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Fundamentals and Applications of Micro- and Nanobers

A comprehensive exposition of micro- and nanober forming, this text provides a uniedframework of all these processes (melt- and solution blowing, electrospinning, etc.)and describes their foundations, development and applications. It provides an up-to-date,in-depth physical and mathematical treatment, and discusses a wide variety of applicationsin different elds, including nonwovens, energy, healthcare and the military. It furtherhighlights the challenges and outstanding issues from the perspective of an interdisciplinarybasic science and technology, incorporating both fundamentals and applications.Ideal for researchers, engineers and graduate students interested in formation of micro-

and nanobers and their use in functional smart materials.

Alexander L. Yarin is a Professor of Mechanical Engineering at the University of Illinoisat Chicago and concurrently a Professor of the College of Engineering at KoreaUniversity in Seoul, South Korea.

Behnam Pourdeyhimi is a Distinguished Chaired Professor of Materials in the College ofTextiles and the Executive Director of the Nonwovens Institute.

Seeram Ramakrishna is a Professor of Materials Engineering and Director of the Centerfor Nanobers and Nanotechnology at the National University of Singapore.

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Fundamentals and Applicationsof Micro- and Nanobers

ALEXANDER L. YARINUniversity of Illinois, Chicago

BEHNAM POURDEYHIMINorth Carolina State University

SEERAM RAMAKRISHNANational University of Singapore

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University Printing House, Cambridge CB2 8BS, United Kingdom

Published in the United States of America by Cambridge University Press, New York

Cambridge University Press is part of the University of Cambridge.

It furthers the Universitys mission by disseminating knowledge in the pursuit ofeducation, learning and research at the highest international levels of excellence.

www.cambridge.orgInformation on this title: www.cambridge.org/9781107060296

Alexander Yarin, Benham Pourdeyhimi and Seeram Ramakrishna 2014

This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University Press.

First published 2014

Printed in the United Kingdom by MPG Printgroup Ltd, Cambridge

A catalogue record for this publication is available from the British Library

Library of Congress Cataloguing in Publication data

ISBN 978-1-107-06029-6 Hardback

Additional resources for this publication at www.cambridge.org/9781107060296

Cambridge University Press has no responsibility for the persistence or accuracy ofURLs for external or third-party internet websites referred to in this publication,and does not guarantee that any content on such websites is, or will remain,accurate or appropriate.

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Contents

Preface page ix

1 Introduction 1

1.1 History and outlook 11.2 Melt spinning 41.3 Dry spinning 171.4 Wet or solvent spinning, gel spinning 181.5 Spunbonding 181.6 References 23

2 Polymer physics and rheology 25

2.1 Polymer structure, macromolecular chains, Kuhn segment,persistence length 25

2.2 Elongational and shear rheometry 252.3 Rheological constitutive equations 352.4 Micromechanics of polymer solutions and melts 452.5 Solidication 482.6 Crystallization 502.7 References 59

3 General quasi-one-dimensional equations of dynamics of free liquid jets,capillary and bending instability 63

3.1 Mass, momentum and moment-of-momentum balance equations 633.2 Closure relations 653.3 Capillary instability of free liquid jets 673.4 Bending perturbations of Newtonian liquid jets moving in air with high

speed 783.5 Buckling of liquid jets impinging on a wall 833.6 References 85

4 Melt- and solution blowing 89

4.1 Meltblowing process 904.2 Turbulence of surrounding gas jet 94

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4.3 Bending and apping of exible solid threadlines in a gas jet 1024.4 Aerodynamically driven stretching of polymer jets 1094.5 Aerodynamically driven bending instability of polymer

jets: linearized theory 1124.6 Meltblowing of a single planar polymer jet 1174.7 Fully three-dimensional blowing of single and multiple polymer jets 1244.8 Subsonic and supersonic solution blowing of monolithic and coreshell

