics and other materials.

Table 6.9: Values of plane stress intensity factor and strain toughness for various mate-rials

Material KIC (MN/m3/2) GIC(kJ/m2)

ABS 2–4 5

POM 4 1.2–2

EP 0.3–0.5 0.1–0.3

PE-LD 1 6.5

PE-MD and PE-HD 0.5–5 3.5–6.5

PA66 3 0.25–4

PC 1-2.6 5

UPE-glass reinforced 5–7 5–7

PP-co 3–4.5 8

PS 0.7-1.1 0.3-0.8

PMMA 1.1 1.3

PVC-U 1-4 1.3-1.4

Aluminum-alloy 37 20

Glass 0.75 0.01-0.02

Steel-mild 50 12

Steel-alloy 150 107

Wood 0.5 0.12

6.1.3 Creep Behavior

The stress relaxation and the creep test are well-known long-term tests. The stress relaxationtest is difficult to perform and is, therefore, often approximated by data acquired through themore commonly used creep test. The stress relaxation of a polymer is often thought of asthe inverse of creep. The creep test, which can be performed either in shear, compression, ortension, measures the flow of a polymer component under a constant load. It is a commontest that measures the strain, ε, as a function of stress, time, and temperature. Standard creep


tests such as ISO 899, ASTMD2990 and DIN 53 444 can be used. The ISO 899 and ASTMD2990, standard creep tests are presented in Table 6.10.

Table 6.10: Standard methods of measuring tensile creep modulus (Shastri)

Standard ISO 899 - 1 D2990 - 95

Specimen ISO 3167 Type A specimen D 638 Type I specimens may beprepared by injection or compres-sion molding or by machining fromsheets or other fabricated forms.


At 23 ±2 ◦C and 50 ±5% relativehumidity for not less than 40h, priorto testing in accordance with D618Procedure A. The specimens shallbe preconditioned in the test envi-ronment for at least 48 h prior to test-ing. Those materials whose creepproperties are suspected to be af-fected by moisture content shall bebrought to moisture equilibrium ap-propriate to the test conditions priorto testing.

Test procedures Conduct the test in the same atmo-sphere as used for conditioning, un-less otherwise agreed upon by theinterested parties, e.g., for testing atelevated or low temperatures.

For material characterization, selecttwo or more test temperatures tocover the useful temperature range.For simple material comparisons,select the test temperatures from thefollowing: 23, 50, 70, 90, 120, and155 ◦C.

Select appropriate stress levels toproduce data for the application re-quirements. Where it is necessaryto preload the test specimen prior toloading, preloading shall not be ap-plied until the temperature and hu-midity of the test specimen (finallygripped in the testing apparatus) cor-respond to the test conditions, andthe total load (including preload)shall be taken as the test load.

For simple material comparisons,determine the stress to produce 1%strain in 1000 h. Select several loadsto produce strains in the approxi-mate range of 1% strain and plotthe 1000-h isochronous stress-straincurve* from which the stress to pro-duce 1% strain may be determinedby interpolation. * Since only onepoint of an isochronous plot is ob-tained from each creep test, it is usu-ally necessary to run at least threestress levels (preferablymore) to ob-tain an isochronous plot.



Standard ISO 899 - 1 D2990 - 95

For creep testing at a single temper-ature, the minimum number of testspecimens at each stress shall be twoif four or more stress levels are usedor three if fewer than four levels areused.

Unless the elongation is automati-cally and/or continuouslymeasured,record the elongations at the follow-ing time schedule: 1, 3, 6, 12, and30 min; 1, 2, 5, 10, 20, 50, 100, 200,500, 1000 h.

Measure the extension of the speci-mens in accordancewith the approx-imate time schedule: 1, 6, 12, and 30min; 1, 2, 5, 50, 100, 200, 500, 700,and 1000 h.

Units Tensile creep modulus at 1h and ata strain < 0.5%⇒MPaTensile creep modulus at 1000 h andat a strain < 0.5%⇒MPa

Tensile creep modulus in MPa plot-ted vs. time in h.

0

2

4

6

1 10 100 1000 10000

35

31.5

28

24.5

21

17.5

14

10.5

7

3.5

h

T = 23 oC

Time

Stressin MPa

%

100 101 102 103 104

Figure 6.46: Creep response of a PBT at 23 ◦C

Figure 6.46 presents the creep responses of a polybutylene teraphthalate for a range ofstresses in a graphwith a log scale for time. When plotting creep data in a log-log graph,in themajority of the cases, the creep curves reduce to straight lines as shown for polypropylenein Fig. 6.47. Hence, the creep behavior of most polymers can be approximated with a


Figure 6.47: Creep response of a polypropylene plotted on a log-log scale

Power - law model, sometimes referred to as the Norton model, represented by

ε(t) = k(T )σntm, (6.11)

where k, n andm are material-dependent properties.

Isochronous and isometric creep curves: Typical creep test data, as shown inFig. 6.46, can be manipulated to be displayed as short-term stress-strain tests or as stress re-laxation tests. Thesemanipulated creep-test-data curves are called isochronous and isometricgraphs.

0

10

20

30

40

0 2 4 6

1 h 10 h 100 h

1000 h

10000 h

MPa

T= 23 oC

%

Strain

Figure 6.48: Isochronous stress-strain curves for the PBT at 23◦Ccreep responses shown in Fig. 6.46

An isochronous plot of the creep data is generated by cutting sections through the creepcurves at constant times and plotting the stress as a function of strain. The isochronous


curves of the creep data displayed in Fig. 6.46 are presented in Fig. 6.48 [8]. Similar curvescan also be generated by performing a series of short creep tests, where a specimen is loadedat a specific stress for a short period of time, typically around 100 s [6]. The load is thenremoved, and the specimen is allowed to relax for a period of 4 times greater than the timeof the creep test. The specimen is then reloaded at a different stress, and the test is repeateduntil a sufficient number of points exist to plot an isochronous graph.

hTime

100 101 102 103 104

0

30

20

10

ε0=2%

ε0=1%

ε0=0.5%

Str

ess

(M

Pa)

Figure 6.49: Isometric stress-time curves for the PBT at 23 ◦C creep responses shown in Fig. 6.46

This procedure is less time-consuming than the regular creep test and is often used topredict the short-term behavior of polymers. However, it should be pointed out that theshort-term tests described in the previous section are more accurate, less time consuming,and cheaper to perform. The isometric or "equal size" plots of the creep data are generatedby taking constant strain sections of the creep curves and by plotting the stress as a functionof time. Isometric curves of the polypropylene creep data presented in Fig. 6.46 are shownin Fig. 6.49 [8].Creep data can sometimes be presented in terms of secant creep modulus. For this, the

data can be generated for a given stress as presented in Fig. 6.50.For specific applications, plastics should also be tested at higher temperatures. To fur-

ther illustrate the effect temperature has on the mechanical behavior of thermoplastics, Figs.6.51 and 6.52 present 1000 h isochronous curves for a selected number of thermoplsticsat 23 ◦C and 60 ◦C, respectively. Creep of thermoplastic polymers can be mitigated bythe use of fiber-reinforcements. Figures 6.53 and 6.54 show 1000 h isochronous curves forfiber-reinforced thermoplastics at 23 ◦C and 60◦C, respectively.


400

800

1200

1600

2000

2400

1 10 100 1000 10000

Time

MPa

h

T= 23 oC

Stress (MPa)

5

10

15

20

25

100 101 102 103 104

Figure 6.50: Secant creep modulus curves as a function of time for the PBT at 23◦C creep responsesshown in Fig. 6.46

0

15

30

45

0 2 4 6

Shear Strain

%

MpaPES

SAN

PA 66

ABS

PBT PA 6

PA 12POM

Figure 6.51: Isochronous (1000 h) stress-strain curves for selected thermoplastics at 23 ◦C


0

15

30

45

0 1.5 3 4.5

PES

PA 66

SAN

ABS PA 6

PBTPOM

%

MPa

Strain

Figure 6.52: Isochronous (1000 h) stress-strain curves for selected thermoplastics at 60 ◦C

0

30

60

90

0 1 2 3

Strain

MPaPES

PSU

POMPA 66

PA 12PA 6

%

Figure 6.53: Isochronous (1000h) stress-strain curves for various fiber-reinforced (25–35volume%)thermoplastics at 23◦C


0

25

50

75

0 1 2 3

MPa PSU

PBT

POM

PA 66

PA 6

%

Strain

Figure 6.54: Isochronous (1000h) stress-strain curves for various fiber-reinforced (25–35 volume%)thermoplastics at 60 ◦C


Demolding a Safety Cap without Rupturing the Safety Seal

In this case study, an injection molder had extreme difficulties removing a safety capfrom the injectionmoldwithout damaging the safety seal. Furthermore, the safety sealin those caps that were not damaged during demolding, did not break the first time thebottle was opened, as they should have.The cap undergoes the samemode of deformationduring demolding as it doeswhen

the bottle is opened for the first time. The purpose of this analysis is to determine ifboth requirements, not breaking during demolding, and breaking the first time thebottle is opened, can be fullfilled. A solution to the problemmay involve a decision ofmodifying, or not, the mold geometry, as well as adjusting the processing conditionsduring the injection molding process.The geometry of the cap, cap on the bottle, cap in the mold and demolding of the

cap are all presented in Fig. 6.55. As presented in Fig. 6.55 (c) and (d), the safetyseal must jump over the barrier ring inside the mold cavity. During this demolding,the threads that support the safety ring must sustain the axial forces generated duringdemolding. On the other hand, the threads that support the safety ring must breakwhen removing the cap from the bottle (Fig. 6.55(b)).In a simplified form the cap-mold and cap-bottle assembly is shown in Fig. 6.56.

The radial force caused by the pressure required to open the ring enough to slide overthe barrier ring, or over the screw top of the bottle can be calculated using


Cap in the mold Demolding process

Cap on the bottleCap geometry

Figure 6.55: Geometry of the cap inside the mold and on the bottle top.

Fr = kED2i ε (6.12)

where, ε = ΔD/Daverage

whereΔD = Dext − Di. The factor k is given by

k =π(DExt/Di − 1)

√(DExt/Di)2 − 1

5(DExt/Di)2(1 − ν) + 5 + 5ν(6.13)

The radial force is magnified to an axial force, Fa, by the friction μ and the angle αusing

Fa = Frη (6.14)

where, η is the magnification factor presented in Fig. 6.57 and given by

η =Fa

Fr=

μ + tanα

1 − μ tan α(6.15)

The critical factor here is the modulus,E, of the material at the demolding temper-ature and at room temperature when opening the bottle. The moduli were calculated


Di

DExt

Fa

Fa

b

α

Dext

Figure 6.56: Simplified geometry of the cap during removal/demolding.

from the 2% secant strain using the 1 hour isochronous stress-strain curves given inFig. 6.58 for various temperatures.The cap removal forces where calculated using the above equations and the stress-

strain curves for the material. These forces were compared to the forces required tobreak the seal. Figure 6.59 presents these results with the dimensions used for thecalculations. The coefficient of friction for the cap removal from the bottle was takenas 0.5, and for the demolding as 0.45, 0.42 and 0.4, for 20, 40 and 60 ◦C, respectively.The results reveal that for demolding the cap the mold temperature must be as high

as possible, where the stresses generated during demolding are lower than the forcesrequired to break the seal. A higher mold temperature will also lead to higher degreeof crystallinity, which will contribute to additional ring shrinkage, resulting in higherforces when removing the cap from the bottle.

Creep Rupture: During creep, a loaded polymer component will gradually increase inlength until fracture or failure occurs. This phenomenon is usually referred to as creeprupture or, sometimes, as static fatigue. During creep, a component is loaded under aconstant stress, constantly straining until the material cannot withstand further deformation,causing it to rupture. At high stresses, the rupture occurs sooner than at lower stresses.However, at low enough stresses, failure may never occur. The time it takes for a componentor test specimen to fail depends on temperature, load, manufacturing process, environment,etc. It is important to point out that damage is often present and visible before creep rupture


μ=0.8 00.20.40.6

0o 10o 90o80o70o60o50o40o30o20o

0

8

7

6

5

4

3

2

1

Mag

nific

atio

n fa

ctor

, η

Assembly or disassembly angle, α

Figure 6.57: Force magnification factor as a function of assembly or disassembly angle for variouscoefficients of friction.

10

8

0

2

4

6

210 3

Strain, %

Str

ess,

MP

a

23oC40oC

60oC

1 hour isochronous curves

Figure 6.58: Isochronous stress-strain curves for PE-HD at various temperatures.

occurs. This is clearly demonstrated in Fig. 6.60, which presents isochronous creep curvesfor polymethyl methacrylate at three different temperatures. The regions of linear and non-linear viscoelasticity and of visual damage are highlighted in the figure.The standard test to measure creep rupture is the same as the creep test. Results from

creep rupture tests are usually presented in graphs of applied stress versus the logarithm of


500

0

100

200

300

400

20 6040

Temperature, oC

For

ce, N

Forces during ejection

Forces to break the seal during ejection

Forces to break the seal when opening bottle

Forces during opening of bottle

Inside mold On bottle48.1 mm 47.6 mm49.8 mm 48.1 mm50.4 mm 50.4 mm

DiDextDExt

Figure 6.59: Calculated results

(MP

a)

Figure 6.60: Isochronous creep curves for PMMA at three different temperatures (Menges) [1]

time to rupture. An example of a creep rupture test that ran for 10 years is shown in Fig. 6.61.Here, the creep rupture of high-density polyethylene pipes under internal pressurewas testedat different temperatures. Two general regions with different slopes become obvious in theplots. The points to the left of the knee represent pipes that underwent a ductile failure,whereas those points to the right represent the pipes that had a brittle failure. As pointedout, generating a graph such as the one presented in Fig. 6.61, is an extremely involved andlengthy task that takes several years of testing1. Figures 6.62 and 6.63 compare the staticfatigue or creep rupture life curves of several thermoplastics at 20 ◦C and 60 ◦C, respectively.Since these tests are so time consuming, they are usually only carried out to 1,000h (6weeks)and in some cases to 10,000 h (60 weeks). Once the steeper slope, which is typical of thebrittle fracture, has been reached, the line can be extrapolatedwith some degree of confidenceto estimate values of creep rupture at future times.

1These tests were done between 1958 and 1968 at Hoechst AG, Germany.


20.01 1 100 10000 1000000

Time to failure (hrs)

4

6

8

20

80oC 65oC 50oC 35oC 20oC

10

10-2 100 102 104 106

Figure 6.61: Creep rupture behavior for a high-density polyethylene (Gaube and Kausch) [1]

0.1 1 10 100 1000 10000 100000 1000000

PVC-C PVDF

PVC-U

ABS

POM

PB

PP-H

PP-Cop

PE-HD

PE-HD (Type 2) PE-X

MPa

6

12.5

1520

30

40

60

8

10

h

Time to fail1 10 50 Years

20 oC

Figure 6.62: Creep rupture behavior of a several thermoplastics at 20 ◦C

Although the creep test is considered a long-term test, in principle it is difficult to actuallydistinguish it from monotonic stress strain tests or even impact tests. In fact, one can plotthe full behavior of the material, from impact to creep, on the same graph as shown forPMMA under tensile loads at room temperature in Fig. 6.64. The figure represents strainas a function of the logarithm of time. The strain line that represents rupture is denoted byεB . This line represents the maximum attainable strain before failure as a function of time.Obviously, a material tested under an impact tensile loading will strain much less than the


0.1 1 10 100 1000 10000 100000 1000000

60 oC

PVDF

PVC-C

PBPVC-U

ABSPOM

PP-H

PE-X

PP-Cop

PE-HD

Time to fail

PE-HD (Type 2)

101 50 Years

h

MPa

8

10

15

20

30

40

2

6

Figure 6.63: Creep rupture behavior of a several thermoplastics at 60 ◦C

Figure 6.64: Plot of material behavior at room temperature from impact to creep for a PMMA undertensile loads (Menges) [1]

same material tested in a creep test. Of interest in Fig. 6.64 are the two constant stress linesdenoted by σ1 and σ2. For example, it can be seen that a PMMA specimen loaded to ahypothetical stress of σ1 will behave as a linear viscoelastic material up to a strain of 1%, atwhich point the first microcracks start forming or the craze nucleation begins. The crazingappears a little later after the specimen’s deformation is slightly over 2%. The test specimencontinues to strain for the next 100 h until it ruptures at a strain of about 8%. From the figureit can be deduced that the first signs of crazing can occur days and perhaps months or yearsbefore the material actually fractures. The stress line denoted by σ 2, where σ1 > σ2, is alimiting stress under which the component will not craze. Figure 6.64 also demonstratesthat a component loaded at high speeds (i.e., impact) will craze and fail at the same strain.A limiting strain of 2.2% is shown. Because these tests take a long time to perform, it isoften useful to test the material at higher temperatures, where a similar behavior occurs in ashorter period of time.


Figure 6.65 shows tests performed on PMMA samples at five different temperatures.When comparing the results in Fig. 6.65 to the curve presented in Fig. 6.64, a clear time-temperature superposition becomes visible. In the applied stress versus logarithm of timeto rupture curves, such as the one shown in Fig. 6.61, the time-temperature superposition isalso evident.

Figure 6.65: Strain at fracture for a PMMA in creep tests at various temperatures (Menges) [1]


Rupture of Water Filled Polyethylene Balls in Ethylene Glycol

Water filled high density polyethylene balls packed in an ethylene glycol filled storagetower formpart of an air conditioning system. Only threemonths after the constructionof the cooling tower, the polyethylene balls started failing.Figure 6.66 presents the original balls, one ball that was infiltrated by ethylene

glycol, and a ball that had cracked and lost the water to the tank.

New Ball Ball permeated with ethylene glycol Cracked ball

Figure 6.66: Photographs of the polyethylene balls


Loads and thickness distribution FEM results9.5 MPa

Figure 6.67: Load case with thickness distribution and FEM calculated stress field

20.01 1 100 10000 1000000

4

6

8

20

80o C 65oC 50oC 35oC 20oC

10

10-2 100 102 104 106

10 monthsTime to failure (hrs)

Figure 6.68: Creep rupture curves for PE-HD

Since the balls are lighter than the ethylene glycol, and the buoyancy forces wereknown, it was possible to calculate the forces acting on the the balls located at the topof the tank. A sample load case with thickness distribution (left) and stress field (right)is presented in Fig. 6.67. A secant modulus of a 1 year isochronous curve was used inthe FEM calculations.


As can be seen, the highest stresses of 9.8MPa, occurred at the edge of the dimples,the same location where the cracks occurred. It is important to point out here that theultimate stress of comparable polyethylene materials, measured using ASTM D638standardized tests, was 18MPa. However,when comparing the 9.8MPa stress to creeprupture data for PE-HD, presented in Fig. 6.68, it can be seen that the balls will fail atabout 10 months. As is presented in the Industrial Application 8.2 in Chapter 8, theballs were subjected to environmental stress cracking, accelerating the failure from 10months to only 3 months.

6.1.4 Dynamic Mechanical Tests

Figure 6.69: Schematic diagram of the torsion pendulum test equipment

The simplest dynamic mechanical test is the torsion pendulum. The standard procedurefor the torsional pendulum, shown schematically in Fig. 6.69 [15], is described in DIN 53445andASTMD2236. The technique is applicable to virtually all plastics, through a wide rangeof temperatures; from the temperature of liquid nitrogen, -180 ◦C, to 50 − 80 ◦C above theglass transition temperature in amorphous thermoplastics and up to the melting temperaturein semicrystalline thermoplastics. With thermoset polymers one can apply torsional tests upto the degradation temperatures of the material.The torsion pendulumapparatus consist of an inertiawheel, grips, and the specimen containedin a temperature-controlled chamber. The rectangular test specimen can be cut from apolymer sheet or part, or it can be made by injection molding. To execute the test, the inertiawheel is deflected, then released and allowed to oscillate freely. The angular displacementor twist of the specimen is recorded over time. The frequency of the oscillations is directlyrelated to the elastic shear modulus of the specimen, G ′, and the decay of the amplitudeis related to the damping or logarithmic decrement, Δ, of the material. The elastic shearmodulus (in Pascals) can be computed using the relation

G′ =6.4π2ILf2

μbt3, (6.16)


where I is the polar moment of inertia (g/cm2), L the specimen length (cm), f the frequency(Hz), b the width of the specimen, t the thickness of the specimen, and μ a shape factor thatdepends on the width-to-thickness ratio. Values of μ vary between 5.0 for b/t = 10 and5.333 for b/t = inf [16]. The logarithmic decrement can be computed using

Δ = Ln

(An

An+1

), (6.17)

whereAn represents the amplitude of the nth oscillation.2Although the elastic shearmodulus,G′, and the logarithmic decrement,Δ, are sufficient to characterize a material, one can alsocompute the loss modulusG′′ by using

G′′ =(

G′Δπ

). (6.18)

The logarithmic decrement can also be written in terms of loss tangent, tanδ, where δ is theout-of-phase angle between the strain and stress responses. The loss tangent is defined as

tanδ =G′′

G′ =Δπ

. (6.19)

Because the frequency in the torsional pendulum test depends on the stiffness of thematerial under consideration, the test’s rate of deformation is also material dependent, andcan therefore not be controlled. To overcome this problem, the dynamicmechanical analysis(DM) test, or sinusoidal oscillatory test was developed. In the sinusoidal oscillatory test,a specimen is excited with a predetermined low-frequency stress input, which is recordedalong with the strain response. The shapes of the test specimen and the testing procedurevary significantly from test to test. The various tests and their corresponding specimens aredescribed by ASTM D4065 and the terminology, such as the one already used in the aboveequations, is described by ASTMD4092. If the test specimen in a sinusoidal oscillatory testis perfectly elastic, the stress input and strain response would be in phase, as

τ(t) = τ0 = sin ωt (6.20)

andγ(t) = γ0 = sin ωt. (6.21)

For an ideally viscous test specimen, the strain response would lag π/2 radians behindthe stress input as,

γ(t) = γ0 = sin(

ωt +π

2

). (6.22)

Polymers behave somewhere in between the perfectly elastic and the perfectly viscousmaterials and their response is described by

γ(t) = γ0 = sin ( ωt + δ) . (6.23)

2WhenΔ > 1, a correction factor must be used to compute G′.


The shear modulus takes a complex form of

G∗ =τ(t)γ(t)

=τ0

γ0(cos δ + i sin δ) = G′ + G′′, (6.24)

which is graphically represented in Fig. 6.70. G ′ is usually referred to as storage modulusandG′′ as loss modulus. The ratio of loss modulus to storage modulus is referred to as losstangent.

Figure 6.70: Vector representation of the complex shear modulus

Figure 6.71 [1] shows the elastic shearmodulus and the loss tangent for various polypropy-lene grades. In the graph, the glass transition temperatures and the melting temperatures canbe seen. The vertical scale in plots such as Fig. 6.71 is usually a logarithmic scale. However,a linear scale better describes themechanical behavior of polymers in design aspects. Figures6.72 to 6.75 [1] present the elastic shear modulus on a linear scale for several thermoplasticpolymers as a function of temperature. The shear modulus of high temperature applicationplastics are presented in Fig. 6.76.