bers 1604.9 Blowing of natural biopolymer bers 1654.10 References 174

5 Electrospinning of micro- and nanobers 179

5.1 Electrospinning of polymer solutions 1795.2 Leaky dielectrics 1805.3 Taylor cone and jet initiation 1835.4 Straight part of the jet 1975.5 Electrically driven bending instability: experimental observations 2095.6 Electrically driven bending instability: theory 2165.7 Branching, garlands, multineedle and needleless electrospinning 2315.8 Co-electrospinning and emulsion spinning of coreshell bers 2405.9 Alignment of electrospun nanober mats 2495.10 Electrospinning of polymer melts 2525.11 References 254

6 Additional methods and materials used to form micro- and nanobers 262

6.1 Island-in-the-sea multicomponent bers and nanobers 2626.2 Fibers from melt fracture in meltblowing processes 2626.3 Fibers from ash spinning processes 2646.4 Fibers from polymer solutions in Couette ow 2646.5 Centrifugal spinning, forcespinning 2666.6 Electrospinning of liquid crystals, conducting polymers, biopolymers

and denatured proteins 2666.7 Nanobers containing nanoparticles and nanotubes 2696.8 Drawing of optical microbers 2726.9 Polarization-maintaining optical microbers and multilobal bers 2786.10 References 294

7 Tensile properties of micro- and nanobers 297

7.1 Tensile tests on individual nanobers 2977.2 Tensile tests on nanober mats 3037.3 Phenomenological model of stressstrain dependence of

nanober mats 304

vi Contents

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7.4 Micromechanical model of stressstrain dependence of nanober mats 3067.5 References 317

8 Post-processing 319

8.1 Carbonization, sol-gel transformation, calcinations and metallization 3198.2 Chemical cross-linking 3208.3 Physical cross-linking 3318.4 References 336

9 Applications of micro- and nanobers 337

9.1 Filters and membranes 3379.2 Electrodes for fuel cells, batteries, supercapacitors and electrochemical

reactions 3389.3 Thorny devil nanobers: enhancement of spray cooling and pool boiling 3449.4 Nanouidics 3539.5 References 357

10 Military applications of micro- and nanobers 359

10.1 Nanobers and chemical decontamination 36010.2 Nanobers for biowarfare decontamination 36410.3 Functionalization of nanobers for protective applications 37010.4 Sensors 37410.5 Nanober decontamination wipes 37510.6 Respirator masks 37510.7 References 377

11 Applications of micro- and nanobers, and micro- and nanoparticles:healthcare, nutrition, drug delivery and personal care 380

11.1 Nanobrous scaffolds for tissue regeneration 38111.2 Drug delivery 39111.3 Desorption as drug-delivery mechanism 39311.4 Modulation of drug release rate 40711.5 Health suppliments (vitamin-loaded nanober mats) 41711.6 Cosmetic facial masks 41811.7 Electrosprayed nanoparticulate drug-delivery systems 41911.8 References 423