Figure 6.71: Elastic shear modulus and loss factor for various polypropylene grades


0

200

400

600

800

1000

1200

1400

1600

-40 -20 0 20 40 60 80 100 120 140 160 180 200 220

PS

SANPMP

SBPE-HD

PB

PE-LD

EVAC

Temperature

oC

MPa

Figure 6.72: Elastic shear modulus for several thermoplastics

0

200

400

600

800

1000

1200

1400

-40 -20 0 20 40 60 80 100 120 140 160 180 200 220

Temperature

oC

PBT PET

PC+ABS

PPE+PSPC

PSU

PPE

MPa



0

200

400

600

800

1000

1200

1400

1600

-100 -50 0 50 100 150 200 250

Temperature

PA 12

PA 610

PA 6

PA 66

oC

MPa


0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

-150 -100 -50 0 50 100 150 200 250

POM

PPS

PAR 25

PK

PAR 15PES

PEI

Temperature

oC

MPa



0

200

400

600

800

1000

1200

100 150 200 250 300 350

PES

PSO

PC

PAEK

Temperature

MPa

oC

Figure 6.76: Elastic shear modulus for several high-temperature application thermoplastics

6.1.5 Fatigue Tests

Dynamic loading of any material that leads to failure after a certain number of cycles iscalled fatigue or dynamic fatigue. Dynamic fatigue is of extreme importance since a cyclicor fluctuating load will cause a component to fail at much lower stresses than it does undermonotonic loads. Fatigue testing results are plotted as stress amplitude versus number ofcycles to failure. These graphs are usually called S-N curves, a term inherited from metalfatigue testing. Figure 6.77 presents S-N curves for several thermoplastic and thermosetpolymers tested at a 30-Hz frequency and at about a zero mean stress, σ m.

Figure 6.77: Stress-life (S-N) curves for several thermoplastic and thermoset polymers tested at a30-Hz frequency at about a zero mean stress (Riddell)


Figure 6.78: Temperature rise during uniaxial cyclic loading under various stresses at 5 Hz(Crawford) [12]

We must point out here that most fatigue data presented in the literature and in resinsupplier data sheets do not present the frequency, specimen geometry, or environmentalconditions at which the tests were performed. Hence, such data are not suitable for usein design. The data we present in this section are only intended to illustrate the variousproblems that arise when measuring fatigue life of a polymer. The information shouldalso serve to reflect trends and as a comparison between various materials and conditions.Fatigue in plastics is strongly dependent on the environment, the temperature, the frequencyof loading, the surface, etc. For example, surface irregularities and scratches make crackinitiation at the surface more likely in a polymer component that has been machined thanin one that was injection molded. An injection molded article is formed by several layersof different orientation. In such parts, the outer layers act as a protective skin that inhibitscrack initiation. In an injection molded article, cracks are more likely to be initiated insidethe component by defects such as weld lines and filler particles. The gate region is alsoa prime initiator of fatigue cracks. Corrosive environments also accelerate crack initiationand failure caused by fatigue. Corrosive environments and weathering will be discussed inmore detail later in this chapter. It is interesting to point out in Fig. 6.77 that thermosetpolymers show a higher fatigue strength than thermoplastics. An obvious cause for this istheir greater rigidity. However, more important is the lower internal damping or friction,which reduces temperature rise during testing. Temperature rise during testing is one of themain factors leading to failure when experimentally testing thermoplastic polymers undercyclic loads. The heat generation during testing is caused by the combination of internalfrictional or hysteretic heating and low thermal conductivity. At a low frequency and lowstress level, the temperature inside the polymer specimen will rise and eventually reachthermal equilibrium when the heat generated by hysteretic heating equals the heat removedfrom the specimen by conduction. As the frequency is increased, viscous heat is generatedfaster, causing the temperature to rise even further. This phenomenon is shown in Fig. 6.78,in which the temperature rise during uniaxial cyclic testing of polyacetal is plotted. Afterthermal equilibrium has been reached, a specimen eventually fails by conventional brittlefatigue, assuming the stress is above the endurance limit.However, if the frequency or stress level is increased even further, the temperature will

rise to the point at which the test specimen softens and ruptures before reaching thermal


Figure 6.79: Fatigue and thermal failures in acetal tested at 1.67 Hz (Crawford) [12]

Figure 6.80: Fatigue and thermal failures in acetal tested at various frequencies (Crawford) [12]

equilibrium. This mode of failure is usually referred to as thermal fatigue. This effectis clearly demonstrated in Fig. 6.79. The points marked T denote those specimens thatfailed because of thermal fatigue. The other points represent the specimens that failed byconventional mechanical fatigue. A better picture of how frequency plays a significant rolein fatigue testing of polymeric materials is generated by plotting results such as those shownin Fig. 6.79 for several frequencies (Fig. 6.80). The temperature rise in the componentdepends on the geometry and size of test specimen. For example, thicker specimens willcool slower and are less likely to reach thermal equilibrium. Similarly, material around astress concentrator will be subjected to higher stresses that will result in temperatures higherthan the rest of the specimen, leading to crack initiation caused by localized thermal fatigue.To neglect the effect of thermal fatigue, cyclic tests with polymersmust be performed at verylow frequencies that make them much lengthier than those performed with metals and othermaterials exhibit high thermal conductivity.


32

36

40

44

48

1000 10000 100000 1000000 10000000

48oC

46oC

58oC

21Hz

53oC64oC

7Hz

54oC

50oC

28Hz 7Hz

7Hz

54oC

52oC

46oC3Hz

37oC 30oC

25oC

28oC

56oC 74oC

≈≈

≈

σU = 1 N/mm 2

7Hz

Cycles to failure

N/mm 2

103 104 105 106 107

Figure 6.81: Fatigue curves for a glass fiber-reinforced PA6 tested with three different imposedstress cycles (23 ◦C)

It is important to understand that although most fatigue data curves state the testingtemperature, the resultant data points all have their corresponding temperature at failure.For example, the curves presented in Fig. 6.81 were tested at 23 ◦C; however, each specimenfailed at a different temperature. The curves also illustrate how the shape of the imposedstress cycles affect the fatigue life of the polymer.Stress concentrations have a great impact on the fatigue life of a component. Figures 6.82

and 6.83 compare S-N curves for PVC-U and PA 66, respectively, for specimens with andwithout a 3-mm circular hole acting as a stress concentrator. Material irregularities causedby filler particles or by weld lines also affect the fatigue of a component. Figures 6.84 and6.85 compare S-N curves for regular PC and ABS test specimens to fatigue behavior ofspecimens with a weld line and specimens with a 3-mm circular hole.The previous fatigue graphs pertained to tests with zero mean stress, σm. However, many

polymer components subjected to cyclic loading have other loads and stresses applied tothem, leading to non-zero mean stress values. This superposition of two types of loadingwill lead to a combination of creep, caused by the mean stress, and fatigue, caused by thecyclic stress, σa. Test results from experiments with cyclic loading and non-zero meanstresses are complicated by the fact that some specimens fail because of creep and othersbecause of conventional brittle fatigue. Figure 6.86 illustrates this phenomenon for both caseswith and without thermal fatigue, comparing them to experiments in which a simple staticloading is applied. For caseswith two ormore dynamic loadingswith different stress or strainamplitudes, a similar strain deformation progression is observed. The strain progression,Δε, is the added creep per cycle caused by different loadings, similar to ratcheting effects inmetal components where different loadings are combined.Fiber-reinforced composite polymers are stiffer and less susceptible to fatigue failure.

Reinforced plastics have also been found to exhibit lower hysteretic heating effects, making


Figure 6.82: Fatigue curves for a PVC-U using specimens with and without 3-mm hole stressconcentrators tested at 23 ◦C and 7 Hz with a zero mean stress

Figure 6.83: Fatigue curves for a PA66 using specimens with and without 3-mm hole stressconcentrators tested at 23 ◦C and 7 Hz with a zero mean stress

Figure 6.84: Fatigue curves for a PC using regular specimens and specimens with 3-mm hole stressconcentrators and weldlines tested at 23 ◦C and 7 Hz with a zero mean stress


Figure 6.85: Fatigue curves for ABS (Novodur PH/AT) using regular specimens and specimenswith 3-mm hole stress concentrators and weldlines tested at 23 ◦C and 7 Hz with a zero mean stress

Figure 6.86: Creep and thermal fatigue effects during cyclic loading


them less likely to fail by thermal fatigue. Figure 6.87 presents the flexural fatigue behaviorfor glass fiber-filled and unfilled PA66 tested at 20 ◦C and a 0.5 Hz frequency with a zeromean stress. Parallel to the fiber orientation, the fatigue life was greater than the life ofthe specimens tested perpendicular to the orientation direction and the unfilled materialspecimens.

Figure 6.87: Flexural fatigue curves for a PA66 and a glass fiber-filled polyamide 66 tested at 20 ◦Cand 0.5 Hz with a zero mean stress (Bucknall, Gotham and Vincent) [1]

The fatigue life of the unfilled specimen and the behavior perpendicular to the orien-tation direction were similar. However, the unfilled material failed by thermal fatigue athigh stresses, whereas both the specimens tested perpendicular and parallel to the orienta-tion direction failed by conventional fatigue at high stress levels. Fiber-reinforced systemsgenerally follow a sequence of events during failure consisting of debonding, cracking, andseparation.

Figure 6.88: Fatigue curves for a glass-filled polyester mat tested at 20 ◦C and a frequency of1.67 Hz (Hertzberg and Mason) [1]

Figure 6.88 clearly demonstrates this sequence of events with a glass-filled polyester mattested at 20 ◦C and a frequency of 1.67 Hz. In most composites, debonding occurs after


Figure 6.89: Fatigue curves for a 50% by weight glass fiber-reinforced polyester resin sheet moldingcompound tested at 23 ◦C and 93 ◦C and 10 Hz (Denton) [1]

just a few cycles. It should be pointed out that reinforced polymer composites often donot exhibit an endurance limit, making it necessary to use factors of safety between 3 and4. The fracture by fatigue is generally preceded by cracking of the matrix material, whichgives a visual warning of imminent failure. It is important to mention that the fatigue life ofthermoset composites is also affected by temperature. Figure 6.89 shows the tensile strengthversus number of cycles to failure for a 50% glass fiber-filled unsaturated polyester tested at23 ◦C and 93 ◦C. At ambient temperature, the material exhibits an endurance limit of about65 MPa, which is reduced to 52 MPa at 93 ◦C.

6.1.6 Strength Stability Under Heat

Polymers soften and eventually flow as they are heated. It is, therefore, important to knowwhat the limiting temperatures are at which a polymer component can still be loaded withmoderate deformations. Figure 6.90 presents the shear modulus as a function of temperaturefor various thermoplastics with the region of maximum temperature.Three tests are commonly performed on polymer specimens to determine this limiting

temperature for a specific material. They are the Vicat temperature test (ISO 306, ASTMD648, and DIN 53460), shown in Fig. 6.91, the heat-distortion temperature (HDT) test (ISO75 and ASTM D648) shown in Fig. 6.92 and the Martens temperature test (DIN 53458or 53462). In the Vicat temperature test, a needle loaded with weights is pushed againsta plastic specimen inside a glycol bath. This is shown schematically in Fig. 6.91. Theuniformly heated glycol bath rises in temperature during the test. The Vicat number orVicat temperature is measured when the needle has penetrated the polymer by 1 mm. Theadvantage of this test method is that the test results are not influenced by the part geometry


0

500

1000

1500

2000

2500

0 50 100 150 200 250

PC-GF30

PBT

PA 6-GF 30

PA6

PC

oC

Temperature

MartensVicat BISO 75/AUpper limit of acceptable temperature

N/mm2

Figure 6.90: Shear modulus as a function of temperature for several thermoplastics

or manufacturing technique. The practical limit for thermoplastics, such that the finishedpart does not deform under its own weight, lies around 15K below the Vicat temperature. Todetermine the heat distortion temperature, the standard specimen lies in a fluid bath on twoknife edges separated by a 10-cm distance. A bending force is applied on the center of thespecimen. The standard Vicat temperature tests ISO 306 and ASTM D648 are presented inTable 6.11.

Figure 6.91: Apparatus to determine a material’s shape stability under heat using the Vicattemperature test


Table 6.11: Standard methods of measuring vicat softening temperature (Shastri)


Specimen 10mmx10mmx4mmfrommiddleregion of the ISO3167multipurposetest specimen.

Use at least two specimens to testeach sample. The specimen shall beflat, between 3 and 6.5 mm thick,and at least 10 mm x 10 mm in area,or 10 mm in diameter.


If conditioning of the test specimensis required, then condition at 23 ◦C±2 ◦C and 50 ±5% relative humidityfor no less than 40 h prior to test-ing in accordance with Test MethodD618.

Apparatus The indenting tip shall preferablybe of hardened steel 3 mm long,of circular cross section 1.000±0.015 mm2 fixed at the bottom ofthe rod. The lower surface of theindenting tip shall be plane and per-pendicular to the axis of the rod andfree from burrs.

A flat-tipped hardened steel needlewith a cross-sectional area of 1.000±0.015mm2 shall be used. The nee-dle shall protrud at least 2 mm fromthe end of the loading rod.

Heating bath containing a suitableliquid (e.g., liquid paraffin, glycerol,transformer oil, and silicone oil) thatis stable at the temperature used anddoes not affect the material undertest (e.g., swelling or cracking) inwhich the test specimen can be im-mersed to a depth of at least 35 mmis used. An efficient stirrer shall beprovided.

Immersion bath containing the heattransfer medium (e.g., silicone oil,glycerine, ethylene glycol, and min-eral oil) that will allow the spec-imens to be submerged at least35 mm below the surface.

Test procedures At least two specimens to test eachsample.

Use at least two specimens to testeach sample. Molding conditionsshall be in accordance with theapplicable material specification orshould be agreed upon by the coop-erating laboratories.




Specimens tested flatwise.The temperature of the heatingequipment should be 20 to 23 ◦C atthe start of each test, unless previoustests have shown that, for the mate-rial under test, no error is caused bystarting at another temperature.

Specimens tested flatwise.The bath temperature shall be 20 to23 ◦C at the start of the test unlessprevious tests have shown that, fora particular material, no error is in-troduced by starting at a higher tem-perature.

Mount the test specimen horizon-tally under the indenting tip of theunloaded rod. The indenting tipshall at no point be nearer than 3mmto the edge of the test specimen.

Place the specimen on the supportso that it is approximately centeredunder the needle. The needle shouldnot be nearer than 3 mm to the edgeof the test specimen.

Put the assembly in the heatingequipment.

Lower the needle rod (without extraload) and then lower the assemblyinto the bath.

After 5 min, with the indenting tipstill in position, add the weights tothe load carrying plate so that thetotal thrust on the test specimen is50 ±1 N.

Apply the extra mass required to in-crease the load on the specimen to10 ±0.2 N (Loading 1) or 50 ±1.0 N(Loading 2)

Set the micrometer dial-gauge read-ing to zero.

After waiting five minutes, set thepenetration indicator to zero.

Increase the temperature of the heat-ing equipment at a uniform rate:Heating rate⇒ 50 ±5 ◦C /h

Start the temperature rise at one ofthese rates:50±5 ◦C /h (RateA) or 120±12 ◦C/h(Rate B) The rate selection shall beagreed upon by the interested par-ties.

Note the temperature at which theindenting tip has penetrated intothe test specimen by 1 ±0.01 mmbeyond the starting position, andrecord it as the Vicat softening tem-perature of the test specimen.

Record the temperature at which thepenetration depth is 1 mm. If therange of the temperatures recordedfor each specimen exceeds 2 ◦C ,then record the individual tempera-tures and rerun the test.

Values and units Vicat softening temperature⇒ ◦C Vicat softening temperature⇒ ◦C

Similar to the Vicat temperature test, the bath’s temperature is increased during the test.The HDT is the temperature at which the rod has bent 0.2 to 0.3 mm (see Fig. 6.92). TheVicat temperature is relatively independent of the shape and type of part, whereas the heat-distortion data are influenced by the shaping and pretreatment of the test sample.Figure 6.93 presents the heat distortion temperature for selected thermoplastics and ther-

mosets as a function of bending stress, measured using ISO 75, and Table 6.12 presents HDTfor selected thermoplastics measured using ASTM D648. The standard HDT tests ISO 75and ASTM D648 are presented in Table 6.13.


Figure 6.92: Apparatus to determine a material’s shape stability under heat using the heat-distortiontemperature test (HDT)

In the Martens temperature test, the temperature at which a cantilevered beam has bent6 mm is recorded. The test sample is placed in a convection oven with a constantly risingtemperature. In Europe, the HDT test has replaced the Martens temperature test.

Table 6.12: Heat distortion temperature for selected thermoplastics

Material HDT(◦C) HDT(◦C)1.86 (MPa) 0.45 (MPa)

HDPE 50 50

PP 45 120

uPVC 60 82

PMMA 60 100

PA66 105 200

PC 130 145

It is important to point out that these test methods do not provide enough informationto determine the allowable operating temperature of molded plastic components subjectedto a stress. Heat distortion data are excellent when comparing the performance of differentmaterials and should only be used as a reference, not as a direct design criterion.


20

40

60

80

100

120

140

160

180

200

220

240

0 2 4 6 8 10 12 14

Bending stress σB

oC

PPE+ PS - GF 30

PC- GF 40

PC

PC-GF 30

PMMA

PS

CACABCP

Soft

Hard

B A Process

PF, Type 12

PF, Type 31

MF, Type 152

UPE, Type 1140

PPE+PS

UF, Type 131.5

ABS

PVC U

UPE, Type 1130

UPE, Type 1120

CACABCPC

N/mm 2

Figure 6.93: Heat distortion temperature for selected thermoplastics as a function of bending stress


Table 6.13: Techniques for measuring temperature of deflection under load (Shastri)

Standard ISO 75 - 1 and 75 - 2 D648 - 98c

Specimen Flatwise⇒ 80mmx10mmx4mm,cut from the ISO 3167 Type A spec-imen.

Edgewise ⇒ 120 ±10 mm x 12.7±0.3 mm x 6.35 mm (5"x1/2"x1/4")

Conditioning Specimen conditioning, includingany post molding treatment, shall becarried out at 23◦C ±2◦C and 50±5% R.H. for a minimum length oftime of 88 h, except where specialconditioning is required as speci-fied by the appropriatematerial stan-dard.

At 23 ◦C ±2 ◦C and 50 ±5% rela-tive humidity for not less than 40 hprior to testing in accordance withProcedure A of Method D618.

Apparatus The contact edges of the supportsand the loading nose radius arerounded to a radius of 3.0 ±0.2 mmand shall be longer than the widthof the test specimen. Specimen sup-ports should be about 100 mm apart(edgewise specimens).

The contact edges of the supportsand loading nose shall be roundedto a radius of 3.0 ±0.2 mm.Specimen supports shall be 100±2 mm apart, or 64 mm apart (flat-wise specimens).

Heating bath shall contain a suitableliquid (e.g., liquid paraffin, glyc-erol, transformer oil, and siliconeoils) that is stable at the temperatureused and does not affect thematerialtested (e.g., swelling, softening, orcracking). An efficient stirrer shallbe provided with a means of controlso that the temperature can be raisedat a uniform rate of 120K/h±10K/h.This heating rate shall be consideredto be met if over every 6 min inter-val during the test, the temperaturechange is 12 K ±1 K

Immersion bath shall have a suitableheat-transfer medium (e.g. mineralor silicone oils)whichwill not affectthe specimen andwhich is safe at thetemperatures used. It should bewellstirred during the test and providedwith means of raising the tempera-ture at a uniform rate of 2 ◦C ±0.2◦C . This heating rate is met if overevery 5 min interval the temperatureof the bath shall rise 10 ◦C ±1 ◦Cat each specimen location.

A calibrated micrometer dial-gaugeor other suitable measuring instru-ment capable of measuring to an ac-curacy of 0.01 mm deflection at themid point of the test specimen shallbe used.

The deflection measuring deviceshall be capable of measuring spec-imen deflection to at least 0.25 mmand is readable to 0.01 mm or better.



Standard ISO 75 - 1 and 75 - 2 D648 - 98c

Test procedures At least two unannealed specimens At least two specimens shall be usedto test each sample at each fiberstress of 0.455 MPa ±2.5% or 1.820MPa ±2.5%.

The temperature of the heating bathshall be 20 to 23 ◦C at the start ofeach test, unless previous tests haveshown that, for the particularmateri-als under test, no error is introducedby starting at other temperatures.

The bath temperature shall be aboutroom temperature at the start of thetest unless previous tests have shownthat, for a particular material, noerror is introduced by starting at ahigher temperature.

Apply the calculated force to givethe desired nominal surface stress.

Apply the desired load to obtainthe desired maximum fiber stress of0.455 MPa or 1.82 MPa to the spec-imen.

Allow the force to to act for 5 minto compensate partially for the creepexhibited at room temperature whensubjected to the specified nominalsurface stress. Set the reading of thedeflection measuring instrument tozero.

Fiveminutes after applying load, ad-just the deflection measuring deviceto zero/ starting position.

Heating rate⇒ 120 ±10 ◦C/hDeflections⇒ 0.32 mm (edgewise)for 10.0 to 10.3 mm height 0.34 mm(flatwise) for height equal to 4 mm.

Heating rate⇒ 2.0 ±0.2◦C/minThe deflection when the specimenis positioned edgewise is: 0.25 for aspecimen with a depth of 12.7 mm.

Note the temperature at which thetest specimen reaches the deflectioncorresponding to height of the testspecimen as the temperature of de-flection under load for the appliednominal surface stress.

Record the temperature at which thespecimen has deflected the specificamount, as the deflection tempera-ture at either 0.455 MPa or 1.820MPa.

Values and units HDT at 1.8 MPa and (0.45 MPa or8 MPa)⇒ ◦C

HDT at 0.455MPa or 1.820MPa⇒◦C

References

1. H. Domininghaus. Plastics for Engineers. Hanser Publishers, 1993.

2. L.R.G. Treloar. The Physics of Rubber Elasticity, 3rd. Ed. Clarendon Press, Oxford, 1975.

3. Courtesy ICIPC. Colombia.

4. E. Guth and R. Simha. Kolloid-Zeitschrift, 74(266), 1936.

5. E. Guth. Proceedings of the American Physical Society. Physical Review, 53(321), 1938.

6. H.M. Smallwood. J. Appl. Phys., 15(758), 1944.

6.1 References 261

7. L. Mullins and N.R. Tobin. J. Appl. Polym. Sci., 9(2993), 1965.

8. W. Retting. Rheol. Acta, 8(758), 1969.

9. E. Schmachtenberg. PhD thesis, IKV, RWTH-Aachen, Germany, 1985.

10. M. Weng. PhD thesis, IKV-RWTH-Aachen, Germany, 1988.


12. R.J. Crawford. Plastics Engineering, page 47. Pergamon Press, 2nd edition, 1987.

13. ASTM. Plastics (ii), 08.02,. ASTM Philadelphia, 1994.

14. R.J. Crawford. Rotational Molding of Plastics. Research Studies Press, Somerset, 1992.

15. J.L. O’Toole. Modern Plastics Encyclopedia. McGraw Hill, New York, 1983.

16. L. E. Nielsen. Mechanical Properties of Polymers. Van Nostrand Reinhold, New York, 1962.

263

CHAPTER 7

PERMEABILITY PROPERTIES

It is well known that the major consumption of plastics worldwide goes to packaging appli-cations. The main requirement in this sector and for the health of consumers is to guaranteethe product’s organoleptic quality during a predetermined shelf life. Plastic packaging isintended to minimize environment/package and product/package interactions and degrada-tion reactions that could lead to a loss of product quality. Such losses can affect nutritionalcontent, aroma, taste, freshness, and color to name a few [1].In general, food and beverages can exhibit undesired composition and physical changes if

water, some vapors, and gases are allowed to permeate across the packaging films. Althoughseveral substances or permeants, such as water vapor, oxygen, nitrogen, carbon dioxide, andcarbon monoxide, have to be considered, the most relevant are water vapor and oxygen. Fora great number of foods and beverages, the maximum values of gain or loss of gases havebeen reported in the literature (see Table 7.1); hence, the maximum gas quantity that canenter or leave the package before affecting the product or causing undesired organolepticchanges can be calculated.To meet the packaging requirements of a specific food or beverage, plastic multilayer

structures are used. They can be coextruded, extrusion coated, or laminated.

264 7 Permeability Properties

Table 7.1: Maximum values of gain or loss of gases for some food and beverage [1]

Food and beverage Oxygen gainproducts G (mg O2/g of product)

Beer 0.001 – 0.004

Wine 0.003

Fruit Juice 0.02

Soda beverages 0.04

Coffee 0.11

Cheese 0.42

Milk and other milk by-products 0.015

Because of their low density, polymers are relatively permeable by gases and liquids.A more in-depth knowledge of permeability is necessary when dealing with packagingapplications and with corrosive protection coatings. The material transport of gases andliquids through polymers consists of various steps:They are:

• Absorption of the diffusing material at the interface of the polymer, a process alsoknown as adsorption

• Diffusion of the attacking medium through the polymer• Delivery or secretion of the diffused material through the polymer interface, alsoknown as desorption

With polymeric materials, these processes can occur only if the following conditions arefulfilled:

• The molecules of the permeating materials are inert• The polymer represents a homogeneous continuum• The polymer has no cracks or voids that channel the permeating material

7.1 SORPTION

We talk about adsorptionwhen environmentalmaterials are deposited on the surface of solids.Interface forces retain colliding molecules for a certain time. Possible causes include vander Waals’ forces in the case of physical adsorption, chemical affinity (chemical sorption),or electrostatic forces. With polymers, we have to take into account all of these possibilities.A gradient in concentration of the permeating substance inside the material results in

a transport of that substance, which we call molecular diffusion. The cause of moleculardiffusion is the thermal motion of molecules that permit the foreign molecule to move alongthe concentration gradient using the intermolecular and intramolecular spaces. However, thepossibility to migrate essentially depends on the size of the migrating molecule.


Figure 7.1: Schematic diagram of permeability through a film

The rate of permeation for the case shown schematically in Fig. 7.1 is defined as the massof penetrating gas or liquid that passes through a polymer membrane per unit time. The rateof permeation, m, can be defined using Fick’s first law of diffusion as

m = −DAρdc

dx, (7.1)

whereD is defined as the diffusion coefficient,A is the area, and ρ the density. If the diffusioncoefficient is constant, Eq. 7.1 can be easily integrated to give

m = −DAρc1 − c2

L. (7.2)

The equilibrium concentrations c1 and c2 can be calculated using the pressure, p, and thesorption equilibrium parameter, S:

c = Sp, (7.3)

which is often referred to as Henry’s law. The sorption equilibrium constant, also referred toas solubility constant, is almost the same for all polymer materials. However, it does dependlargely on the type of gas and on the boiling, T b, or critical temperatures, Tcr, of the gas, asshown in Fig. 7.2.

7.2 DIFFUSION AND PERMEATION

Diffusion, however, is only one part of permeation. First, the permeating substance has toinfiltrate the surface of the membrane; it has to be absorbed by the membrane. Similarly, thepermeating substance has to be desorbed on the opposite side of the membrane. CombiningEqs. 7.2 and 7.3, we can calculate the sorption equilibrium using

m = −DSρAp1 − p2

L, (7.4)

where the product of the sorption equilibrium parameter and the diffusion coefficient isdefined as the permeability of a material

P = −DS =m · L

A · Δp · ρ , (7.5)


Figure 7.2: Solubility (cm3/cm3) of gas in natural rubber at 25 oC and 1 bar as a function of thecritical and the boiling temperatures

which can also be written as [P

x

]=

Vgas

t · A · (p2 − p1), (7.6)

where Px is the gas permeability (ml · m−2· day−1· atm−1), Vgas is the gas volume enteringor leaving from the package (ml), t is the time (day), A is the exposed packaging surfacearea (m2), Δp is the pressure drop (atm), p1 is the gas partial pressure outside the package(atm), and p2 is the gas partial pressure inside the package (atm). Equation 7.5 does not takeinto account the influence of pressure on the permeability of the material and is only validfor dilute solutions.

Table 7.2: Permeability of various gases through several polymer films. permeabilityunits are in cm3-mil/100in2/24h/atm (after Rosato) [2]

Polymer CO2 O2 H2O

PET 12-20 5-10 2-4

OPET 6 3 1

PVC 4.75-40 8-15 2-3

PE-HD 300 100 0.5

PE-LD - 425 1-1.5

PP 450 150 0.5

EVOH 0.05-0.4 0.05-0.2 1-5

PVDC 1 0.15 0.1


The Henry-Langmuir model takes into account the influence of pressure and works verywell for amorphous thermoplastics. It is written as

P = −DS(1 +KR′

1 + bΔp) (7.7)

whereK = c′Hb/S, with c′H being a saturation capacity constant and b an affinity coefficient.The constant R′ represents the degree of mobility, where R ′ = 0 for complete immobilityand R′ = 1 for total mobility. Table 7.2 presents permeability of various gases at roomtemperature through several polymer films.For water vapor the term water vapor transmission rate (WVTR) is used, and for oxygen

permeation the term oxygen transmission rate (OTR)1 is typically used. For water vaporpermeation the following equation is more practical to use,

WV TR =Wwater vapor

t · A , (7.8)

where WV TR is the water vapor transmission rate (g· m−2· day−1), Wwater vapor is theweight of water vapor (g), t is the time (day), and A is the exposed packaging surface area(m2). The oxygen permeability coefficient data for the polymers often used in multilayerfilms are presented in Table 7.3. The water vapor transmission rate WVTR data for thepolymers often used in multilayer films are presented in Table 7.4.

Table 7.3: Oxygen permeability coefficient data for polymers commonly used in mul-tilayer films [4]

Oxygen permeability coefficient at 0% RH [ml · 20 · mm · m−2· day−1· atm−1]Polymer 5 ◦C 20 ◦C 23 ◦C 35 ◦C

EVOH (32% ethylene) 0.06 0.2 0.25 0.6

EVOH (44% ethylene) 0.3 0.8 1.2 2.4

High barrier PVDC extrusion 0.74 2.6 3.2 8.1

PVDC (2mm) coated BOPP 2.2 10 13 32

PAN 3 - 15.5 39

Oriented PA-6 9.7 28 33 64

Cast PA-6 28 - 100 194

Oriented PET 13 40 46 400

Rigid PVC - 240 260 370

BOPP - 2900 3200 -

LDPE - 10000 10900 -

Every polymer offers different barrier properties depending on gas or vapor type, macro-molecular structure, temperature, and relative humidity. Polar plastic materials are typically

1OTR is the steady state rate at which the oxygen permeates through to a film at specified conditions of temperatureand relative humidity, ml · m−2· day−1. Standard test conditions of 23 ◦C and 0% RH are used [3].


good gas barriers, while non-polar plastic materials are good barriers to water vapor. There-fore, a multilayer package requires various layers of different polymers (polar and non-polar)to fit the required barrier conditions.With the maximum values of gain or loss of gases and water vapor, the calculation of

the maximum allowed permeability to guarantee a predetermined shelf life can be estimated[5, 6].

Table 7.4: Water vapor transmission rate (WVTR) data for polymers used in multilayerfilms [4]

WVTR of monolayer films 40 ◦C, 0/90% RHPolymer [g · 30 · mm · m−2· day−1]

EVOH (27% ethylene) 85





Extrudable high barrier PVDC 3

BOPP 5

HDPE 5

PP 9

LDPE 15

Rigid PVC 40

PAN 80

[P

x

]Gas max

=G · Wprod

θ · A · (P2 − P1), (7.9)

where[

Px

]Gas max

is the maximum allowed permeability for a gas (ml· m−2· day−1·atm−1), G is the allowed gas gain or loss (mg of gas/g of product), W prod is the productweight (g), θ is the shelf life (day).[

P

x

]vapor max

=Ln(me−mi

me−mc)

θ · AWprod

· Pv

b

(7.10)

Alternatively, in terms of the water vapor or water vapor transmission rate (WVTR), themaximum allowed permeability to guarantee a predetermined shelf life can be calculated as

WV TR =Ln( me−mi

me−mc)

θ · AW · 1

b

. (7.11)

where[

Px

]vapor max

is the maximum allowed permeability for a gas (ml· m−2· day−1·atm−1), me is the product humidity at equilibrium (g water/g product), m i is the initial


Figure 7.3: Typical moisture sorption isotherm

humidity of the product (g water/g product), m c is the critical humidity of the product (gwater/g product), Pv is the water vapor pressure (atm), b is the secant slope of sorption ordesorption isotherm betweenmi and mc (g water/g product),Wprod is the product weight(g), θ is the shelf life (day).To obtain the value of product humidity at equilibriumm e and the secant slope of sorp-

tion and desorption b, the moisture sorption isotherm of the particular food is required. Amoisture sorption isotherm is a graph where the moisture content of the food for differentwater activities (usually approximated to the relative humidity) can be obtained as depictedin Fig. 7.3. There are several books that provide food isotherms [7]. It is convenient (andrecommended) to measure the isotherm of a specific food by measuring the weight gainedby the product to the equilibrium when it is confined in an atmosphere of controlled rela-tive humidity. The relative humidity can be controlled by using different combinations ofsalts. Nowadays, sophisticated devices have improved themeasurement ofmoisture sorptionisotherms because they deliver the weight of the food samples while exposed to the stream ofgases with a carefully controlled relative humidity. This new technology has contributed tothe automation of the measurement, the enhancing of the temperature, the relative humiditycontrolled in a very narrow range and increasing the amount of points that can be obtainedin moisture sorption isotherms [8].Permeability coefficients can be also corrected with the relative humidity at the storage

or shelf conditions. If the polar polymers are placed in intermediate layers, the relativehumidity influencing the polymer can be calculated based on the water vapor permeabilityof the adjacent layers as it is shown in the following equation [9]:

RHj = RHout −⎡⎣⎛⎝ n∑

j=1

xj

Pj+

xn

2 · Pn)(

RHout − RHin∑nj=1

xj

Pj

⎞⎠⎤⎦ , (7.12)

where RH is the average relative humidity in j-layer, RHout - Relative humidity outsidethe package, RHin - Relative humidity inside the package, Pj - Permeation coefficient ofthe polymer in j-layer (ml·μ m · m−2· day−1· atm−1), Pn - Permeation coefficient of the


2.9 3.0 3.1 3.33.2 3.83.73.53.4 3.6 3.9

3.9

2.9

3.0

3.1

3.3

3.2

3.8

3.7

3.5

3.4

3.6

2.3

2.4

2.5

2.6

2.7

2.8

Figure 7.4: Sorption, diffusion, and permeability coefficients as a function of temperature forpolyethylene and methyl bromine at 600 mm of Hg (after Knappe)

polymer in n-layer (ml·μm · m−2· day−1· atm−1), xj - Thickness of j-layer in the structure(μ m), xn - Thickness of n-layer in the structure, (μ m).In the case of multilayered films commonly used as packagingmaterial, we can calculate

the permeation coefficient PC for the composite membrane using

1PC

=1

LC

n∑i=1

Li

Pi. (7.13)

Sorption, diffusion, and permeation are processes activated by heat and, as expected,follow an Arrhenius type behavior. Thus, we can write

S = S0e−ΔHs/RT (7.14)

D = D0e−ED/RT (7.15)

P = P0e−EP /RT (7.16)

whereΔHS is the enthalpy of sorption,ED andEP are diffusion and permeation activationenergies, R is the ideal gas constant, and T is the absolute temperature. The Arrheniusbehavior of sorption, diffusion, and permeability coefficients, as a function of temperaturefor polyethylene and methyl bromine at 600 mm of Hg, are shown in Fig. 7.4. Figure 7.5presents the effect that temperature has on the diffusion coefficient of a selected number ofplastics.

Figure 7.6 presents the permeability ofwater vapor through several polymers as a functionof temperature. It should be noted that permeability properties drastically change oncethe temperature increases above the glass transition temperature. This is demonstrated in


0.1

1

10

100

1000

0 20 40 60 80 100 120 140

PC

PC-GF 20

UP-Bispherol A

EP anhydride hard

UP- Standard

EP amino hardened

oC

Temperature

10-6 mm 2/s

Figure 7.5: Diffusion coefficients as a function of temperature for PC, EP, and UP

Figure 7.6: Permeability of water vapor as a function of temperature through various polymer films

Table 7.5,which presentsArrhenius constants for diffusionof selectedpolymers andCH 3OH.

The diffusion activation energy,ED, depends on the temperature, the size of the gasmoleculed, and the glass transition temperature of the polymer. This relationship is well representedin Fig. 7.7 with the size of nitrogen molecules, dN2 , as a reference.


Figure 7.7: Graph to determine the diffusion activation energy ED as a function of glasstransition temperature and size of the gas molecule dx, using the size of a nitrogen molecule,dN2, as a reference. Rubbery polymers (•): 1 =Silicone rubber, 2 =Polybutadiene,3 =Natural rubber, 4 =Butadiene/Acrylonitrile K 80/20, 5 =Butadiene/Acrylonitrile K 73/27,6 =Butadiene/Acrylonitrile K 68/32, 7 =Butadiene/Acrylonitrile K 61/39, 8 =Butyl rubber,9 =Polyurethane rubber, 10 =Polyvinyl acetate (r), 11 =Polyethylene terephthalate (r).Glassy polymers (◦): 12 =Polyvinyl acetate (g), 13 =Vinylchloride/vinyl acetate copolymer,14 =Polyvinyl chloride, 15 =Polymethyl methacrylate, 16 =Polystyrene, 17 =Polycarbonate.Semicrystalline polymers (×): 18 =High-density polyethylene, 19 =Low-density polyethylene,20 =Polymethylene oxide, 21 =Gutta percha, 22 =Polypropylene, 23 =Polychlorotrifluoroethylene,24 =Polyethyleneterephthalate, 25 =Polytetraflourethylene, 26 =Poly(2,6-diphenylphenyleneoxide)(after Rosato)

Table 7.5: Diffusion constants below and above the glass transition temperature (aftervan Krevelen)

Polymer Tg D0(H2O) ED

( ◦C) (cm2/s) (kcal/mol)T < Tg T > Tg T < Tg T > Tg

Polymethylmethacrylate 90 0.37 110 12.4 21.6

Polystyrene 88 0.33 37 9.7 17.5

Polyvinyl acetate 30 0.02 300 7.6 20.5

Table 7.5 contains values of the effective cross-section size of important gas molecules.Using Fig. 7.7 with the values from Table 7.2 and the equations presented in Table 7.6,the diffusion coefficient, D, for several polymers and gases can be calculated. Table 7.7also demonstrates that permeability properties are dependent on the degree of crystallinity.Figure 7.9 presents the permeability of polyethylenefilms of different densities as a functionof temperature. Again, the Arrhenius relation becomes evident.


Figure 7.8: Permeation of nitrogen through polyethylene films of various densities

Table 7.6: Important properties of gases

Gas d Vcr Tb Tcr dN2/dx(nm) (cm3) (K) (K)

He 0.255 58 4.3 5.3 0.67

H2O 0.370 56 373 647 0.97

H2 0.282 65 20 33 0.74

Ne 0.282 42 27 44.5 0.74

NH3 0.290 72.5 240 406 0.76

O2 0.347 74 90 55 0.91

Ar 0.354 75 87.5 151 0.93

CH3OH 0.393 118 338 513 0.96

Kr 0.366 92 121 209 0.96

CO 0.369 93 82 133 0.97

CH4 0.376 99.5 112 191 0.99

N2 0.380 90 77 126 1.00

CO2 0.380 94 195 304 1.00

Xe 0.405 119 164 290 1.06

SO2 0.411 122 263 431 1.08

C2H4 0.416 124 175 283 1.09



Gas d Vcr Tb Tcr dN2/dx(nm) (cm3) (K) (K)

CH3Cl 0.418 143 249 416 1.10

C2H6 0.444 148 185 305 1.17

CH2Cl2 0.490 193 313 510 1.28

C3H8 0.512 200 231 370 1.34

C6H6 0.535 260 353 562 1.41

Table 7.7: Equations to compute D using data from Tables 7.2 and 7.5a

Elastomers log D =ED

2.3R

„1

T− 1

TR

«− 4

Amorphous thermoplastics log D =ED

2.3R

„1

T− 1

TR

«− 5

Semicrystalline thermoplastics log D =

„ED

2.3R

„1

T− 1

TR

«− 5

«(1 − X )

Figure 7.9: Permeation of nitrogen through polyethylene films of various densities

Figures 7.10 and 7.11 present the permeability of water vapor through several polymersas a function of film thickness.

7.3 Measuring S, D, and P 275

0.1

1

10

100

1000

10 100 1000

12 and 3

45

67

8

9and 10

1112

13

14

1: CTA2: PVC- P (25% plasticizer)3: ABS4: SAN5: PA- Cop

Film thickness

30

28

24

23

2926

25

1716

15

18

19 27

6: PA6 7: PS 8: PS-HI 9: EVA10: PVC-P (22% plasticizer)

11: EVA 12: PVC-U (E-PVC) 13: PVC-U (S-PVC) 14: PET 15: PET/PE (12/50)

23oC

cm3

m2•d•bar

Figure 7.10: Permeability of water vapor through polymer films as a function of film thickness

1

10

100

1000

10000

10 100 1000Film thickness

16: PET/ PE (12/75)17: PET/ PE-X (15/50)18: PA/ PE (35/50)19: PA/ PE-X (35/60)22: PE/LD23: PP24: PE-HD25: PA/ PE(40/60)26: PA/ PE-X(60/75)27: PA/ PP (40/75)

28: PP-O 29: PVC/PE (250/75) 30: PVDC

23oC

30

614

13

12

115

17 18

1926

25 27

29

μm

1615

cm3

m2•d•bar

8

222

8

7

123

24

43

10, 28

Figure 7.11: Permeability of water vapor through polymer films as a function of film thickness

7.3 MEASURING S, D, AND P

The permeability P of a gas through a polymer can be directly measured by determiningthe transport of mass through a membrane per unit time. The sorption constant S can bemeasured by placing a saturated sample into an environment, which allows the sample to


desorb and measure the loss of weight. As shown in Fig. 7.12, it is common to plot the ratioof concentration of absorbed substance c(t) to saturation coefficient c∞ with respect to theroot of time.

Figure 7.12: Schematic diagram of sorption as a function of time

The diffusion coefficient D is determined using sorption curves as the one shown inFig. 7.12. Using the slope of the curve, a, we can compute the diffusion coefficient as

D =π

16L2a2, (7.17)

where L is the thickness of the membrane.

Another method uses the lag time, t0, from the beginning of the permeation processuntil the equilibrium permeation has occurred, as shown in Fig. 7.13. Here, the diffusioncoefficient is calculated using

D =L2

6t0. (7.18)

Figure 7.13: Schematic diagram of diffusion as a function of time

Some of the most important techniques used to determine gas permeability of polymersare listed in Table 7.8. Table 7.9 presents the comparable ISO 15105 and ASTM D1434tests. Other ASTM gas and vapor transmission rate tests are presented in Tables 7.10, 7.11and 7.12.


Table 7.8: ASTM and ISO standards used for testing gas permeability

ASTM

D1434-82 Determining Gas Permeability Characteristics of Plastic Film and Sheeting

F1927-07 Determination of Oxygen Gas Transmission Rate, Permeability and Permeanceat Controlled Relative Humidity Through BarrierMaterials Using a CoulometricDetector

D1434 Determining Gas Permeability Characteristics of Plastic Film and Sheeting

D3985 OxygenGas transmission rate Through Plastic Film and SheetingUsing aCoulo-metric Sensor

F1307-02 Oxygen transmission rate through dry packages using a coulometric sensor

F1249-06 Water Vapor Transmission Rate Through Plastic Film and Sheeting Using aModulated Infrared Sensor

E96/E96M-05 Water Vapor Transmission of Materials

F372-99 Water Vapor Transmission Rate of Flexible Barrier Materials Using an InfraredDetection Technique

E398-03 Water Vapor Transmission Rate of Sheet Materials Using Dynamic RelativeHumidity Measurement

F372-99 Water Vapor Transmission Rate of Flexible Barrier Materials Using an InfraredDetection Technique

D6701-01 Determining Water Vapor Transmission Rates Through Nonwoven and PlasticBarriers

ISO

1663:2007 Rigid cellular plastics – Determination of water vapour transmission properties

15105 Determination of Gas Permeability Characteristics of Plastic Film and Sheeting

15106-1:2003 Plastics – Film and sheeting – Determination of water vapour transmission rate(Humidity detection sensor method).

15106-2:2003 Plastics – Film and sheeting – Determination of water vapour transmission rate(Infrared detection sensor method).

15106-3:2003 Plastics – Film and sheeting – Determination of water vapour transmission rate(Electrolytic detection sensor method).


Table 7.9: Standard test method for determining gas permeability characteristics ofplastic film and sheeting

Standard ISO 15105-1: 2002 ASTM D1434-82

Specimen Three specimens which should belarger than the gas transmission areaof themeasurement cell andbecapa-ble of being mounted airtight. Theside of the material facing the airshould be marked. Measure thethickness of each specimen in accor-dance with ISO 4593.

Should have the appropriate size tofit the test cell (normally circular)and be free of imperfections such aswrinkles, creases or pinholes. Thethickness should be measured to thenearest 2.5 μm.

Conditioning Dry the specimens for at least 48 hat the same temperature at whichthe test is carried out using a dryingagent.

Condition the specimens at 23 ±2 ◦C in a desiccator for at least 48 hprior to test.

Apparatus Gas transmission cell that allows gasto permeate through the specimen,pressure sensor to detect pressurechanges due to permeability, gassupplies and feeder, a cell-volumecontrol, and a vacuum pump.

Manometric Gas transmission cell,composed of a cell manometersystem, a cell reservoir system,adapters, a cell vacuum valve, platesurfaces, a pressure gage, a barom-eter, and a vacuum pump.

Test procedures Insertion of test piece. Purging thetwo parts of the cell with a sufficientamount of air. Supply the vector gasat constant rate.

Mount the sample in the transmis-sion cell so as to form a sealedsemibarrier between two chambers.One chamber contains the test gasat a specific high pressure while theother chamber has the gas at lowerpressure and receives the permeat-ing gas.

Values and units [dm3/(h ·m2)] [dm3/(h · m2)]


Table 7.10: Standard testmethod for determiningwater vapor transmission rates throughnonwoven and plastic barriers

Standard ASTM D6701- 01

Scope To determine the rate of water vapor transmission ranging between 500 to100,000 g/m2day though nonwoven and plastic barrier materials.

Specimen Cut specimens, free of imperfections, representative of the width of the samplingunit.

Apparatus This test utilizes water vapor transmission apparatus composed of test cells, testcell guard film, water vapor sensor, post sensor dryer, mass flowmeter, computersystem and temperature control.

Test procedures Seal the test film in a diffusion cell composed of a dry chamber, guard film, anda wet chamber. The first test made is the one for water vapor transmission rate ofthe guard film and air gap between an evaporator assembly that generates 100%relative humidity. Record water vapor concentration with electronic sensors. Inthis case the computer calculates the transmission rate of the air gap and guardfilm based on the sensor readings. Finally, the water vapor transimission rateis calculated by the processor and when the measured results indicate that thespecimen has reached equilibrium the test is considered finished.

Values and Units Metric units are to be regarded

Table 7.11: Standard test methods for water vapor transmission of materials

Standard ASTM E 96/E 96M - 05

Scope To determine the water vapor transmission (WVT) of materials, such as paper,plastic films, other sheet materials, fiberboards, gypsum and plaster products,wood products, and plastics. The test methods are limited to specimens not over11/ 4" (32 mm) in thickness. The Desiccant Method and the Water Method, areprovided for the measurement of permeance, and two variations include serviceconditions with one side wetted and service conditions with low humidity onone side and high humidity on the other.

Specimen Three specimens shall be tested using the same method, with the vapor flow inthe specific direction in which the product is to be used.

Apparatus Test dish, test chamber, balance and weights, and thickness-measuring gage.Continued on next page


Standard ASTM E 96/E 96M - 05

Test procedures In the Desiccant Method the test specimen is sealed to the open mouth of a testdish containing a desiccant, and the assembly placed in a controlled atmosphere.Periodic weighings determine the rate of water vapor movement through thespecimen into the desiccant. In the Water Method, the dish contains distilledwater, and the weighings determine the rate of vapor movement through thespecimen from the water to the controlled atmosphere. The vapor pressuredifference is nominally the same in both methods except in the variation, withextremes of humidity on opposite sides.

Values and Units English (inch-pound) units and the SI units shown in parenthesis.

Table 7.12: Standard test method for oxygen gas transmission rate through plastic filmand sheeting using a coulometric sensor

Standard ASTM D3985 - 05

Scope To determine the steady-state rate of transmission of oxygen gas through plasticfilms, sheets and laminates, and plastic-coated papers and fabrics. It allows thedetermination of oxygen gas transmission rate (O2GTR), the permeance of thefilm to oxygen gas (PO2), and oxygen permeability coefficient (P’O2) in the caseof homogeneous materials. This test method is one of many techniques used tomeasure of O2GTR.

Specimen Test specimen should be free of imperfections and be representative of the ma-terial being tested. If the specimen is symmetric, the two surfaces must bemarked.

Apparatus Oxygen gas transmission apparatus composed of a diffusion cell, diffusion cellpneumatic fittings, a catalyst bed, a flowmeter, a coulometric sensor, a loadresistor, and a voltage recorder

Test procedures The oxygen gas transmission rate is determined after the sample has equilibratedin a dry test environment, which is considered to be one in which the relativehumidity is less than 1 %. The specimen is mounted as a sealed semi-barrierbetween two chambers at ambient atmospheric pressure. One chamber is slowlypurged by a stream of nitrogen and the other chamber contains oxygen. As oxy-gen gas permeates through the film into the nitrogen carrier gas, it is transportedto the coulometric detector where it produces an electrical current, proportionalto the amount of oxygen flow rate into the detector.

Values and Units The SI unit of oxygen permeability is mol/m·s·Pa


7.4 DIFFUSION OF POLYMER MOLECULES AND SELF-DIFFUSION

The ability to infiltrate the surface of a hostmaterial decreaseswithmolecular size. MoleculesofM > 5 × 103 can hardly diffuse through a porous-free membrane. Self-diffusion occurswhen a molecule moves, say in the melt, during crystallization. Also, when bonding rubber,the so-called tack is explainedby the self-diffusionof themolecules. Thediffusion coefficientfor self-diffusion is of the order of

D ∼ T

η, (7.19)

where T is the temperature and η the viscosity of the melt.In practical cases, such conditions are often not present. Nevertheless, this chapter shall

start with these ideal cases, since they allow for useful estimates and serve as learning toolsfor these processes.


Industrial Applications Dealing with Multilayer FilmsThis section presents several industrial applicationswhere the previouslymentioned

equations were used to predict the permeability of multilayer structures used in thepackaging industry. The models, developed by Noriega and coworkers [1, 10], werecompared to actual measurements. The calculations use a statistical combination ofm materials and n layers satisfying the following criteria:

– Compatibility between polymeric materials to be combined – if the compatibilityis not guaranteed, a tie layer is included in the structure between two incompatiblepolymers

– External and internal layers of the package are selected based on the thermal seala-bility behavior of the polymer, as well as on the water vapor permeability

– Hygroscopic polymers must always be placed in intermediate layers of the filmstructure

– The given maximum number of layers in the package structure must be kept be-cause of processing equipment restrictions

– The given thickness range (minimum and maximum) for the design of the mul-tilayer film structure should be satisfied

The multilayer structures are designed to both meet the maximum allowed perme-ability thus guaranteeing a determined shelf life and satisfy the previous criteria. Inaddition, to minimize the cost of the film per package area, the following equation wasused,


cost =n∑

j=1

(ρj · Cj · xj), (7.20)

where Cost is the total cost of multi - layer structure (US$/m2), xj is the thickness ofj-layer in the structure (μ m), Cj is the total cost of multi - layer structure (US$/m2),and ρj is the density of the polymer in the j-layer (kg/m3).

Table 7.13: Water vapor permeability for several film structures: comparison betweenmeasured and model calculated data [1]

Structure Measured Calculated Variation( g

m2·day·atm) ( g

m2·day·atm) (%)

PET (12 μm)/PP (38 μm) 18.11 17.32 4

PET (12 μm)/PP WHITE (38 μm) 19.38 20.9 -8

PET (12 μm)/PP (33 μm) 22.09 19.86 10

BOPP (25 μm)/BOPP(25 μm) 7.76 7.45 4

BOPP(20 μm)/BOPP (20 μm) 10.41 10.77 -4

BOPP (17.5 μm)/BOPP MET. (17.5 μm) 1.04 1.04 -0.04

A validation study of the computational model to calculate the permeability ofmultilayer films developed by Noriega and coworkers [1, 10] was performed and agood agreement between the experimental data and the predicted data was obtained.Table 7.13 shows the results for water vapor permeability for various laminated films.Tables 7.14 to 7.16 show the results for oxygen permeability including different

types of barrier films. It can be observed that the low barrier films show the highestdeviation between measured and calculated data, while medium barrier films showless deviation than low barrier films, and finally, high-oxygen barrier films show avery good agreement with the model calculated data.

Table 7.14: Oxygen permeability for several low barrier films: comparison betweenmeasured and model calculated data [1]

Structure Measured Calculated Variation( ml

m2·day·atm) ( ml

m2·day·atm) (%)

BOPP (20μm)/BOPP PEARL (30μm) 715.890 959.080 -34

BOPP (20μm)/BOPP (20μm) 774.960 956.910 23

BOPP (25μm)/BOPP(25μm) 783.070 579.960 26


The high deviation for low-oxygen barrier films can be explained considering thehigh precision cell of the OTR equipment adequate for high barrier measurements.

Table 7.15: Oxygenpermeability for severalmediumbarrier films: comparison betweenmeasured and model calculated data [1]


m2·day·atm) ( ml

m2·day·atm) (%)

PET (12 μm)/BOPP PEARL (30μm) 96.950 90.520 7

PET (12 μm)/PP (38μm) 113.520 90.120 2

PET (12 μm)/PP WHITE (38 μm) 113.190 90.124 20

PET (12 μm)/PP WHITE (51 μm) 96.340 88.560 8

PET (12 μm)/PP (33μm) 109.920 90.730 17

The developed computational model has demonstrated that is a good tool for mul-tilayer packaging design.

Table 7.16: Oxygen permeability for several high barrier films: comparison betweenmeasured and model calculated data [1]


m2·day·atm) ( ml

m2·day·atm) (%)

PA (46 μm)/EVOH-F (8 μm)/PP (28 μm)/PE-m (25 μm)

0.845 0.812 3.83

PP (18 μm)/EVOH F (4 μm)/PP (18 μm) 1.671 1.687 -0.93

PE (21 μm)/EVOH L (4 μm)/PE (16 μm) 0.873 0.857 1.80


Shelf life prediction for fertilizer packaged in a multilayer plastic film

Problem statement: Estimate the shelf life for a moisture gain in a fertilizer accordingto the following conditions:

– Initial moisture content of fertilizer: 0.5% by weight– Critical moisture content of fertilizer: 1.0% by weight (maximal content of waterbefore any detrimental effect on product quality)– Storage temperature: 21 ◦C


R2

0.000

0.010

0.020

0.030

0.040

0.050

0.55 0.6 0.65 0.7 0.75 0.8 0.85RH

y = 0.1283179x - 0.0689574

= 0.9992711

Figure 7.14: Moisture adsorption isotherm for a NPK fertilizer at 21 ◦C

– Storage relative humidity: 80% RH– Fertilizer weight: 25 kg– Packaging area: 1 m2

– Packaging multilayer structure: according to the Table 7.17

Table 7.17: Multilayer structure of fertilizer packaging film

Layer Composition Thickness (μm)

1 LLDPE 302 70% MDPE + 30% LLDPE 1203 LLDPE 30

Total 180

For the calculation of the shelf life, a moisture absorption isotherm for a particularfertilizer has to be obtained. The adsorption isotherm forNPK fertilizer (10%nitrogen,20% phosphorous and 20% potassium) at 21 ◦C was published by Allaire and Parent[11](see Fig. 7.14). In the range of interest, a linear regression could be used tocalculate the relative humidity for initial and critical moisture content.According to Fig. 7.14, the slope b could estimated as follow:

b ≈ mc − mi

HRc − HRi=

0.01 − 0.0050.6153− 0.5764

= 0.1285 (7.21)

The equilibrium moisture content at 80% RH was calculated from the isothermand the value obtained was 0.0337 g of moisture per g of fertilizer. The WVTR ofPolyethylene filmwas estimated using the computationalmodel developed byNoriegaand coworkers [1]. The estimatedWVTRwas 0.77 g of moisture/(day.m 2). This is the

7.4 References 285

idealized WVTR not considering micro-perforations and considering 100% integrityat the seals of the sacks.The shelf life could be calculated by using Eq. 7.22:

Θgain =ln[ me−mi

me−mc]

WV TR · AW · 1

b

= 799days (7.22)

Conclusions: The shelf life of the fertilizer under the storage conditions and usingthe multilayer packaging film is 799 days. The calculation is an idealized situationnot considering micro-perforations and considering 100% integrity at the seals of thesacks.

References

1. O. Estrada M. P. Noriega and C. A. Vargas. Design of plastic multi-layer structure that fit therequirements of a specific food or beverage. SPE-ANTEC, 2003.

2. D. Rosato and D.V. Rosato. Blow Molding Handbook. Hanser Publishers, Munich, 1989.

3. Exxon Mobil Chemicals. OTR test method. 2001.

4. EVAL Europe. . Introduction to kuraray eval resins. Technical catologue. 2000

5. G. L. Robertson. Food Packaging: Principles and Practice. Marcel Dekker Publishers, 1993.

6. R. J. Hernandez, S. Selke, and J. D. Culter. Plastics Packaging: Properties, Processing, Applica-tions, and Regulations. Hanser Publishers, 2000.

7. H. A. Iglesias and J. Chirife. Handbook of food isotherms. Food science and technology. Aca-demic Press, 1982.

8. E. Laine and M. Aarnio. Device for the investigation of the humidity-related behaviours ofmaterials. Department of Physics, University of Turku, Finland.

9. EVALCA. Gas barrier properties of resins. Technical Bulletin, (110), 1996.

10. M. P. Noriega I. D. Lopez, O. Estrada and K. Osorio. Optimization model based on a heuristicalmethod for barrier films design. SPE-ANTEC, 2005.

11. S. E. Allaire and L. E. Parent. Physical properties of granular organic-based fertilisers, part 2:dynamic properties related to water. Biosystems Eng, 87(2):225–236, 2004.

287

CHAPTER 8

ENVIRONMENTAL EFFECTS AND AGING

The environment or the media in contact with a loaded or unloaded component has a sig-nificant impact on its properties, life span, and mode of failure. The environment can bea natural one, such as rain, hail, solar ultra-violet radiation, and extreme temperatures, oran artificially created one, such as solvents, oils, detergents, and high temperature environ-ments. Damage in a polymer component from natural environmental influences is usuallyreferred to as weathering.

8.1 WATER ABSORPTION

While all polymers absorb water to some degree, some are sufficently hydrophilic that theyabsorb large enough quantities of water to significantly affect their performance. Water willcause the polymer to swell and serves as a platicizer, consequently lowering its performance,such as in electrical and mechanical behavior. Figure 8.1 presents the water saturation pointfor a selected number of thermoplastics. Increases in temperature result in an increase offree volume between the molecules, allowing the polymer to absorb more water. The stan-dard tests ISO 62 and ASTM D570, presented in Table 8.1, are used to measure the waterabsorption of polymers.

288 8 Environmental Effects and Aging

0.1

1

10

0 20 40 60 80 100 120 140 160 180oC

PA11

POM

PSU

PC

PPE+PS(Flame retardant)

PPE+PS U. PPE+PS-GTPP

PSU

H2O steam

x

2

4

6

8

2

4

6

%

Temperature

Figure 8.1: Temperature dependence of the water saturation point for various thermoplastics

Table 8.1: Standard methods of measuring water absorption (Shastri)


Specimen geometry 50 ±1 mm square or diameter disksx 3 ±0.2 mm thick for 24 h immer-sion and <1 mm thick for saturationvalues.

50.8 mm diameter x 3.2 mm diskfor molded plastics. The thicknessshall be measured to the nearest0.025 mm.

Conditioning Dry specimens in an oven for 24±1hat 50 ±2 ◦C, allow to cool to ambi-ent temperature in the desiccator andweigh to the nearest 1 mg.

Specimens of a material whose wa-ter absorption value is appreciablyaffected by temperatures close to110 ◦C, shall be dried in an oven for24 h at 50 ±3 ◦C, cooled in a des-iccator, and immediately weighedto the nearest 0.001 g. Specimensof a material whose water absorp-tion value is not appreciably affectedby temperatures up to 110 ◦C, shallbe dried for 1 h at 105 to 110 ◦C.(No weighing requirement is givenin the method; however the authorsassume that the specimen should beweighed immediately to the nearest0.001 g.)


8.1 Water Absorption 289


When data comparisons with otherplastics are desired, the specimensshall be dried in oven for 24 h at 50±3 ◦C, cooled in a desiccator, andimmediately weighed to the nearest0.001 g.

Apparatus Three specimens shall be preparedin accordance with the relevant ma-terial standard. When none exists,specimens shouldbecompression orinjectionmolded in accordance withISO 293 or ISO 294-1. The volumeofwater shall be at least 8ml per cm2

of the total surface area of the testspecimen.

Three specimens shall be tested. Nospecimen preparation conditions aregiven. No specifics given on the vol-ume of water required.

Test procedures Place the specimens in a container ofdistilled water, controlled at 23 ◦Cwith a tolerance of ±0.5 or ±2.0 ◦Caccording to the relevant materialstandard. In absence of such stan-dard, the tolerance shall be ±0.5 ◦C.After immersion for 24 ±1 h, takethe specimens from thewater and re-move all surface water with a clean,dry cloth or with filter paper.

The specimens shall be placed ina container of distilled water main-tained at 23 ±1◦C, and rest on edgeand be entirely immersed. At 24(+0.5, -0) h, the specimens shall beremoved one at a time and wipedoff with a dry cloth and weighed tothe nearest 0.0001 g immediately.Long-term immersion – To deter-mine the saturation value, the speci-mens are tested according to the 24 hprocedure, except afterweighing thespecimen are replaced in the water.

Re-weigh the specimens to the near-est 1mgwithin 1min of taking themout of the water (Method 1). Satu-ration values in water or air at 50%relative humidity at 23 ◦C.

The weighings shall be repeated atthe end of the first week and everytwo weeks thereafter until the in-crease in weight per two-week pe-riod, as shown by three consecutiveweighings, averages less than 1%of the total increase in weight or 5mg, whichever is greater. The dif-ference between the saturated anddry weight shall be considered thewater absorbed when substantiallysaturated.




If it is desired to allow for the pres-ence of water soluble matter, dry thetest specimens again for 24 ±1 hr inthe oven controlled at 50±2◦C, aftercompletion of Method 1. Allow thespecimen to cool to ambient temper-ature in the desiccator and reweighto the nearest 1 mg (Method 2).The percentage of water absorbed isa total of the%weight increase afterimmersion either by Method 1 or 2.

Materials that are known or sus-pected to contain appreciableamounts of water-soluble ingredi-ents, shall be reconditioned for thesame time and at the same temper-ature as used for conditioning thespecimen originally. If the weightof the specimen is less than theoriginal conditioned weight, thenthat difference in weight shall beconsidered as water-soluble matterlost during the immersion test. Thepercentage of water absorbed isa total of the % weight increase(to be noted whether it is 24 h orsaturation) and the % soluble matterlost.

Values and units Water absorption (24 h)⇒wt Water absorption (24 h) (24 h or sat-uration)⇒wt

Figures 8.2 and 8.3 present the percentage of water absorption as a function of relativehumidity for a selected number of thermoplastics.

0

2

4

6

8

10

12

14

16

18

20

0 20 40 60 80 100

Relative humidity %

%PVAL

PMMA

CA

PA66

PVB

CR PVC

Figure 8.2: Equilibrium water content as a function of relative humidity for several thermoplastics

8.2 Weathering 291

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100%

%PA6

PA6/610/66

PA66

PA610

PA11

Relative humidity %

Figure 8.3: Equilibrium water content as a function of relative humidity for various polyamides

8.2 WEATHERING

When exposed to the elements, polymeric materials begin to exhibit environmental cracks,which lead to early failure at stress levels significantly lower than those in the absence ofthese environments. Figure 8.4 shows an electronmicrographof the surface of a high-densitypolyethylenebeer crate after nine years of use and exposure toweathering. The surface of thePE-HD exhibits brittle cracks, which resulted from ultraviolet rays, moisture, and extremesin temperature.

Figure 8.4: Electron micrograph of the surface of a high-density polyethylene beer crate after nineyears of use and exposure to weathering (Ehrenstein) [1]


Figure 8.5: Surface of a polyoxymethylene specimen irradiated with ultraviolet light for 100 h in alaboratory environment (Ehrenstein)[1]

Standard tests are available to evaluate effects of weathering on properties of polymericmaterials. It is often unclear which weathering aspects or what combinations of aspectsinfluencematerial decay themost. Hence, laboratory tests are often done to isolate individualweathering factors such as ultraviolet radiation. For example, fig. 8.5 shows the surface ofa POM specimen irradiated with ultraviolet light for 100 h in a laboratory environment.Several standards for analyzing the weathering resistance of plastics exist. A review of thesestandards is presented in Table 8.2.

Table 8.2: Standards for measuring weathering resistance of plastics [2]

Weathering type Standard Description

Conventional

Outdoor application ASTM G7 Recommended practice for atmospheric envi-ronmental exposure to testing of nonmetallicmaterials

ISO 877 Methods of exposure to direct weathering, indi-rect weathering using glass-filtered daylight andto intensified weathering by daylight using fres-nel mirrors

SAE J576 Plastic materials for use in optical parts suchas lenses and reflex reflectors or motor vehiclelighting devices

SAE J1976 Outdoor weathering of exterior materialsContinued on next page

8.2 Weathering 293


Indoor application ASTM G24 Standard practice for conducting exposures todaylight filtered through glass

Indoor application ISO 877 Methods of exposure to direct weathering, indi-rect weathering using glass-filtered daylight andto intensified weathering by daylight using fres-nel mirrors

GM9538P Weathering exposure test for trims

Accelerated natural

Outdoor applications ASTM G90 Performing accelerated outdoor weathering ofnonmetallic materials using concentrated natu-ral sunlight

ASTM G7 Recommended practice for atmospheric envi-ronmental exposure to testing of nonmetallicmaterials

ISO 877 Methods of exposure to direct weathering, indi-rect weathering using glass-filtered daylight andto intensified weathering by daylight using fres-nel mirrors

SAE J576 Plastic materials for use in optical parts suchas lenses and reflex reflectors or motor vehiclelighting devices

SAE J1961 Accelerated exposure of automotive exteriormaterial using solar fresnel-reflective apparatus

Indoor applications SAE J2230 Accelerated exposure of automotive interiortrim materials using outdoor under-glass con-trolled sun-tracking temperature and humidityapparatus

Accelerated artificial

Xenon arc ASTM G26 Standard practice for operating light-exposureapparatus (Xenon arc type)with andwithoutwa-ter for exposure of nonmetallic material

ISO 4892 Test metrods of exposure to laboratory lightsources




Xenon arc SAE J2212 Accelerated exposure of automotive interiorma-terial using a controlled irradiance air-cooledXenon arc apparatus

SAE J2019 Accelerated exposure of automotive exteriormaterial using a controlled irradiance air-cooledXenon arc apparatus

Fluorescent ASTM G53 Standard practice for operating light andwater-exposure apparatus (fluorescent UV-condensation type) for exposure of nonmetallicmaterial

Carbon arc ASTM G53 Standard practice for operating light and water-exposure apparatus for exposure of nonmetallicmaterial

Table 8.3: Critical wavelengths for degradation of the most important polymers [3]

Polymer Wavelength range (nm)

Polyethylene (PE) 300 to 310, 340

Polypropylene (PP) 290 to 300, 330, 370

Polyvinyl chloride (PVC) 320 to 330, 3701

Polyamide (PA) 290 to 315

Polymethylmetacrylate (PMMA) 290 to 315

Polycarbonate (PC) 280 to 310

Polyethersulphone (PES) 325

Table 8.4: Standards for measuring weathering resistance of plastics [2, 4]

Name Wavelength range (nm) % of total solar radiation

Ultraviolet (UV) 295 to 400 6.8%

Visible (VIS) 400 to 800 55.4%

Infrared (IR) 800 to 2450 37.8%

1For vinyl acetates copolymers

8.2 Weathering 295

Solar radiation: According to the Planck’s theory, "the shorter the wavelength, the higherthe energy of the radiation." Hence, the most dangerous solar radiation for polymers is UVradiation The critical ranges of wavelengths for degradation of the most important polymersare presented in Table 8.3. UV light can be divided in three ranges: UV-A from 315 to 400nm, UV-B 280 to 315 nm, and UV-C from 200 to 280 nm. Solar radiation is composed ofa wide spectrum of wavelengths from 295 to 2450 nm distributed as presented in Table 8.4.Only a small portion of UV-B and the UV-A radiation arrives at the earth’s surface from thesun.

Table 8.5: Terms related to the solar radiation intensity [2]

Term Explanation Units

Irradiance The radiant flux on a surface perunit of area.

W· m −2

The spectral range where the ir-radiancewasmeasured has to beindicated

kLy /year = kcal· cm−2· year−1

Spectral irradiance Irradiance measured as a func-tion of wavelength

W· m−2· nm−1

Radiance exposure Time integral of irradiance J · m−2

kLy = kcal· cm−2

Ly = 0.04184 MJ · m−2

Spectral radiant expo-sure

Radiant exposure measured as afunction of wavelength

J· m−2· nm−1

When reproducing solar radiation, not only does one need to reproduce the wavelengths,but also the intensity as a wavelength function must be considered. The terms related to thesolar radiation intensity are presented in Table 8.5. When the weathering performance of apart or material is tested in the laboratory, the selection of the lamp that better reproducessolar radiation (wavelength and intensity) is critical, the Xenon arc lamp being the mostsuitable. If only UV radiation resistance is tested, a UVA 340 fluorescent lamp can be used.Solar radiation at the earth’s surface depends on the geographical place, the season, andthe tilt angle. Solar maps that report the average irradiance according to the geographicalplace can be found elsewhere. To standardize the irradiance in weathering tests, a calibratedpyranometer is strongly recommended.


The standard techniques to measure outdoor weathering effects on plastics are described bythe ISO 877.2 and ASTM D1435 tests, described in Table 8.6.

Table 8.6: Standard practice for outdoor weathering of plastics

Standard ISO 877.2: 94 ASTM D1435

Specimen Test specimens can be any shape orsize and their dimensions should bethose specified in the test methodused for the properties to be mea-sured after the weathering exposure.The number of specimens also de-pends on the test method used formeasuring the properties of interestafterweathering. It is recommendedto expose twice the amount of spec-imens required for the specific testmethod to be used after weathering.

Test specimens can be any shape orsize. They can be specimens thatare directly used to evaluate physi-cal properties or they can be largerspecimens fromwhich smaller spec-imens can be cut for subsequent testsand evaluations.

Conditioning The test specimens should be con-ditioned in accordance with the ma-terial properties as well as the testprocedure to be used after the ex-posure. The conditioning procedurehas to be recorded based on the de-scriptions given in ISO 291. Thespecimens should be identified onthe non-exposed side.

The test specimens should be iden-tified in accordance with PracticeG147, such that the markings do notinterferewith the exposure or testingprocedures. The specimens shouldbe identified on the non-exposedside.

Apparatus Exposure equipment is essentiallyan appropriate rack. Racks andspecimen holdersmust be from inertmaterials, such as noncorrosive alu-minum alloy, stainless steel or ce-ramics, to avoid introducing effectsinto the test results. The rack setupshould be placed facing the equatorandmust be capable of providing thedesired angle of inclination for ex-posure and should be such that spec-imens are at least 0.5 m from theground or any other obstruction.

Unless otherwise specified, racksshould be placed facing the equa-tor, that is, at an angle equal tothe latitude of the site. Other com-monly used exposure angles (mea-sured from the horizontal) are: 45◦

(most common), 90◦, and 5◦ (Thisangle is used in lieu of 0◦ to avoidstanding water). This set-up andprocedure is described in detail bythe G7 Practice for Atmosphericand Environmental Exposure Test-ing of Non-Metallic Materials.


8.2 Weathering 297

Standard ISO 877.2: 94 ASTM D1435

Test procedures Attach the specimen to the rackmaking sure that the method ofmounting does not impose signifi-cant stress on the specimen whichwould cause an effect on the testresults. Establish a procedure forcleaning the specimens and visuallycompare themwith unexposed spec-imens. Plot changes in properties asa function of exposure time.

Record the initial appearance andphysical properties of the specimensand draw a diagram of the test spec-imen layout. Specimens shouldbe grouped according to exposuretimes. Ensure that the radiometershave the same orientation as the testspecimens. Establish a procedurefor cleaning the specimens and vi-sually comparing them with unex-posed specimens. Plot changes inproperties as a function of exposuretime.

Values and units According to properties beingtested.

According to properties beingtested.

Accelerated laboratory tests: Because of the slowness of outdoor weathering tests,there is great interest in accelerated weathering tests exist in the industry. Some acceler-ated weathering tests make use of artificial lamps and devices to simulate real weatheringconditions. When accelerated weathering tests are intended to simulate real weathering con-ditions, one must first find a correlation between the tests and the real weathering conditions[5]. To assure this:

• Experience has shown that the correlation between natural and accelerated weatheringis dependent on the nature of the application, such as the particular property beingconsidered, thickness of the product, color, and surface finish. Hence, a universalcorrelation does not exist. The correlation factors between natural and acceleratedweathering are, therefore, done empirically.

• Every individual polymer has some properties that are more sensitive to weatheringthan others. Hence, these properties have to be selected for tracking the weatheringprogress, as well as to correlate the natural and accelerated weathering tests. Someexamples of these sensitive properties in particular polymers are:

– Transparency in PMMA

– Impact resistance in ABS

– Elongation and impact resistance in PC

– Elongation in most of the elastomers

– MFI and brightness in polypropylene

– Carbonyl group, MFI, and elongation in polyethylene

– Intrinsic viscosity (IV) in polyethylene terephthalate


• Once the most sensitive properties are defined, natural and accelerated weatheringexperiments are performed, and a comparison of a particular property with the twotypes of test can be done. A statistical regression analysis of a scatter plot of natu-ral weathering vs. accelerated weathering can be done, the Pearson and Spearmancorrelation methodologies being the most widely used [5, 6].

• If a good correlation was observed, the acceleration factor, which is a measure of howrapidly a test can be conducted using an accelerated weathering method comparedwith natural weathering, can be determined. The acceleration factor can be calculatedusing

Facceleration =tnatural

taccelerated. (8.1)

• A compromisemust bemade between correlation and acceleration because experiencehas shown that the faster the test, the likelihood that the results correlate diminishes.Some researchers have postulated that acceleration factors of10orhigher are extremelymaterial/environment specific [5].

• Several factors that negatively affect the correlation between natural and acceleratedweathering have been reported in the literature. The most relevant factors are [5]:

– Exposure to an unrealistic light spectrum (UV radiation that is not observed insolar radiation spectrum)

– Exposure to extreme radiation intensity

– Unrealistic specimen temperatures (for example, temperature differences in-duced by color or unrealistic temperature cycling)

– Unrealistic moisture effect

Several other factors have been found to be important in outdoor aging of plastic parts,including among others, the presence of salinity, micro-organisms, ozone, oxygen, and con-taminants. Oxygen can react with some labile groups of the polymer to produce very unstablesubstances during weathering, such as hydroperoxides and peroxides. Because of the de-composition of hydroperoxides and peroxides (depending on the type of polymer), scissionor crosslinking of macromolecules has been reported, affecting the initial properties of theplastic part. The use of antioxidants able to scavenge free radicals and decompose hydroper-oxides has been reported as a good means of enhancing the weathering resistance of plasticparts. For polymers that have unsaturated groups (C=C bonds), degradation in the presenceof ozone has been observed. The simulation of ozone resistance is particularly important insome rubbers if they are intended to be used in automotive and electrical applications.The presence of acid rain, some combustion gases, pollutants, pesticides, and agrochem-

ical substances can accelerate the weathering of the polymers. They produce discoloringand decrease the effectiveness of protection additives. Therefore, in some agricultural ap-plications, such as greenhouse and mulch films, specially accelerated weathering tests areperformed, including the effect of pesticides, fungicides, and agrochemical substances. Fi-nally, the effect of micro-organisms on the weathering resistance of some polymers, espe-cially flexible PVC, has been reported. To reduce the negative effect of micro-organisms in

8.2 Weathering 299

outdoor exposure of some plastics, special plasticizers and biocides additives must be addedto the polymer.


Weathering industrial applications

Figure 8.6 is a plot of impact strength of notched PMMA specimens as a function ofhours of UV radiation exposure in a controlledDIN 53487 test and years of weatheringunder standard DIN 53486 conditions. The correlation between the two tests is clear.The ASTM-D 4674 test evaluates the color stability of polymer specimens exposed toultraviolet radiation. Standard tests also exist to test materials for specific applications,such as the ASTM-D 2561 test, which evaluates the environmental stress crackingresistance of blow-molded polyethylene containers.

Figure 8.6: Impact strength of notched PMMA specimens as a function of hours of UV radiationexposure in a controlled test and weathering exposure time (Ehrenstein) [7]

Figure 8.7: Impact strength of PVC pipe as a function weathering exposure time in the UnitedKingdom (Davis and Sims) [3]

As can be seen, the effect of ultraviolet radiation,moisture, and extreme temperatureis detrimental to the mechanical properties of plastic parts. One example in whichweathering completely destroys the strength properties of a material is shown for PVCin fig. 8.7. The figure shows the decay of impact strength of PVC pipes exposedto weathering in the United Kingdom. As can be seen, the impact strength rapidlydecreases in the first six months and is only 11% of its original value after only two


Figure 8.8: Impact strength as a function of weathering time of PVC exposed in different geographiclocations (Davis and Sims) [3]

Figure 8.9: Impact strength of an ABS as a function of hours to actual sunshine exposure (Ruhnkeand Biritz) [1]

years. The location and climate of a region can play a significant role in the weatheringof polymer components. Figure 8.8 shows the decrease in impact strength of rigid PVCas a function of time at five different sites. After five years of weathering, the PVCexposed in Germany still has 95% of its original impact strength, whereas the samplesexposed in Singapore have less than 5% of their initial strength.The strength losses and discoloration in a weathering process are mainly attributed

to the ultraviolet rays received from sunshine. This can be demonstrated by plottingproperties as a function of actual sunshine received instead of time exposed. Figure 8.9is a plot of percent of initial impact strength for an ABS as a function of total hours ofexposure to sunlight in three different locations: Florida, Arizona, and West Virginia.The curve reveals the fact that by "normalizing" the curves with respect to exposureto actual sunshine, the three different sites with three completely different weatherconditions2 lead to the same relation between impact strength and total sunshine.

2Florida has a subtropical coastal climate with a yearly rainfall of 952 mm and sunshine of 2750 hours. Arizonahas a hot dry climate with 116 mm of rainfall and 3850 hours of sunshine. West Virginia has a milder climate with992 mm of rainfall and 2150 hours of sunshine.


Figure 8.10: Influence of pigment concentration on the impact strength reduction of ABS specimensexposed to weathering (Ruhnke and Biritz) [1]

The effect of weathering can often be mitigated with the use of pigments, such asTiO2 or soot, which absorb ultraviolet radiation, making it more difficult to penetratethe surface of a polymer component. For example, ABS with white or black pigmentsexhibit a noticeable improvement in properties after exposure to ultraviolet radiation.Figure 8.10 shows the reduction of impact strength in ABS samples as a functionof exposure time to sunshine for four pigment concentrations: 0.5%, 0.7%, 1%, and2%. It is clear that the optimal pigment concentration is around 1%. Beyond 1% ofpigmentation, there is little improvement in the properties.

8.3 CHEMICAL DEGRADATION

Liquid environments can have positive and negative effects on the properties of polymericmaterials. Some chemicals or solvents can have detrimental effects on a polymer component.Figure 8.11 shows results of creep rupture tests done on PVC tubes as a function of the hoopstress. It can be seen that the lifespan of the tubes in contact with iso-octane and isopropanolhas been significantly reduced as compared to the tubes in contact with water.The measured data for the pipes exposed to iso-octane clearly show a slope reduction

with a visible endurance limit, making it possible to do long-life predictions. On the otherhand, the samples exposed to isopropanol do not exhibit such a slope reduction, suggestingthat isopropanol is a harmful environment which acts as a solving agent and leads to gradualdegradation of the PVC surface.The question of whether a chemical is harmful to a specific polymeric material needs to

be addressed if the polymer component is to be placed in a possibly threatening environment.Similar to polymer solutions, a chemical reaction between a polymer and another substanceis governed by Gibbs free energy equation. If the change in enthalpy, ΔH , is negative, achemical reaction will occur between the polymer and the solvent.The effect of the solubility parameter of several solvents on the fatigue response of

polystyrene samples is presented in fig. 8.12. When the absolute difference between thesolubility parameter of polystyrene, which is 9.1 (cal/cm3)1/2, and the solubility parameterof the solvent decreases, the fatigue life drops significantly.


Figure 8.11: Effect of different environments on the stress rupture life of PVC pipe at 23 ◦C(Riddell) [8]

Figure 8.12: Effect of solubility parameter of the surroundingmedia on the fatigue life of polystyrenespecimens (Hertzberg and Mason) [9]

It should be pointed out again that some substances are more likely to be absorbed by thepolymer than others. A polymer that is in a soluble environment is more likely to generatestress cracks and fail. This is illustrated in fig. 8.13, which shows the strain for crackformation in polyphenylene oxide samples as a function of solubility parameter of varioussolutions. The specimens in solutions that were ±1 (cal/cm3)1/2 away from the solubilityparameter of the polymer develop cracks at fairly low strains, whereas those specimens insolutions with a solubility parameter further away from the solubility of the polymer formedcrazes at much higher strains.Environmental stress cracking or stress corrosion in a polymer component only occurs if

crazes or microcracks exist. The standardized methods for evaluating environmental stress-cracking of ethylene plastics are the ISO 4599 and ASTM D1693 presented in Table 8.7.


ε crit

(%)

Figure 8.13: Strains at failure as a function of solubility parameter for polyphenylene oxidespecimens: (filled circle) cracking, (open circle) crazing (Bernier and Kambour) [1]

19 mm

13 mm

38 mm

Figure 8.14: Set-up for the ASTM-D1693 test

Table 8.7: Standard test method for environmental stress-cracking of ethylene plastics

Standard ISO 4599-1986 D1693 -01

Specimen Flexural specimen with thicknessbetween 2 and 4 mm. A radius ofcurvature between 30 and 500 mmcan be used.

38mm x 13mm flexural specimenbar with a 19mm longitudinal notchin its center.



Standard ISO 4599-1986 D1693 -01

Conditioning Specimens should be conditionedfor 48 h in a determined atmosphere23 ± 2 ◦C and (50 ± 5) % R.H. (ISO291) before exposure to the test andreference environments.

The test specimens are slowly bentand placed in a holding clamp. Theclamp and specimens are introducedin a test tube and then immersed ina reagent (fig. 8.14). The sealedtest tube is placed in a constant-temperature bath. Three test condi-tions are specified depending of thekind of polymer that is being tested.

Apparatus Perforated formers made fromchemical-resistant material with anarc of roughly the same length as thetest specimen. Chemical-resistantmaterial clamps. Glass containerswith a well sealed lid for holdingthe mounted test specimens. Testenvironment media.

Holding clamp, test tube withthe reagent media and a constant-temperature bath for placing thetubes with the samples.

Test procedures Clamp the specimen to the formers,starting with zero strain and endingwith the former having the smallestradius. After being mounted, placethe specimens in contact with thetest environment. A strain period of1000 h is adequate. After the pre-strain time, observe the test visually.Determine the indicative property assoon as possible after demountingthe specimen, within 24 h.

Specimens are inspected periodi-cally for cracks, any crack con-stitutes failure, not just the onesthat reach the edge of the spec-imen. Cracks generally developat the notch, perpendicular to thenotch, and run to the edge of thespecimen. They can also appear be-neath the surface and create a de-pression. If a depression developsinto a surface crack, the time atwhich the depression was noted isassumed as the time of failure.

Values and units Strain (Dimensionless) Strain (Dimensionless)


Rupture of Water Filled Polyethylene Balls in Ethylene Glycol

As discussed in the Industrial Applications 6.5 in Chapter 6, water filled high den-sity polyethylene balls packed in an ethylene glycol filled storage tower that form partof an air conditioning system failed after approximately three months of installation.


One aspect that contributed to he failure were the high loads the balls experienceddue to the buoyancy forces. Using creep data for PE-HD, a creep rupture failure waspredicted to be approximately 10 months after installation. A further study was per-formed to see if this failure was accelerated by environmental stress cracking causedby the combination of the high stresses and the ethylene glycol environment. For thisanalysis, the crack surfaces of several failed balls were photographed and analyzed.Figure 8.15 shows a micrograph of such a crack. To introduce high contrast to thesurface, and make the detail of crack visible in the photographs, the cracks were goldcoated.

Water side (Inside the ball)Water side (Inside the ball)

Ethylene glycol side (Outside the ball)Ethylene glycol side (Outside the ball)

Last zone to fail

Figure 8.15: Micrograph of a gold coated crack found in a failed PE-HD ball

Abs

orba

nce

Abs

orba

nce

4000 600100015003000 2000 800

1748

IR spectrum of inner core of a cacked ball

IR spectrum of reference ball

Wavenumber, cm-1

Figure 8.16: Comparison of IR-spectra of a failed and a reference ball


The micrograph clearly shows that the crack initiated in the side exposed to ethy-lene glycol and progressed to the inside, where the last zone to fail is evident fromthe lip on the crack surface. The fact that all the cracks moved from the ethyleneglycol environment to the water inside the ball, is one sign that the balls failed byenvironmental stress cracking, brought upon by the combination of high stresses andethylene glycol. To confirm this theory, an IR spectrum was performed on the PE-HDballs. Figure 8.16 presents two IR spectra measured on a sample taken from the innercore of a failed ball’s wall and one taken from an unused reference ball. There areclear differences between the two spectra. The spectrum from the failed ball shows aclear peak around 1748 cm-1, pointing to penetration of ethylene glycol into the innerstructure of the PE-HD balls. This peak was observed in every spectrum taken fromcracked balls.Consequently, it can be concluded that the PE-HD balls failed by a combination

of creep rupture and environmental stress cracking. While the creep rupture data andanalysis of Chapter 6 predicted a failure at about 10 months, the effect of the ethyleneglycol environment, which attacked the surface of the balls, accelerated the failure toapproximately three months.


Fracture of a Polycarbonate Clamp

In this case study a feature of a polycarbonate clamp was fracturing after assembly.The photograph presented in fig. 8.17 shows a typical failed part.

Crack

Bolt and nut

Figure 8.17: Photograph of the failed polycarbonate clamp.

The crack initiated in the vicinity of a bolt that held the clamp assembly tight. Thebolt and nut felt oily to the touch and had a strong smell. An infrared spectrum of thefailed part’s surface revealed significant contamination in the 3,000 cm -1 wavenumberrange.


4000 6001000150020003000

Abs

ortiv

ityA

bsor

tivity

Crack surface of failed polycarbonate part

Polycarbonate spectrum

Wavenumber, cm-1

Figure 8.18: Infrared spectra of polycarbonate and the crack surface of the failedpolycarbonate clamp

4000 6001000150020003000

Abs

ortiv

ityA

bsor

tivity

Mineral oil

Oil from bolts

Wavenumber, cm-1

Figure 8.19: Infrared spectra of the oil


Figure 8.18 presents a comparisonof the spectrumof a standard polycarbonate resinand the spectrum taken from the crack surface. It is evident from the two spectra thatchemical attack occurred in the failed part.An additional infrared spectrum was performed on the oil from the bolt surface

(fig. 8.19) and compared to the spectrum of a mineral oil. Both spectra agree with eachother. Furthermore, the spectra from the oils are in agreement with the contaminant onthe crack surface in the region of 3,000 cm-1 wavenumber. This points to the fact thatthe chemical that attacked the surface of the clamp was the oil from the bolt and nut,and that it led to environmental stress cracking. To solve the problem, themanufacturerchanged to a polycarbonate blend, which is resistant to chemical attack form the oil.

8.4 THERMAL DEGRADATION OF POLYMERS

Because plastics are organic materials, they are threatened by chain breaking, splitting offof substituents, and oxidation. This degradation generally follows a reaction that can bedescribed by the Arrhenius principle. The period of dwell or residence time permittedbefore thermal degradation occurs is given by

tpermited ≈ eΔ

RT , (8.2)

where Δ is the activation energy of the polymer, R the gas constant, and T the absolutetemperature.

Figure 8.20: Test procedure to determine flashpoint of polymers

A material that is especially sensitive to thermal degradation is PVC; in addition, thehydrogen chloride that results during degradation attacks metal parts. Ferrous metals act asa catalyzer and accelerate degradation. An easy method for determining the flashpoint ofmolding batches is by burning the hydrocarbons which are released at certain temperatures.This is shown schematically in fig. 8.20. For PVC, a vial with soda lye, instead of a flame,should be used to determine the conversion of chlorine. Figure 8.21 presents the allowableexposure time as a function of the environment’s temperature for various thermosets.


10

100

1000

10000

100000

140 160 180 200 220 240 260 280 300 320

GF- UP Mat

UP, Type 802

PF, Type 31 MF, Type 156

PF, Type 12

Storage temperature (1/K)

Decay from σB of 50%

Decay from σ bB of 30%

Decay on σ bB = 50 N/mm2

oC

h

101

102

103

104

105

Figure 8.21: Allowable thermal loading times as a function of temperature for various thermosets

DegradationOptimal melt

Piston-type machine

Leathery

Plastic

Viscoelastic

Thermal loading time

Figure 8.22: Schematic of thermal loading of polymer melts for injection molding processes(Albers) [1]


200

220

240

260

280

300

320

340

0 4 8 12

Residence time

oC

min

Indicator: 10% viscosity drop

Type 1 Type 2

Figure 8.23: Processing windows with thermal loading time for two PBT resins

Thermal degradation can be critical during processing. Figure 8.22 schematically depictsprocessing windows for injection molding with respect to optimal melt conditions and ther-mal degradation caused by thermal loading. An actual thermal degradation versus thermalloading time is presented for two types of PBT in Fig. 8.23. The upper bounding of theprocessing window is controlled by a 10% drop in viscosity criteria.

Table 8.8: Standard methods of measuring flammability of polymers (linear burningrate of horizontal specimens) (Shastri)

Standard ISO 1210 , Method A D635 - 98

Specimen 125mmx13mmx3mm(additionalspecimen thickness <3 mm may beused)

125mmx 12.5 mm in thickness nor-mally supplied (3 - 12 mm cut fromsheet or molded).

Conditioning Specimen conditioning, includingany post molding treatment, shall becarried out at 23 ◦C ±2 ◦C and 50±5 % R.H. for a minimum length oftime of 88 h, except where specialconditioning is required as speci-fied by the appropriatematerial stan-dard.

As received, unless otherwise spec-ified.

Apparatus Laboratory burner in accordancewith ISO 10093

Laboratory burner in accordancewith D5025 - 94.



Standard ISO 1210 , Method A D635 - 98

Test procedures Three specimens At least 10 specimens

Values and units Burning rate ⇒ mm/min (If addi-tional specimens with thicknesses <3 mm are tested, the specimen thick-ness must also be reported)Averagetime of burning⇒ s

Average extent of burning⇒ mm

Table 8.9: Standard methods of measuring flammability (flame and after-glow times ofvertical specimens) (Shastri)

Standard ISO 1210 Method B D3801 - 96

Specimen 125 mm x 13 mm x 3 mm (Addi-tional specimen thickness <13 mmmay be used)

125 mm x 13 mm x 3 mm (Addi-tional specimen thickness <13 mmmay be used)

Conditioning Two sets of five specimens at 23±2 ◦C and 50 ±5% relative humid-ity for at least 48h; two sets of fivespecimens at 70 ±1/2 ◦C for 168 h±2 h

One set of five specimens at 23±2 ◦C and 50 ±5% relative humid-ity for at least 48h; second set of fivespecimens at 70 ±1/2 ◦C for 168 h

Apparatus Laboratory burner in accordancewith ISO 10093. Barrel length is100 ±10 mm and inside diameter of9.5 ±0.3 mm

Bunsen Tirrill type burner of tubelength 95 ±6 mm and inside diame-ter 9.5 (+1.6 mm, - 0.0 mm)

Test procedures Technical grade methane gas or nat-ural gas having a heat content of ap-proximately 37 MJ/m3

Technical grade methane gas or nat-ural gas having energy density ap-proximately 37 MJ/m3

Values and units Flame classification Flame classification

Contact to flames is considered extreme thermal loading of polymers. The flammabilityof polymers is critical inmany products such as clothing, construction, electric and electronicequipment, and under-the-hood automotive applications, to name a few. There are variousstandard tests with which one can determine and assess the flammability of polymers. Theflammability of horizontally oriented specimens is measured using the standard tests ISO


1210 and ASTMD635 presented in Table 8.8. ISO 1210 also prescribes the flammability ofvertical specimens along with the ASTM D3801 test. The vertical specimen flammabilitytests are presented in Table 8.9.To asses the flammability of polymers, the UL Subject 94 of theUnderwriters Laborato-

ries has been adopted throughout the world. In the tests, horizontal and vertical specimensare exposed to flames from a Bunsen burner. The evaluation includes burning speed, burneddistance, after burn, and dripping. The evaluation is done in steps of increasing rigor: "no,""HB," "V-2," "V-1," "V-0," "5VA," or "5VB." The UL Subject 94 has been adopted by theCAMPUS databank.

The ignitability of polymers is measured using the standard tests ISO 4589 and ASTMD2863 presented in Table 8.10. The ISO 4589 has also been adopted by the CAMPUSdatabank.

Table 8.10: Standard methods of measuring ignitability (Shastri)

Standard ISO 4589 - 2 , Procedure A D2863 - 97

Specimen 80mmx 10mmx4mmcut from thecenter of the ISO3167multipurposespecimen (ISO 4589-2, Form 1)

70 - 150 mm x 6.5 mm x 3 mm

Conditioning Specimen conditioning, includingany post molding treatment, shall becarried out at 23 ◦C ±2 ◦C and 50±5 % R.H. for a minimum length oftime of 88h, except where specialconditioning is required as speci-fied by the appropriatematerial stan-dard.

As received, unless otherwiseagreed upon

Apparatus Test chimneydimensionsof450mmin height x 75 mm minimum di-ameter cylindrical bore. The upperoutlet should be restricted as nec-essary to produce an exhaust veloc-ity of at least 90 mm/s from a flowrate within the chimney of 30 mm/s.The base of the chimney will prefer-ably have a layer of glass beads (3-5 mm in diameter) between 80 and100 mm deep. The specimen shallbe held by a small clamp which isa least 15 mm away from the near-est point at which the specimen mayburn.

Test column of heat-resistant glasstube 450 mm in height x 75 mmminimum inside diameter. The baseof the column contain a non- com-bustible material which can evenlydistribute the gas mixture. A layerof glass beads (3-5 mm in diameter)between 80 and 100 mm deep hasbeen found suitable. The specimenshall be held by a small clamp thatwill support the specimen at its baseand hold it vertically in the center ofthe column.




The moisture content of the gas en-tering the chimney shall be < 0.1%(m/m) and the variation in oxygenconcentration rising in the chimney,below the level of the test specimen,is <0.2% (V/V)

The flow control and measuring de-vices shall be such that the volumet-ric flow of each gas into the columniswithin 1%of the range being used.

Apparatus The flame ignitor is a tube with anoutlet of 2 ±1 mm diameter whichprojects a 16 ±4mmflame verticallydownward from the outlet when thetube is vertical within the chim-ney. The flame fuel shall be propanewithout premixed air.

The flame ignitor is a tube with asmall orifice 1-3 mm in diameter,which projects a flame 6 to 25 mmlong. Theflame fuel can be propane,hydrogen or other gas flame.

Test procedures A minimum of 15 specimens shallbe prepared in accordance with therelevant material standard. Whennone exists, or unless otherwisespecified, specimens shall be di-rectly compression or injectionmolded in accordance with ISO 293or ISO 294-1.

A sufficient number of specimens(normally 5 to 10)

Test specimens shall be marked50 mm from the end to be ignited.

No marking indicated, authorswould assume that some indicationis needed to know when the burnlength of 50 mm is achieved.

Select the initial concentration ofoxygen to be used based on expe-rience with similar materials, or ig-nite the specimen in air and notethe burning behavior. Select an ini-tial concentration ca. 18%, 21%, or25% (V/V) depending on the burn-ing behavior.

Select the initial concentration ofoxygen to be used based on expe-rience with similar materials, or ig-nite the specimen in air and note theburning behavior. Select an initialconcentration ca. 18%, or 25% de-pending on the burning behavior.

Specimen is mounted such that thetop of the specimen is at least100 mm below the top of the chim-ney, and the lowest exposed part ofthe specimen is 100 m above the topof the gas distribution device.

Specimen is mounted vertically inapproximate center of the columnwith the top of specimen at least100 mm below the top of the col-umn.

Gas flow rate of 40 ±10 mm/s Gas flow rate of 40 ±10 mm/sContinued on next page



Apply the flame, with a sweepingmotion to the top of the specimenfor up to 30 s, removing it every 5 sto determine if the top is burning.

Ignite the entire top of the specimenso that the specimen is well lit, re-move the flame.

Test procedures Commence timing the period ofburning. If the burning ceases butspontaneous combustion occurs in< 1 s, continue timing. If periodand extent of burning does not ex-ceed 180s and 50 mm, the oxygenconcentration would need to be in-crementally increased. Adjust theoxygen concentration either up ordown until there are two concentra-tions which differ by <1.0% and inwhich one specimen met the crite-ria and the other did not. Repeat thetest on four more specimens.

Start timing. If the burning time andthe extent of burning does not ex-ceed 180 s and 50 mm, the oxygenconcentration would need to be in-crementally increased. Adjust theoxygen either up or down until thecritical concentration of oxygen isdetermined. This is the lowest levelwhich meets the 180 s/50 mm crite-ria. At the next lower oxygen con-centration that will give a differencein oxygen index of 0.2% or less,the specimen should not meet the180 s/50mmcriteria. Repeat the teston three more specimens, but start-ing at a slightly different flow rate,yet in the criteria of 30-50% (V/V)

Values and units Average Oxygen Index⇒% (V/V) Average Oxygen Index⇒% (V/V)

References


2. Weathering testing guidebook. Atlas, 2001.

3. A. Davis and D. Sims. Weathering of Polymers. Applied Science Publishers, 1983.

4. Table 4. Commision Internationale De L’Eclairage Publication Number CIE 85, 1st Edition, 1989.

5. The effect of various light sources on the degradation of polymers - a fundamental approach. atlasmaterial testing solutions. In Polyolefins 2001 conference, 2001.

6. L. Crewdson. Correlation of outdoor and laboratory accelerated test at currently used and higherirradiance levels part II. Atlas material testing solutions, 23(46), 1993.

7. G.W. Ehrenstein. Polymeric Materials. Hanser Publishers, Munich, 2001.

8. M.N. Riddell. Plastics Engineering, 40(4):71, 1974.

9. R.W. Hertzberg and J.A. Mason. Fatigue of Engineering Plastics. Academic Press, New York,1980.

315

CHAPTER 9

ELECTRICAL, OPTICAL, AND ACOUSTICPROPERTIES

9.1 ELECTRICAL PROPERTIES

In contrast tometals, commonpolymers are poor electron conductors. Similar to mechanicalproperties, their electric properties depend to a great extent on the flexibility of the polymer’smolecular blocks. The intent of this chapter is to familiarize the reader with electricalproperties of polymers by discussing dielectric, conductive, and magnetic properties.

9.1.1 Dielectric Behavior

Dielectric coefficient: The most commonly used electrical property is the dielectriccoefficient, εr , also known as the electric permittivity. This property describes the abilityof a material to store an electric charge. Table 9.1 lists the relative dielectric coefficientsof important polymers. The measurements were conducted using the standard test DIN 53483 in condensers of different geometries which, in turn, depended on the sample type. TheASTM standard test is described by ASTM D150 and the ISO test. Both the ASTM D150and the IEC 60250 tests are presented in Table 9.2. Figures 9.1 [1] and 9.2 [1] presentthe dielectric coefficient for selected polymers as a function of temperature and frequency,respectively.

316 9 Electrical, Optical, and Acoustic Properties

0

5

10

15

20

0 40 80 120 160

PA66

PVC

PF Hp

PF 31.5

PVC+40% TCP

Temperature

B- Glass PMMA

PC

PS PSU PI PE ρ= 0.96 PTFE PET

oC

Die

lect

ric c

onst

ant ε

Figure 9.1: Dielectric constant as a function of temperature for various polymers (Domininghaus) [1]

0

5

10

1 100 10000 1000000 100000000 10000000000

PF

PMMA PVC B-Glass PA66

PSPCTFE

PCPE ρ= 0.96

Hz100 102 104 106 108 1010

Frequency

Die

lect

ric c

onst

ant

ε

Figure 9.2: Dielectric constant as a function of frequency for various polymers (Domininghaus)[1]


Table 9.1: Relative dielectric coefficient, εr , of various polymers

Polymer Relative dielectric coefficient, εr800 Hz 106 Hz

ABS 4.6 3.4CA, type 433 5.3 4.6EP (unfilled) 2.5-5.4Expanded PS 1.05 1.05PA6 (moisture content dependent) 3.7-7.0PA66 (moisture content dependent) 3.6-5.0PE (density dependent) 2.3-2.4 2.3-2.4PC 3.0 3.0PET 3.0-4.0 3.0-4.0MF type 154 5.0 10.0PF type 31.5 6.0-9.0 6.0PF type 74 6.0-10.0 4.0-7.0PP 2.3 2.3PPE 2.7 2.7PS 2.5 2.5PTFE 2.05 2.05UF type 131.5 6.0-7.0 6.0-8.0

Dielectric polarization: The two most important molecular types for the polarization ofa dielectric in an electric field are displacement polarization and orientation polarization.Under the influence of an electric field, the charges deform in field direction by aligningwiththe atomic nucleus (electron polarization) orwith the ions (ionic polarization). This is usuallycalled displacement polarization and is shown in Fig. 9.3. Because of their structure, somemolecules possess a dipole moment in the spaces that are free of an electric field. Hence,when these molecules enter an electric field, they will orient according to the strength of thefield. This is generally referred to as orientation polarization and is schematically shown inFig. 9.3.

Figure 9.3: Polarization processes

It takes some time to displace or deform the molecular dipoles in the field direction andan even longer time for the orientation polarization. The more viscous the surrounding


medium, the longer it takes. In alternating fields of high frequency, the dipole movementcan lag behind at certain frequencies. This is called dielectric relaxation, which leads todielectric losses that appear as dielectric heating of the polar molecules.

Table 9.2: Standard methods of measuring relative permittivity and dissipation factorof polymers (Shastri)

Standard IEC 60250 : 69 D 150 - 95

Specimen geometry > 80 mmx > 80mm x 1mm (greaterthickness may be used for those ma-terials that cannot be molded reli-ably at 1 mm thickness)

Test specimens are of suitable shapeand thickness determined by thema-terial specification or by the accu-racy of measurement required, andthe frequency at which the measure-ments are to be made.


Clean the test specimen with a suit-able solvent or as prescribed in thematerial specification. Use Recom-mendedPracticeD1371as aguide tothe choice of suitable cleaning pro-cedures.

Test procedures 100 Hz and 1 MHz. Frequency not specified butrecorded.

Null methods are used at frequen-cies up to 50 MHz and results arecompensated for electrode edge ef-fects.

Null method with resistive or in-ductive ratio arm capacitance bridgesuggested for frequencies of < 1Hzto a few MHz.

Values and units Relative permittivity⇒ unitless Relative permittivity⇒ unitlessDissipation Factor⇒ unitless Dissipation Factor⇒ unitless

In contrast to this, the changes in the displacement polarization happen so quickly that itcan even follow a lightwave. Hence, the refractive index, n, of light is determined by thedisplacement contribution, εv, of the dielectric constant. The relation between n and εv isgiven by

n =√

εv. (9.1)

Hence, we have a way of measuring polarization properties because the polarization ofelectrons determines the refractive indexof polymers. It should be noted that ion ormolecularsegments of polymers aremainly stimulated in themiddle of the infrared spectrum. Anumberof polymers have permanent dipoles. The best known polar polymer is polyvinyl chloride,


Figure 9.4: Frequency dependence of different polarization cases

and C=O groups also represent a permanent dipole. Therefore, polymers with that kindof building block suffer dielectric losses in alternating fields of certain frequencies. Forexample, Fig. 9.4 shows the frequency dependence of susceptibility.In addition, the influence of fillers on the relative dielectric coefficient is of considerable

practical interest. The rule of mixtures can be used to calculate the effective dielectric coeffi-cient of a matrix with assumingly spherically-shaped fillers. Materials with air entrapmentssuch as foams, have a filler dielectric coefficient of εair = 1. Whether a molecule is stim-ulated to its resonant frequency in alternating fields or not depends on its relaxation time.The relaxation time, in turn, depends on viscosity, temperature, and radius of the molecule.

Dielectric dissipation factor: Typical ranges for the dielectric dissipation factor ofvarious polymer groups are:

• Non-polar polymers (PS, PE, PFE): tanδ < 0.005• Polar polymers: tanδ = 0.001 – 0.02• Thermosets resins filled with glass, paper, or cellulose: tanδ = 0.02 – 0.5Figures 9.5 [1] and 9.6 [1] present the dissipation factor tan δ as a function of temperature

and frequency, respectively. The standard tests to measure the dielectric dissipation factorof polymers are the IEC 60250 and ASTM D150, presented in Table 9.2.

Electrical and thermal loss in a dielectric: The electric losses through wire insu-lation running high frequency currents must be kept as small as possible. Insulators areencountered in transmission lines or in high frequency fields, such as the housings of radarantennas. Hence, we would select materials that have low electrical losses for these typesof applications. On the other hand, in some cases we want to generate heat at high frequen-cies. Heat sealing of polar polymers at high frequencies is an important technique used inthe manufacturing of soft PVC sheets, such as the ones encountered in automobile vinylseat covers. To assess whether a material is suitable for either application, one must knowthe loss properties of the material and calculate the actual electrical loss. Polyethylene andpolystyrene are perfectly suitable as insulators in high frequency applications. To measurethe necessary properties of the dielectric, the standard DIN 53 483 and ASTM D 150 testsare recommended.


0.00001

0.0001

0.001

0.01

0.1

0 40 80 120 160

Temperature

PA66PF 31.5

PVC

PF Hp

PMMA

PETPSU

PIPC

B-Glass

PTFE

PS

PE ρ= 0.96

PVC+40%TCP

oC

101

102

103

104

105

Figure 9.5: Dielectric dissipation factor as a function of temperature for various polymers(Domininghaus) [1]

0.00001

0.0001

0.001

0.01

0.1

1

1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10

Frequency

PF

PMMA

PA66

PVCPCTFE

PC

B-Glass

PS

PE ρ= 0.96

Hz

101

102

104

105

100 104102 106 108 1010

103

Figure 9.6: Dielectric dissipation factor as a function of frequency for various polymers(Domininghaus) [1]


9.1.2 Electric Conductivity

Electric resistance: The current flow resistance, R, in a plate-shaped sample in a directvoltage field is defined by Ohm’s law as

R =U

I, (9.2)

where U is the consumed voltage and I the current. The resistance is often described as theinverse of the conductance,G,

R =1G

. (9.3)

The simple relationship found in the above equations is seldom encountered because thevoltage,U , is rarely steady and usually varies in a cyclic fashion between 10−1 to 1011 Hertz[2].

1.E+11

1.E+13

1.E+15

1.E+17

1.E+19

0 10 20 30 40 50 60 70 80 90 100

PS

PE

PBT

POM

Temperature

oC

Ω•cm

1011

1013

1015

1017

1019

Spe

cific

res

ista

nce

Figure 9.7: Specific electric resistance of polymers as a function of temperature

Figures 9.7 to 9.9 compare the specific resistance of various polymers and show itsdependence on temperature. Here, we can see that similar to other polymer properties,such as the relaxation modulus, the specific resistance not only decreases with time but alsowith temperature. The surface of polymer parts often shows different electric direct-currentresistance values than their volume. The main cause is surface contamination (e.g., dust andmoisture). We therefore have to measure the surface resistance using a different technique.Other tests often used to measure surface resistance are the ASTM D257, DIN 53 480, andDIN 53 482 tests.The surface resistance of variousfilled thermoplastics is presented inFig. 9.10as a function

of filler weight percentage. Figure 9.11 shows the effect of moisture content on the specificelectric resistance of polyamides.


1.E+05

1.E+07

1.E+09

1.E+11

1.E+13

1.E+15

1.E+17

1.E+19

-100 -50 0 50 100 150 200

PCCP hard

CAB/CA hard

CP soft

CAB/CA soft

EVAC

PA6 dryPA12

Ω•cm

Temperature

ABS

ak = 12 kJ/m 2

105

107

108

109

1010

1011

1012

1013

oC

Spe

cific

res

ista

nce


1.E+05

1.E+08

1.E+11

1.E+14

1.E+17

1.E+20

-100 -50 0 50 100 150 200

Temperature

Ω•cm

oC

PUR-Elast

EP

UP, Normal

PET-GF 50

PVDF

PBT-GF 30

105

108

1011

1014

1017

1020


Physical causes of volume conductivity: Polymers with a homopolar atomic bond,which leads to pairing of electrons, do not have free electrons and are not considered to beconductive. Conductive polymers – still in the state of development – in contrast, allowfor movement of electrons along the molecular cluster because they are polymer salts. Theclassification of these polymers with different materials is given in Fig. 9.12. Potential usesof electric conductive polymers in electrical engineering include flexible electric conductorsof low density, strip heaters, anti-static equipment, high frequency shields, and housings.


0 10 20 30 40 50 60 70

Coated ceramic fiber

PP + antistatic additive

PC + carbon fiber

PA66 + carbon fiber

POM +carbon fiber

PP + carbon black

- Region for antistatic additives

- Antistatic materials

- Materials for slow electrostatic discharge.

- Materials for fast electrostatic discharge

- Materials for grounding- Highly conductive materials - Materials for electromagnetic shielding-Conductive in mA domain

% Weight of conductive additive

100

103

106

1010

1012

1016

Electric surface resistance

% % % %

Ω

Figure 9.10: Surface resistance for several thermoplastics as a function of filler content

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

1.E+15

0 1 2 3 4 5 6 7

Water content

PA6

PA66

%

Ω•cm

1012

109

1010

1011

1014

1015

1013

Figure 9.11: Specific electric resistance for PA6 and PA66 as a function of moisture content

In semiconductor engineering, some applications include semiconductor devices (Schottky-Barriers) and solar cells. In electrochemistry, applications include batteries with high energyand power density, electrodes for electrochemical processes and electrochrome instruments.Because of their structure, polymers cannot be expected to conductions. Yet the extremely

weak electric conductivity of polymers at room temperature and the fast decrease of conduc-tivity with increasing temperatures is an indication that ions do move. They move becauseengineering polymers always contain a certain amount of added low molecular constituents


Figure 9.12: Electric conductivity of polyacetylene (trans-(CH)x) in comparison to other materials

Figure 9.13: Resistance R of a polymer filled with metal powder (iron)

that act as moveable charge carriers. This is a diffusion process that acts in field directionand across the field. The ions "jump" from potential hole to potential hole as activated byhigher temperatures. At the same time, the lower density speeds up this diffusion process.The strong decrease of specific resistance with the absorption of moisture is caused by ionconductivity.Conductive polymers are useful for certain purposes. When we insulate high energy

cables, for example, as a first transition layer, we use a polyethylene filled with conductivefiller particles such as soot. Figure 9.13 demonstrates the relationship between filler contentand resistance. When contact tracks develop, resistance drops spontaneously. The number ofinter-particle contacts,M , determines the resistance of a composite. AtM 1 orM = 1 there


Figure 9.14: Resistance in metal flakes and powder-filled epoxy resins (Reboul) [3]

1

100

10000

1E+06

1E+08

1E+10

1E+12

1E+14

1E+16

1E+18

0 5 10 15 20 25 30 35

Specific area

Carbon black content

Weight %

Ω•cm

95 m2/g

1200 m2/g150 m2/g

100

102

104

106

108

1010

1012

1014

1016

1018

Figure 9.15: Specific resistance in carbon black-filled polypropylene


is one contact per particle. At this point, the resistance starts dropping. When two contactsper particle exist, practically all particles participate in setting up contact and the resistancelevels off. The sudden drop in the resistance curve indicates why it is difficult to obtain amedium specific resistance by filling a polymer. Figure 9.14 [3] presents the resistance inmetal flakes or powder-filled epoxy resins, and Fig. 9.15 presents the specific resistance ofcarbonblack-filled polypropylenes. Figure 9.14 showshow the critical volume concentrationfor the epoxy systems filled with copper or nickel flakes is about 7% concentration of filler,and the critical volume concentration for the epoxy filled with steel powder is around 15%.A similar effect is seen in the carbon black-filled polypropylene. In addition, the effect ofcarbon black surface area is significant.

9.1.3 Application Problems

10

100

1000

0 0.5 1 1.5 2 2.5 3 3.5

PPE+PS-GF 30

PC

POM

PE

EP

Thickness

kV/mm

mm

Figure 9.16: Dielectric strength of various plastics as a function of test specimen thickness

Electric breakdown: The electric breakdown of insulation must be prevented because itmay lead to the failure of an electric component ormay endanger people handling the compo-nent. To design the insulation for long continuous use with a great degree of confidence, weneed to know the critical load of the insulating material. The standard tests used to generatethis important material property data for plate- or block-shaped specimens are ASTM D149andDIN 53 481. From the properties already described,we know that the electric breakdownresistance or dielectric strength must depend on time, temperature, material condition, loadapplication rate, and frequency. It is furthermore dependent on electrode shape and samplethickness as is demonstrated in Figs. 9.16 and 9.17, which present the dielectric strengthof various thermoplastics as a function of test specimen thickness. In practice, however,it is very important that the upper limits measured on the experimental specimens in thelaboratory are never reached.


10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5

PA11

PA6-GF 301.5 % H 20

PA6 humid air

PA6 dry

PA6-GF 30 dry

PA11- GF 30

Thickness

mm

kV/mm

Die

lect

ric s

tren

gth

Ed

Figure 9.17: Dielectric strength of various polyamides as a function of test specimen thickness

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18 20

PET

PC

PS

CA

CAB

kV/mm

Load time

h

Die

lect

ric s

tren

gth

Ed

Figure 9.18: Dielectric strength of various thermoplastics as a function of load time


40

60

80

100

120

140

0.01 0.1 1 10 100 1000 10000

150

kV/mm

PE-LD

h

Time

Die

lect

ric s

tren

gth

Ed

Figure 9.19: Dielectric strength of PE-LD as a function of load time

The rule of thumb is to use long-term load values of only 10% of the short-term laboratorydata. Figures 9.18 to 9.20 present dielectric strength as a function of load time for severalthermoplastics.

0

10

20

30

40

50

60

1 10 100 1000

Time

PF (oil)

PA-GF 301 mm

PA60.25 mm

Thickness= 0.25 mmPC

PC1mm

PC-GF 301 mm

h

kV/mm

1h 1d 1 Wo. 1 Mo.

Testing media: air, (oil)

Die

lect

ric s

tren

gth

Ed

Figure 9.20: Dielectric strength of various thermoplastics as a function of load time

Figure 9.21 shows the progression of dielectric breakthrough during time, starting withdielectric breakthrough and followed by heat breakthrough and erosion. The temperatureand frequency also significantly affect the dielectric strength of polymers. Figures 9.22 and


0

1

Load time

Electric breakthrough Thermal breakthrough

Erosion

Without thermal breakthrough (Polyolefins)

10-2 100 10210-4 104 10610-6 108s

Figure 9.21: Dielectric strength breakthrough progression in time

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120

kV/mm PE-LDs= 0.45 mm

PE-HD0.45 mm

POM0.2 mm

oC

Temperature

Die

lect

ric s

tren

gth

Ed

Figure 9.22: Dielectric strength of PE and POM as a function of temperature

9.23 show the effect of temperature on dielectric strength of selected thermoplastics, andFig. 9.24 represents the dielectric strength as a function of frequency. Figure 9.25 shows thecombined effect of frequency and temperature on the dielectric strength of PF paper. Aswith other properties, additives such as plasticizers can significantly influence the dielectricstrength of polymer sheets, as illustrated in Figs. 9.26 and 9.27 for a PVC-P with 25% and35% plasticizers, respectively.


0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120 140 160

Temperature

kV/mm

PC

PC-GF 30

PA6-GF 30 dry

PA11

PA12

PA6, 66dry

Thickness= 1 mm

Die

lect

ric s

tren

gth

Ed

Figure 9.23: Dielectric strength of selected plastics as a function of temperature

0

20

40

60

80

100

0.01 1 100 10000 1000000 100000000

20oC

60oC

100oC

PTFE

PE

PF

Frequency

kV/mm

10-2 100 102 104 106 108

Figure 9.24: Dielectric strength of selected plastics as a function of frequency


0

20

40

60

80

100

120

140

160

-20 0 20 40 60 80 100

Temperature

oC

kV/mm

PF-PaperHertz

0

0.5

5

50

500

50000

500000

5000

Die

lect

ric s

tren

gth

Ed

Figure 9.25: Dielectric strength of PF paper measured at several frequencies as a function oftemperature

0

10

20

30

40

-50 0 50 100 150

Temperature

kV/mmPVC-P

TDF

TKP

DOP

Thickness: 0.1 cmSpherical electrode 20 mm0.5 kV/s, 50 Hz

∅

25% Plasticizer content

oC

Die

lect

ric s

tren

gth

Ed

Figure 9.26: Dielectric strength of a PVC-P, with various plasticizers (25%), as a function oftemperature


0

10

20

30

40

-50 0 50 100 150

TDF

TKP

DOP

kV/mm35% Plasticizer content

PVC-P

Temperature

oC

Die

lect

ric s

tren

gth

Ed

Figure 9.27: Dielectric strength of a PVC-P with various plasticizers (35%) as a function oftemperature

Figure 9.28: Drop of the dielectric strength of PP films with increasing strain (Menges and Berg) [4]


Figure 9.29: Increase of dielectric dissipation with increased strain in PP foils (Menges and Berg) [4]

Experimental evidence shows that the dielectric strength decreases as soon as crazesform in a specimen under strain and continues to decrease with increasing strain. Thisis demonstrated in Fig. 9.28 [4]. On the other hand, Fig. 9.29 [4] demonstrates how thedielectric dissipation factor, tan δ, rises with strain. Hence, one can easily determine thebeginning of the viscoelastic region (beginning of crazing) by noting the starting point ofthe change in tan δ. It is also known that amorphous polymers act more favorably to electricbreakdown resistance than partly crystalline polymers. Semicrystalline polymers are moresusceptible to electric breakdownas a result of breakdownalong inter-spherulitic boundaries[5]. Long-termbreakdownof semicrystalline polymers is either linked to "treeing" or occursas a heat breakdown, burning a hole into the insulation. In general, with rising temperatureand frequency, the dielectric strength continuously drops.

Table 9.3: Dielectric strength and resistivity for selected polymers (Crawford)

Polymer Dielectric strength Resistivity(MV/m) (Ohm-m)

ABS 25 1014

Acrylic 11 1013

CA 11 109

CAB 10 109

Epoxy 16 1013

Modified PPO 22 1015

PA66 8 1013

PA66 + 30% GF 15 1012

PEEK 19 1014

PET 17 1013

PET + 36% GF 50 1014

PF (mineral filled) 12 109



Polymer Dielectric strength Resistivity(MV/m) (Ohm-m)

PC 23 1015

PE-PE 27 1014

PE-PE 22 1015

POM (homopolymer) 20 1013

POM (copolymer)acrylic 20 1013

PP 28 1015

PS 20 1014

PTFE 45 1016

PVC-U 14 1012

PVC-P 30 1011

SAN 25 1014

Insulation materials – mostly LDPE – are especially pure and contain voltage stabilizers.These stabilizers are low-molecular cyclic aromatic hydrocarbons. Presumably, they diffuseinto small imperfections or failures, fill the empty space, and thereby protect them frombreakdown. Table 9.3 [6] gives dielectric strength and resistivity for selected polymericmaterials.The standard tests used to measure dielectric strength of polymers are IEC 60243and ASTM D149, presented in Table 9.4. Another test to measure the dielectric strength ofpolymers is the electric tracking test where the voltage required to cause tracking is recorded.The standard IEC 60112 andASTMD3638 tests, described in Table 9.5, are used to evaluatethe comparative tracking index (CTI).

Table 9.4: Standard methods of measuring electric strength of polymers (Shastri)

Standard IEC 60243-1 : 88 D 149 - 95a, Method B

Specimen geometry > 80 mm x > 80 mm x 1 mm or3 mm, sufficiently wide to preventdischarge along the surface.

Thickness not specified but mea-sured. It shall be of sufficient sizeto prevent flashover under the con-ditions of the test.

Conditioning Specimen conditioning, includingany post molding treatment, shall becarried out at 23 ◦C ±2 ◦C and 50±5% R.H. for a minimum length oftime of 88 h, except where specialconditioning is required.

If not specified in the applicable ma-terial specification, follow the pro-cedures in Practice D 618.



Standard IEC 60243-1 : 88 D 149 - 95a, Method B

Apparatus Two coaxial cylinder electrodes(25 mm diameter x 25 mm and75 mm diameter x 15 mm) withedges rounded to 3 mm radius.

Electrode Type 6:Two coaxial cylinder electrodes(25 mm diameter x 25 mm and75 mm diameter x 15 mm) withedges rounded to 3 mm radius.

Test procedures Immersion in transformer oil in ac-cordance with IEC 296. Power fre-quencies between 48 – 62 Hz 20 sstep-by-step.

Immersion in mineral oil, meetingD3487 Type I or II requirements.60 Hz, unless otherwise specified 60±5 s step-by-step.

Values and units Dielectric strength⇒ kV/mm Dielectric strength⇒ kV/mm

Table 9.5: Standard methods of measuring comparative tracking index (CTI) of poly-mers (Shastri)

Standard IEC 60112 : 79 D 3638 - 93

Specimen geometry > 15 mm x > 15 mm x 4 mm fromthe shoulder of the ISO 3167 multi-purpose test specimen.

Sample size is 50 mm or 100 mmdisk with minimum thickness of2.5 mm. Thin samples are to beclamped together to get minimumthickness.


In accordance with Procedure A ofPractice D618.

Apparatus Two platinum electrodes of rectan-gular cross-section 5 mm x 2 mmwith one end chisel edged with anangle of 30 ◦ and slightly rounded.

Two platinum electrodes of rectan-gular cross-section 5 mm x 2 mmwith one end chisel edged with anangle of 30 ◦ and slightly rounded.



Standard IEC 60112 : 79 D 3638 - 93

Apparatus Electrodes are symmetrically ar-ranged in a vertical plane, the totalangle between them being 60 ◦ andwith opposing faces vertical and 4.0±0.1 mm apart on the specimen sur-face. Force exerted on the surfaceby the electrode is 1.0 ±0.05 N.

Position the electrodes so that thechisel edges contact the specimen ata 60 ◦ angle and the chisel faces areparallel in the vertical plane and areseparated by 4 ±0.2 mm.

Test procedures 0.1 ±0.002% by mass ammoniumchloride in distilled or deionizedwa-ter (Solution A) with a resistivity of395 ±5 Ohm-cm at 23 ±1 ◦C.

0.1 ±0.002% by mass ammoniumchloride in distilled or deionizedwa-ter (Solution A) with a resistivity of395 ±5 Ohm-cm at 23 ±1 ◦C.

Voltage between 100 V and 600 Vat frequency between 46 – 60 Hz.

Voltage should be limited to 600 Vat a frequency of 60 Hz.

Determine maximum voltage atwhich no failure occurs at 50 dropsin the test on five sites. This is theCTI provided no failure occurs be-low 100 drops when the voltage isdropped by 25 V.

Plot the number of drops of elec-trolyte at breakdown vs. voltage.The voltage which corresponds to50 drops is the CTI.

At least five test sites (can be on onespecimen).

At least five specimen of each sam-ple shall be tested.

Values and units CTI⇒V CTI⇒V

Electrostatic charge: An electrostatic charge is often a result of the excellent insulationproperties of polymers – the veryhigh surface resistance andcurrent-flow resistance. Becausepolymers are bad conductors, the charge displacement of rubbing bodies, which developswithmechanical friction, cannot equalize. This chargedisplacement results froma surplus ofelectrons on one surface and a lack of electrons on the other. Electrons are charged positivelyor negatively up to hundreds of volts. They release their surface charge onlywhen they touchanother conductive body or a body that is inversely charged. Often, the discharge occurswithout contact, as the charge arches through the air to the nearby conductive or inverselycharged body, as demonstrated in Fig. 9.30. The currents of these breakdowns are low. Forexample, there is no danger when a person suffers an electric shock caused by a charge fromfriction of synthetic carpets or vinyls. There is danger of explosion, though, when the sparksignite flammable liquids or gases.As the current-flow resistance of air is generally about 109 Ωcm, charges and flashovers

only occur if the polymer has a current-flow resistance of> 10 9 to 1010 Ωcm. Another effect


Figure 9.30: Electrostatic charges in polymers

of electrostatic charges is that they attract dust particles on polymer surfaces. Electrostaticcharges can be reduced or prevented by the following means:

• Reduce current-flow resistance to values of < 109 Ωcm, for example, by using con-ductive fillers such as graphite.

• Make the surfaces conductive by using hygroscopic fillers that are incompatible withthe polymer and surface.

• Electrostatic charges can also be reduced can by mixing in hygroscopic materials,such as strong soap solutions. In both cases, the water absorbed from the air acts as aconductive layer. It should be pointed out that this treatment loses its effect over time.Especially, the rubbing in of hygroscopic materials has to be repeated over time.

• Reduce air resistance by ionization through discharge or radioactive radiation.

Electrets: An electret is a solid dielectric body that exhibits permanent dielectric polariza-tion. One can manufacture electrets out of some polymers when they are solidified under theinfluence of an electric field, when bombarded by electrons, or sometimes throughmechani-cal forming processes. Applications include films for condensers (polyester, polycarbonate,or fluoropolymers).

Electromagnetic interference (EMI) shielding: Electric fields surge through poly-mers as shown schematically in Fig. 9.30. Because we always have to deal with the influ-ence of interference fields, signal sensitive equipment, such as computers, cannot operatein polymer housings. Such housings must therefore have the function of Faradayic shields.Preferably, a multilayered structure is used – the simplest solution is to use one metalliclayer. Figure 9.31 classifies several materials in a scale of resistances. At least 102 Ωcm areneeded for a material to fulfill the shielding purpose. With carbon fibers or nitrate-coatedcarbon fibers used as a filler, the best protective properties can be achieved. The shieldingproperties are determined using the standard ASTM ES 7-83 test. Figures 9.32 and 9.33present the magnetic shielding as a function of frequency of aluminum-coated polymers andsteel fiber-filled plastics, respectively.


Figure 9.31: Comparison of conductive polymers with other materials: a) Electric resistance ρ ofmetal-plastics compared to resistance ofmetals and polymers; b) Thermal resistanceλ ofmetal-plasticscompared to other materials

0

10

20

30

40

1 10 100 1000MHz

Frequency

dB 0.32

0.64

0.85

1.27

Mag

netic

shi

eldi

ng

Figure 9.32: Electromagnetic shielding of aluminum-coated plastics as a function of frequency andthe square resistance of the plastic

9.1.4 Magnetic Properties

External magnetic fields have an impact on substances that are subordinate to them becausethe external field interacts with the internal fields of electrons and atomic nuclei.

Magnetizability: Pure polymers are diamagnetic; that is, the external magnetic field in-duces magnetic moments. However, permanent magnetic moments, which are induced onferromagnetic or paramagnetic substances, do not exist in polymers. This magnetizabilityM of a substance in a magnetic field with a field intensityH is computed with the magneticsusceptibility,X , as

M = XH. (9.4)


0

10

20

30

40

50

60

1 10 100 1000

0.13

0.25

0.4

1.0

1.5

3.0

Frequency

MHz

dBM

agne

tic s

hiel

ding

Figure 9.33: Electromagnetic shielding of steel fiber-filled (0.7–1.4 vol%) plastics as a function offrequency and the square resistance of the plastic

The susceptibility of pure polymers as diamagnetic substances has a very small and negativevalue. However, in some cases, we make use of the fact that fillers can alter the magneticcharacter of a polymer completely. The magnetic properties of polymers are often changedusing magnetic fillers. Well-known applications are injection molded or extruded magnetsor magnetic profiles, and all forms of electronic storage such as recording tape, floppy ormagnetic disks.

Magnetic resonance: Magnetic resonance occurs when a substance in a permanentmagnetic field absorbs energy from an oscillating magnetic field. This absorption developsas a result of small paramagnetic molecular particles stimulated to vibration. We use thisphenomenon to a great extent to clarify structures in physical chemistry. Methods to achievethis include electron spinning resonance (ESR) and, above all, nuclear magnetic resonance(NMR) spectroscopy. Electron spinning resonance becomes noticeablewhen the field inten-sity of a static magnetic field is altered and the microwaves in a high-frequency alternatingfield are absorbed. Because we can only detect unpaired electrons using this method, we useit to determine radical molecule groups. When atoms have an odd number of nuclei, protons,and neutrons, the magnetic fields caused by self-motivated spin cannot equalize. The align-ment of nuclear spins in an external magnetic field leads to a magnetization vector that canbe measured macroscopically as is schematically demonstrated in Fig. 9.34. This method isof great importance for the polymer physicist to learn more about molecular structures.

9.2 OPTICAL PROPERTIES

Because some polymers have excellent optical properties and are easy to mold and forminto any shape, they are often used to replace transparent materials, including inorganic


High steady magnetic field magnet

High steady magnetic field magnet

High frequency field processing nucleus

Switch

Radio wave generator

High frequency field

Figure 9.34: Schematic of the operating method of a nuclear spin tomograph

glass. Polymers have been introduced into a variety of applications such as automotiveheadlights, signal light covers, optical fibers, imitation jewelry, chandeliers, toys, and homeappliances. Organic materials such as polymers are also an excellent choice for high-impactapplications where inorganic materials such as glass would easily shatter. However, due tothe difficulties encountered inmaintaining dimensional stability, they are not apt for precisionoptical applications. Other drawbacks include lower scratch resistance when compared toinorganic glasses, making them impractical for applications such as automotivewindshields.In this section, we will discuss basic optical properties that include the index of refraction,birefringence, transparency, transmittance, gloss, color, and behavior of polymers in theinfrared spectrum.

9.2.1 Index of Refraction

As rays of light pass through one material into another, the rays are bent by the change inthe speed of light from one medium to the other. The fundamental material property thatcontrols the bending of the light rays is the index of refraction,N . The index of refraction fora specific material is defined as the ratio between the speed of light in a vacuum to the speedof light through the material under consideration. In more practical terms, the refractiveindex can also be computed as a function of the angle of incidence, θ i, and the angle ofrefraction, θr, as follows

N =sin θi

sin θr, (9.5)

where θi and θr are defined in Fig. 9.35.

Figure 9.35: Schematic of light refraction

The index of refraction for organic plastic materials can be measured using the standardASTM D 542 test. It is important to mention that the index of refraction is dependent on


1.45

1.5

1.55

1.6

1.65

1.7

1.75

200 300 400 500 600 700 800

Glass

Polystyrene

Quartz

Acrylic

Wave length

mμ

Figure 9.36: Index of refraction as a function of wavelength for various materials

the wavelength of the light under which it is being measured. Figure 9.36 shows plots ofthe refractive index for various organic and inorganic materials as a function of wavelength.One of the significant points of this plot is that acrylic materials and polystyrene have similarrefractive properties as inorganic glasses.An important quantity that can be deduced from the light’s wavelength dependence on

the refractive index is the dispersion,D, which is defined by

D =dN

dλ. (9.6)

Figure 9.37 shows plots of dispersion as a function of wavelength for the same materialsshown in Fig. 9.36. The plots show that polystyrene and glass have a high dispersion in theultraviolet light domain.

Figure 9.37: Dispersion as a function of wavelength for various materials


It is also important to mention that since the index of refraction is a function of density, itis indirectly affected by temperature. Figure 9.38 shows how the refractive index of PMMAchanges with temperature. A closer look at the plot reveals the glass transition temperature.

Figure 9.38: Index of refraction as a function of temperature for PMMA (λ= 589.3 nm)

9.2.2 Photoelasticity and Birefringence

Photoelasticity andflowbirefringence are applications of theoptical anisotropyof transparentmedia. When a transparent material is subjected to a strain field or a molecular orientation,the index of refraction becomes directional; the principal strains N 1 and N2 are associatedwith principal indices of refraction N1 and N2 in a two-dimensional system. The differencebetween the two principal indices of refraction (birefringence ) can be related to the differenceof the principal strains using the strain-optical coefficient, k, as

N1 − N2 = k(ε1 − ε2) (9.7)

or, in terms of principal stress,

N1 − N2 = C(σ1 − σ2), (9.8)

where C is the stress-optical coefficient. Double refractance in a material is caused when abeam of light travels through a transparent media in a direction perpendicular to the planethat contains the principal directions of strain or refraction index, as shown schematicallyin Fig. 9.39 [7]. The incoming light waves split into two waves that oscillate along the twoprincipal directions. These two waves are out of phase by a distance δ.The out-of-phase distance, δ, between the oscillating light waves is usually referred to as

the retardation. In photoelastic analysis, one measures the direction of the principal stressesor strains and the retardation to determine the magnitude of the stresses. The technique andapparatus used to performed such measurements is described in the ASTM D 4093 test.Figure 9.40 shows a schematic of such a setup,called a polariscope, composed of a narrow

wavelength band light source, two polarizers, two quaterwave plates, a compensator, and amonochromatic filter. The polarizers and quaterwave plates must be perpendicular to eachother (90◦). The compensator is used for measuring retardation, and the monochromaticfilter is needed when white light is not sufficient to perform the photoelastic measurement.


Figure 9.39: Propagation of light in a strained transparent media.

Figure 9.40: Schematic diagram of a polariscope

The parameter used to quantify the strain field in a specimen observed through a polar-iscope is the color. The retardation in a strained specimen is associated with a specific color.The sequence of colors and their respective retardation values and fringe order are shown inTable 9.6 [8]. The retardation and color can also be associated to a fringe order using

fringe order =δ

λ. (9.9)

A black body (fringe order zero) represents a strain free body, and closely spaced colorbands represent a componentwith high strain gradients. The color bands are generally calledthe isochromatics.


Table 9.6: Retardation and fringe order produced in a polariscope

Color Retardation (nm) Fringe order

Black 0 0

Gray 160 0.28

White 260 0.45

Yellow 350 0.60

Orange 460 0.79

Red 520 0.90

Tint of passage 577 1.00

Blue 620 1.06

Blue-green 700 1.20

Green-yellow 800 1.38

Orange 940 1.62

Red 1050 1.81


Green 1350 2.33

Green-yellow 1450 2.50

Pink 1550 2.67


Green 1800 3.10

Pink 2100 3.60


Green 2400 4.13

Figure 9.41 shows the isochromatic fringe pattern in a stressed notched bar. The fringepattern can also be a result of molecular orientation and residual stresses in a molded trans-parent polymer component. Figure 9.42 shows the orientation induced fringe pattern in amoldedpart. The residual stress-inducedbirefringence is usually smaller than the orientation-induced pattern, making them more difficult to measure. Flow induced birefringence is anarea explored by several researchers [9, 10, 11].Likewise, the flow induced principal stresses can be related to the principal refraction

indices. Figure 9.43 [12] shows the birefringence pattern for the flow of linear low-densitypolyethylene in a rectangular die.

9.2.3 Transparency, Reflection, Absorption, and Transmittance

As rays of light pass through one media into another of a different refractive index, light willbe scattered if the interface between the two materials shows discontinuities larger than thewavelength of visible light. Hence, the transparency in semicrystalline polymers is directlyrelated to the crystallinity of the polymer. Since the characteristic size of the crystalline


Figure 9.41: Fringe pattern on a notched bar under tension

Figure 9.42: Transparent injection molded part viewed through a polariscope

domains are larger than the wavelengths of visible light, and since the refractive index ofthe denser crystalline domains is higher compared to the amorphous regions, semicrys-talline polymers are not transparent; they are opaque or translucent. Similarly, high impactpolystyrene, which is actually formed by two amorphous components, polybutadiene rubberparticles and polystyrene, appears white and translucent because of the different indices ofrefraction of the two materials. However, filled polymers can be made transparent if thefiller size is smaller than the wavelength of visible light. The concept of absorption andtransmittance can be illustrated using the schematic and notation shown in Fig. 9.44. Thefigure plots the intensity of a light ray as it strikes and travels through an infinite plate ofthickness d. For simplicity, the angle of incidence, θ i, is 0◦. The initial intensity of theincoming light beam, I , drops to I0 as a fraction ρ0 of the incident beam is reflected out.The reflected light beam can be computed using

Ir = ρ0I. (9.10)


Figure 9.43: Birefringence pattern for flow of LLDPE in a rectangular die

Figure 9.44: Schematic of light transmission through a plate

The fraction of the beam that does penetrate into the material continues to drop becauseof absorption as it travels through the plate. However, as illustrated in Fig. 9.45, part ofthe beam is reflected back by the rear surface of the plate and is subsequently reflected andabsorbed several times as it travels between the front and back surfaces of the plate. Thefraction of incident beam absorbed by the material, α, is transformed into heat inside thematerial and can be written as

α = 1 − τ − ρ, (9.11)

where τ and ρ is the fraction of transmitted and reflected light. Plots of reflection loss as afunction of incidence angle are shown in Fig. 9.46 for various refraction indices.The transmittance becomes less as the wavelength of the incident light decreases, as

shown for PMMA in Fig. 9.47. The figure also demonstrates the higher absorption of thethicker sheet.The transmissivity is generally measured in air and is plotted as a function of wave-

length. Figure 9.48 presents plots of the transmissivity of CAB and PC and compares themto window glass. The transmissivity of polymers can be improved by altering their chemicalcomposition. For example, the transmissivity of PMMA can be improved by substituting


Figure 9.45: Schematic of light reflectance, absorption, and transmission through a plate

Figure 9.46: Influence of incidence angle on reflection losses

Figure 9.47: Ultraviolet light transmission through PMMA

hydrogen atoms by fluorine atoms. The improvement is clearly demonstrated in Fig. 9.49.Such modifications bring polymers a step closer to materials appropriate for usage in fiberoptic applications. Their ability to withstand shock and vibration and cost savings duringmanufacturing make some amorphous polymers important materials for fiber optics appli-cations. However, in unmodified polymer fibers, the initial light intensity drops to 50%after only 100 m, whereas when using glass fibers, the intensity drops to 50% after 3000 m.


0

10

20

30

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

Wave length

CAB 3 mm

PC 4 mm (UV- stabilized.)

%

UV IRVisible light

Glass

μm

Figure 9.48: Transmissivity of CAB, PC, and glass as a function of wavelength

Figure 9.49: Effect of fluorine modification on the transmissivity of light through PMMA

Nucleating agents can also be used to improve the transmissivity of semicrystalline poly-mers. A large number of nuclei will reduce the average spherulite size to values below thewavelength of visible light. The haziness or luminous transmittance of a transparent polymeris measured using the standard ASTM D 1003 test, and the transparency of a thin polymerfilm is measured using the ASTM D 1746 test. The haze measurement (ASTM D 1003) isthe most popular measurement for film and sheet quality control and specification purposes.The standard haze measurement test, ASTM D1003, is presented in Table 9.7.


Table 9.7: Standard test method for haze and luminous transmittance of transparentplastics

Standard ASTM D 1003 - 00

Scope This test method covers the evaluation of specific light-transmitting and wide-angle-light-scattering properties of planar sections of materials such as trans-parent plastics. Two procedures are provided for the measurement of luminoustransmittance and haze. Procedure A uses a hazemeter and Procedure B uses aspectrophotometer. Material with a haze value greater than 30 % is considereddiffusing and should be tested in accordance with ASTM E167.

Specimen Obtain defect free (unless defects are parts of the study) specimens of the mate-rial. Each test specimen must be cut to a size large enough to cover the entranceport of the sphere. A disk 50 mm (2") in diameter, or a square with sides ofthe same dimensions, is suggested. The specimen should have planar surfacesfree of dust, grease, scratches, and blemishes, and it shall be free of visiblydistinct internal voids and particles, unless it is specifically desired to measurethe contribution to haze due to these imperfections. Three specimens must beprepared to test each sample of a given material unless specified otherwise inthe applicable material specification.

Apparatus - Procedure A – Hazemeter- Procedure B – Spectrophotometer

Test procedures The haze value is determined from the ratio of the diffuse transmittance andtotal transmittance measured in the Hazemeter or obtained directly from thespectrophotometer

Values and Units Total luminous transmittance, Tt , to the nearest 0.1 % (indicate the averagewhen reporting average values and specify whether CIE Illuminant C or A isused), diffuse luminous transmittance, Td , to the nearest 0.1 % (indicate theaverage when reporting average values), and percent haze, to the nearest 0.1 %(indicate the average when reporting average values).

9.2.4 Gloss

Strictly speaking, all of the above theory is valid only if the surface of thematerial is perfectlysmooth. However, the reflectivity of a polymer component is greatly influenced by the qualityof the surface of the mold or die used to make the part. Specular gloss can be measuredusing the ASTM D 2457 standard technique, presented in Table 9.8, which describes a partby the quality of its surface. A glossmeter or lustremeter is usually composed of a lightsource and a photometer as shown in Fig. 9.50 [13]. These types of glossmeters are calledgoniophotometers. As shown in the figure, the specimen is illuminated with a light source


from an angle α, and the photometer reads the light intensity from the specimen from avariable angle β. The angle α should be chosen according to the glossiness of the surface.

Table 9.8: Standard test method for specular gloss of plastic films and solid plastics

Standard ASTM D 2457 - 03

Scope This test method describes procedures for the measurement of gloss of plasticfilms and solid plastics, both opaque and transparent. It contains four separategloss angles:- 60-deg, recommended for intermediate-gloss films,- 20-deg, recommended for high-gloss films,- 45-deg, recommended for intermediate and low-gloss films, and- 75-deg, recommended for plastic siding and soffit

Specimen Non rigid and stiff films. Specimen surfaces must have good planarity and mustbe mounted in a film holding device.

Apparatus A glossmeter that consists of an incandescent light source furnishing an incidentbeam, means for locating the surface of the specimen, and a receptor located toreceive the required pyramid of rays reflected by the specimen. The receptorshall be a photosensitive device responding to visible radiation.

Test procedures The gloss could be measured using the glossmeter in accordance with the man-ufacturer’s instructions. The instrument must be calibrated before any measure-ment.

Values and Units Units of reflectance

Figure 9.50: Schematic diagram of a glossmeter


Figure 9.51: Reflective intensity as a function of photometer orientation for specimens with variousdegrees of surface gloss

For example, for transparent films, values for α are 20◦ for high gloss, 45◦ for inter-mediate and 60◦ for low gloss. For opaque specimens ASTM test E 97 should be used.Figure 9.51 presents plots of reflective intensity as a function of photometer orientation forseveral surfaces with various degrees of gloss illuminated by a light source oriented at a 45 ◦

angle from the surface. The figure shows how the intensity distribution is narrow and sharpat 45◦ for a glossy surface, and the distribution becomes wider as the surface becomesmatte.The color of the surface also plays a significant role on the intensity distribution read by thephotometer as it sweeps through various angular positions.

Figure 9.52: Reflective intensity as a function of photometer orientation for black and whitespecimens with equal surface gloss

Figure 9.52 shows plots for a black and awhite surfacewith the same degree of glossiness.The specular gloss is used as a measurement of the glossy appearance of films. However,gloss values of opaque and transparent films should not be compared with each other.

9.2.5 Color

The surface quality of a part is not only determined by how smooth or glossy it is, but also byits color. Color is often one of the most important specifications for a part. In the followingdiscussion it will be assumed that the color is homogeneous throughout the surface. Thisassumption is linked to processing, where efficient mixing must take place to disperse anddistribute the pigments that will give the part color. Color can always be described bycombinations of basic red, green, and blue. Hence, to quantitatively evaluate or measure acolor, one must filter the intensity of the three basic colors. A schematic diagram of a colormeasurement device is shown in Fig. 9.53.Here, a specimen is lit in a diffuse manner using a photometric sphere, and the light

reflected from the specimen is passed through red, green, and blue filters. The intensitycoming from the three filters are allocated the variables X , Y , and Z for red, green, andblue, respectively. The variables X , Y , and Z are usually referred to as tristimulus values.Another form of measuring color is to have an observer compare two surfaces. One surfaceis the sample under consideration illuminated with a white light. The other surface is a


Figure 9.53: Schematic diagram of a colorimeter

white screen illuminated by light coming from three basic red, green, and blue sources. Byvarying the intensity of the three light sources, the color of the two surfaces are matched.This is shown schematically in Fig. 9.54 [14]. Here too, the intensities of red, green, andblue are represented with X , Y , and Z , respectively. The resulting data is better analyzedby normalizing the individual intensities as

x =X

X + Y + Z(9.12)

y =Y

X + Y + Z(9.13)

z =Z

X + Y + Z(9.14)

The parameters x, y, and z, usually termed trichromatic coefficients, are plotted on a three-dimensional graph that contains the whole spectrum of visible light, as shown in Fig. 9.55.This graph is usually referred to as a chromaticity diagram. The standard techniques thatmake use of the chromaticity diagram are the ASTM E 308-90 and the DIN 5033. Threepoints in the diagram have been standardized. These are:

• Radiation from a black body at 2848 K corresponding to a tungsten filament light,denoted by A in the diagram

• Sunlight, denoted by B

• North sky light, denoted by C

It is important to note that colors plotted on the chromaticity diagram are only described bytheir hue and saturation. The luminance factor is plotted in the z direction of the diagram.Hence, all neutral colors such as black, gray, and white lie on point C of the diagram.


Figure 9.54: Schematic diagram of a visual colorimeter

Figure 9.55: Chromaticity diagram with approximate color locations.

9.3 ACOUSTIC PROPERTIES

Sound waves, similar to light waves and electromagnetic waves, can be reflected, absorbed,and transmitted when they strike the surface of a body. The transmission of sound wavesthrough polymeric parts is of particular interest to the design engineer. Of importance is theabsorption of sound and the speed at which acoustic waves travel through a body, for examplein a pipe, in the form of longitudinal, transversal, and bending modes of deformation.


9.3.1 Speed of Sound

The speed at which sound is transmitted through a solid barrier is proportional to Young’smodulus of the material, E, but inversely proportional to its density, ρ. For sound wavestransmitted through a rod, in the longitudinal direction, the speed of sound can be computedas

CrodL =

√E

ρ. (9.15)

Similarly, the transmission speed of sound waves through a plate along its surface directioncan be computed as

CplateL =

√E

ρ(1 − ν2), (9.16)

where ν is Poisson’s ratio.The speed of sound through a material is dependent on the materials’ state. For example,

soundwaves travelmuch slower through a polymermelt than through a polymer in the glassystate and the speed of sound through a polymer in the rubbery state is 100 times slower thanthat through a polymer in a glassy state. In the melt state, the speed of sound drops withincreasing temperature because of density increase. Figure 9.56 [15] presents plots of speedof sound through several polymer melts as a function of temperature. On the other hand,speed of sound increases with pressure as clearly shown in Fig. 9.57 [15].

Figure 9.56: Speed of sound as a function of temperature through various polymers(Offergeld and Menges)

9.3.2 Sound Reflection

Sound reflection is an essential property for practical noise reduction. This can be illustratedusing the schematic in Fig. 9.58. As the figure shows, soundwaves that travel throughmedia1 strike the surface of media 2, and a fraction of the sound waves reflect back into media 1.


T

Figure 9.57: Speed of sound as a function of pressure through various polymers (Offergeld andMenges)

Reflec

ted

Figure 9.58: Schematic diagram of sound transmission through a plate.

In order to obtain high sound reflection, the mass of the media 2 must be high comparedto the mass of media 1. The mass of insulating sound walls can be increased with the use offillers, such as plasticized PVC with barium sulfate or by spraying similar anti noise com-pounds on the insulating walls. It is common practice to use composite plates as insulatingwalls. This is only effective if the flexural resonance frequencies, the walls do not coincidewith the frequency of the sound waves.

9.3.3 Sound Absorption

Similarly to sound reflection, sound absorption is an essential property for practical noiseinsulation. Materials that have the same characteristic impedance as air are the best sound-absorbent materials. The sound waves that are not reflected back out into media 1, penetratemedia 2 or the sound insulating wall (see Fig 9.58). Sound waves that penetrate a polymermedium are damped out similar to that of mechanical vibrations. Hence, sound absorptionalso depends on the magnitude of the loss tangent tan δ, or logarithmic decrement Δ, de-scribed earlier in this chapter. Table 9.9 presents orders of magnitude for the logarithmicdecrement for several types of materials. As expected, elastomers and amorphous polymershave the highest sound absorption properties, whereas metals have the lowest.


Table 9.9: Damping properties for various materials

Material Temperature range Logarithmic decrement Δ

Amorphous polymers T < Tg 0.01-0.1

T > Tg 0.1-1

Elastomers 0.1-1

Semicrystalline polymers Tg < T < Tm ≈ 0.1

Fiber-reinforced polymers Tg < T < Tm < 0.01

Wood T < Tg 0.01-0.02

Ceramic and glass T < Tg 0.001-0.01

Metals T < Tm <0.0001.

In a material, sound absorption takes place by transforming acoustic waves into heat.Because foamed polymers have an impedance of the same order as air, they are poor reflectorsof acoustic waves. This makes them ideal for eliminatingmultiple reflections of soundwavesin acoustic or soundproof rooms. Figure 9.59 [16]presents the sound absorption coefficientfor several foamed polymers as a function of the sound wave frequency. It should be notedthat the speed at which sound travels in foamed materials is similar to that of the solidpolymers, since foaming affects the stiffness and the density in the same proportion.

Figure 9.59: Sound absorption coefficients as a function of frequency for various foams(Griffin and Skochdopole)

When compared to wood, even semi-crystalline polymers are considered sound-proofmaterials. Materials with a glass transition temperature lower than room temperature areparticularly suitable as dampingmaterials. Commonly used for this purpose are thermoplas-tics and weakly cross-linked elastomers. Elastomer mats are often adhered on one or bothsides of sheet metal, preventing resonance flexural vibrations of the sheet metal such as inautomotive applications.

9.3 References 357

References

1. H. Domininghaus. Plastics for Engineers. Hanser Publishers, 1993.

2. E. Baer. Engineering Design for Plastics. Robert E. Krieger Publishing Company, 1975.

3. J.-P. Reboul. Thermoplastic Polymer Additives, Chapter 6. J.T. Lutz, Jr., (Ed.), Marcel Dekker,Inc., New York, 1989.

4. H. Berg. PhD thesis, IKV, RWTH-Aachen, Germany, 1976.

5. H. Wagner. Internal report. AEG, Kassel, Germany, 1974.

6. R.J. Crawford. Rotational Molding of Plastics. Research Studies Press, Somerset, 1992.

7. ASTM. ASTM-D4093. ASTM Vol 08.02, Plastics(II), 1994.

8. ASTM. Plastics (II), 08.02,. ASTM Philadelphia, 1994.

9. H. Janeschitz-Kriegl. Polymer Melt Rheology and Flow Birefringence. Elsevier, Amsterdam,1994.

10. A.I. Isayev. Polym. Eng. Sci., Vol. 23(271), 1983.

11. R. Wimberger-Friedl. Polym. Eng. Sci., Vol. 30(813), 1990.

12. G. Sornberger, J.C. Quantin, R. Fajolle, B. Vergnes, and J.F. Agassant. J. Non-Newt. Fluid Mech,23(123), 1987.

13. ASTM. ASTM-D2457. ASTM Vol 08.02, Plastics(II), 1994.

14. J.M. Adams. The Science of Surface Coatings, Chapter 12, Ed. H.W. Chatfield, D. van NostrandCo., Inc. Princeton, 1962.

15. H. Offergeld. PhD thesis, IKV, RWTH-Aachen, 1990.

16. J.D. Griffin and R. E. Skochdopole. Engineering Design for Plastics, E. Baer, (Ed.), Chapter 15.Robert E. Krieger Publishing Company, Huntington, 1975.

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INDEX

Index Terms Links

A

acoustic properties 353

acoustic properties

pressure effect 354

sound absorption 355

sound reflection 354

sound transmission 354

speed of sound 354

temperature effect 354

activation energy 134

ASTM test 150 319

D1238 148

D149 334

D150 317

D1525 257

D1822 208

D256 205

D2863 312

D2990 226

D3418 106

D3638 335

D3801 311

D570 290

D635 312

Index Terms Links


ASTM test (Cont.)

D638 188

D648 257

D790 198

D792 84

D955 94

E831 94

ATR technique 13

IR spectroscopy 13

B

beam splitters 10

beam splitters

CaF2 10

Ge on CsI 10

Ge on KBr 10

KBr 10

MYLAR® 10

Beam splitters

Quartz 10

Bird-Carreau model 144

birefringence 342

C

char 100

Charpy impact test 203

chemical degradation 301

chromaticity diagram 353

color 351

Index Terms Links


colorimeter 352

complex modulus

elastic modulus 243

loss modulus 243

storage modulus 243

complex shear modulus 243

conductivity 75

contact angle 139

creep data

fracture strain 239

isochronous 229

isometric 229

PBT 228

PMMA 235

PP 227

secant modulus 229

thermoplastics 229

creep rupture 234


thermoplastics 235

creep test 226

crystallinity

degree 80

cure 97

degree of 97

diffusion controlled 99

heat activated 97

mixing activated 97

phase 98

Index Terms Links


curing 97

D

damping properties 355

Deborah number 137

degree of cure 134

density 84

detectors 58

dielectric behavior 315

dielectric dissipation 319

dielectric strength data 326

film thickness effect 332

PE 329

PE-LD 328

PF paper 331

plasticizer effect 332

POM 329

PP 332

PVC-P 331

dielectric strength 328

thickness dependance 327

load time dependance 327

Diffused Reflectance Infrared

Fourier Transform

Spectroscopy 14

IR spectroscopy 14

diffusion activation energy 272

diffusion 84 265


Index Terms Links


diffusivity 84

double refractance 342

DRIFTS 14

IR spectroscopy 14

drop impact test 214

dynamic mechanical analysis (DMA) 241

E

EDS 51

Einstein’s

elastic modulus 132

thermoplastics 243

electric breakdown 326

electric conductivity 321

electrical properties 315

conductive fillers 326

dielectric behavior 315

dielectric coefficient 315

dielectric dissipation factor 319

dielectric polarization 317

electric conductivity 321

electric resistance 321

electrical and thermal loss 319

filler effect 323

frequency dependency 319


Electrolytic conductivity detector 58

electromagnetic interference shielding (EMI) 337

Electron-capture detector 58

Index Terms Links


electrostatic charge 336

elongation rate 132

elongational deformation 127

EMI shielding 337

Energy dispersive X-ray spectroscopy 51

environmental stress cracking 302

EVER GLO

IR sources 10

extrudate swell 137

extrusion die 137

F

fatigue data 249

fatigue data

ABS 249

PA6-GF 249

PA66 249 253

PC 249

POM 248

PVC-U 249

SMC 252

fatigue test 246

creep 249

S-N curves 246

stress concentration effect 249

temperature rise 247

thermal failure 248

Flame ionization detector 58

Index Terms Links


Flame ionization

detectors 58

Flame photometric detector 58

Flame photometric

detectors 58

flammability

5VA 312

5VB 312

HB 312

UL 312

V-0 312

V-1 312

V-2 312

flash point 308

flexural test 198

Fourier transform infrared spectroscopy 8

FTIR 8

functional elements

snap fit magnification factor 235

G

Gas chromatography 55

Gas chromatography

columns 56

cool on-column injectors 56

detectors 58

injectors 55

instrumentation 55

Programmed temperature volatilization 56

Index Terms Links


Gas chromatography (Cont.)

splitless injectors 56

gel point 100 134

GLOBAR

IR sources 9

gloss 349

glossmeter 350

H

HDT

apparatus 254

HDT

data 256

heat deflection temperature 253

heat of fusion 80

heat

released during cure 97

high temperature plastics 243

I

IEC test 317

IEC test

60112 335

60243-1 334

60250 319

60259 317

impact energy

filler effect 222

Index Terms Links


impact strength 200

blends 201

filler effect 222

notch tip radius effect 213

processing conditions effect 213

rate of deformation effect 201


weathering effect 299

impact test

tensile specimen 210

Charpy 203

Izod 208

notched 213 222

test specimen 208

index of refraction 341

infrared spectrophotometer 9

infrared spectroscopy 8

injection molding

shrinkage 96

IR detectors 10

DTGS/CsI 10

DTGS/KBr 10

DTGS/Polyethylene 10

MCT 10

IR sources 9

IR spectroscopy 8

ISO test

1133 148

11357 106

Index Terms Links


ISO test (Cont.)

11357-2 107

11359 94

1183 84

1210 311

178 198

179-1 205

294-4 94

306 257

4589-2 312

527-1 188

62 290

75-1 257

8256 208

899-1 226

isochronous creep curves 229

isometric creep curves 229

Izod impact test 208

L

lag time 276

M

magnification factor 235

Mass selective detector 59

measuring

Charpy impact strength 203

creep modulus 226

CTI 335

Index Terms Links


measuring (Cont.)

density 85

dissipation factor 318

electric strength 334

flammability 310

flexural properties 196

glass transition temperature 107

HDT 259

ignitability 312

melt flow index 148

melting temperature 106

notched Charpy impact strength 205

permittivity 318

shrinkage 96

tensile impact strength 210

tensile properties 188

thermal expansion (CLTE) 95

Vicat softening temperature 255

water absorption 288

Meissner’s extensional rheometer 166

melt flow index 147

melt flow indexer 147

melt fracture 137

melting point 80

MFI 147

Multilayer Film Characterization

FTIR 30

Index Terms Links


N

NERNST

IR sources 10

Nitrogen/phosphorous detector 59

normal stress differences 138

normal stress

coefficients 139

notched impact test 213

nuclear spin tomograph 340

O

optical properties 339

optical properties

color 351

fluorine content effect 348

fringe pattern 345

gloss 349

index of refraction 340

reflection 346

reflectivity 351


transmittance 346

wave length effect 341

P

PAS 14

PAS

IR spectroscopy 14

Index Terms Links


permeability 275


permeation 265 274

Photo-ionization detector 59

Photoacoustic Spectroscopy 14

IR spectroscopy 14

photoelasticity 342

plasticizer Identification 61

Poisson’s ratio 132 196

filler effect 196



polariscope 343

polymer

filled 78

reactive 97

reinforced 135

Programmed temperature volatilization 56

properties

acoustic 353

density 84

electrical 315

magnetic 338

mechanical 185

optical 339

short term tensile 185

surface tension 139

Index Terms Links


R

relaxation time 137

ripping strength

rubber 202

rubber elasticity 185

rubber

filled 186

ripping strength 202

S

scanning electron microscope 51

secant creep modulus 229

second invariant 128

self-diffusion 281

shark skin 137

shear modulus 132

shear thinning 127

solubility 265

sorption constant 275

sorption 264


sound absorption 355

Soxhlet extractor 66

specific enthalpy 82

specific heat 80

filled plastics 82

specific volume 84

spectrogram 7

Index Terms Links


spectrometer 7

Spectroscopy

FTIR 8

spectrum 7

speed of sound 354

spurt flow 137

stick-slip effect 137

strain rate tensor 128

strain rate 128

strength stability under heat 253

strength


stress-strain


semicrystalline 193

viscoelastic effect 193

surface tension 139

T

tensile strength

filler effect 202

tensiometer 140

Thermal conductivity detector 59

thermal conductivity 75

Thermal conductivity

detectors 59

thermal conductivity

filler effect 78

pressure effect 76

Index Terms Links


thermal conductivity (Cont.)

thermoplastics 76

thermal degradation 308

thermal diffusivity 84


thermal expansion 91

filled plastics 91

polyethylene 94

time-temperature-transformation 99

torsion test 241

Transmission 11

IR spectroscopy 11

Trouton viscosity 132

TTT 99

Tungsten filament

IR sources 10

U

UL Subject 94 evaluation 312

V

viscoelastic 127

viscometer 151

viscosity curves 129

viscosity

reacting polymer 134

vitrification line 99

vulcanization 97

Index Terms Links


W

water absorption 287

water absorption

relative humidity dependance 290

temperature dependance 287

weathering 291

impact test 299

laboratory test 299

pigment effect 301

wetting angle 139

projector 139

WLF relation 144

Y

yield stress 136

plastics testing and characterization - industrial applications

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