Subject Index 432

Contents vii

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Preface

Fiber-forming processes and the resulting bers have become a key element in manymodern technologies. Today, practically everyone is directly or indirectly using thesebers. Manmade macroscopic bers are widely used in our garments and many otheritems of everyday life. On the other hand, much smaller microscopic and, especially,nanobers are only beginning their path to prominence. The chemical, physical andtechnological aspects of manufacturing of such bers are still weakly linked and not fullyunderstood. Two main processes associated with formation of micro- and nanobersare melt- or solution blowing and electrospinning. They require concerted interaction ofsynthetic chemistry, responsible for polymers used as raw materials, polymer physics,providing a link to their viscoelastic behavior, rheological characterization of ow proper-ties, non-Newtonian hydrodynamics of polymer solutions and melts, aerodynamics, asso-ciated with gas blowing, and electrohydrodynamics, in the case of electrospinning. Thekey element of the ber-forming processes is a thin jet of polymer solution or melt, whichrapidly changes its three-dimensional conguration under the action of the aerodynamicor electric forces applied to its surface and the internal viscous and elastic stresses. There isa denite and imperative need to interpret and rationalize these phenomena, which requiresacquisition of extensive experimental data and establishment of an appropriate theoreticalframework as an essential element in the further technological design and optimization.In addition to the above-mentioned broad spectrum of disciplines, this involves differentaspects associated with materials science, such as the methods developed in polymercrystallography, and elasticity and plasticity theory. Although many aspects of ber-forming processes can today be considered as uncovered and well described, eitherexperimentally or theoretically/numerically, numerous important details are still to beexplored. The importance of this subject is attested by an exponential increase in scienticpublications devoted to microscopic and nanobers and a broad involvement of theindustries associated with ber media, nonwovens, nano-textured materials, novelbiomedical and healthcare products and optical bers, as well as defense applications.The idea of writing this book was motivated by the need for a comprehensive exposition

of different aspects of ber-forming processes including the fundamental polymer sciencefacts, rheology, non-Newtonian hydrodynamics and electrohydrodynamics, applied math-ematics, materials science, process development and applications. Numerous recent exper-imental and theoretical achievements on this subject can now be tied in an integrated textcovering signicant advances in our understanding of the micro- and nanober-forming

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processes, which are radically different from those well documented for macroscopicbers. There is still no other book in the eld of micro- and nanobers that exposes thesubject with the breadth and depth of the seminal book by A. Ziabicki, Fundamentals ofFibre Formation, published 50 years ago and devoted to macroscopic bers. The presentbook aims at charting the domain of our state-of-the-art knowledge in the eld of micro-and nanobers, and also highlighting the not yet fully understood challenges and out-standing issues from the perspective of interdisciplinary basic science and technology,incorporating both fundamentals and applications. We have endeavoured to contributeto a wide audience of researchers, engineers and post-graduate students from variousdisciplines, i.e. engineering, applied chemistry and physics and materials science, as wellas technology and process development, interested in the formation of micro- and nano-bers and their use in functional smart materials, such as novel lter media, nonwovens,membranes, biomedical and healthcare products, uffy electrodes for fuel cells andbatteries, polarization-maintaining optical bers, etc.The book is a monograph signicantly based on the results published by the authors in

the peer-reviewed journals over the last 12 years. These works covered a wide range ofthe inter-related topics and in part inspired the idea to write a comprehensive monographencompassing the scattered mosaic of our own journal publications and the relatedimportant results of the other groups. The present book is the culmination of these efforts.The structure of the book is rooted in its goals. The introductory Chapter 1 exposes thehistory of articial macroscopic ber technology and some basic aspects of the existingtechnology and its foundations. Chapter 2 contains the basic facts from the eld ofpolymer physics and rheology needed for the understanding and description of owsof polymer solutions and melts, their solidication and crystallization. The fundamentalsof the hydrodynamics of free liquid jets moving in air, i.e. the quasi-one-dimensionalequations of such jets and basic instability phenomena are described in Chapter 3. Theseequations are applied to the analysis of polymer melt- and solution blowing in Chapter 4.In Chapter 5 these equations are supplemented by elements of electrohydrodynamics andsimilarly applied to the analysis of electrospinning of polymer nanobers. Several othermethods of forming of polymer nanobers and optical glass microbers are summarizedin Chapter 6. Polymer bers and their nonwovens are frequently subjected to post-processing, aimed at improving their properties, which is discussed in Chapter 7. Thetensile properties and strength of the individual nanobers and nanober mats aredescribed in Chapter 8. Chapter 9 introduces a range of applications of nanobers andtheir mats as lters and membranes, catalyst supports, uffy electrodes, nanotexturedcoatings that facilitate heat removal from high heat-ux surfaces, and in nanouidics.Military applications of nanober mats for decontamination, and protection fromnuclear, biological and chemical warfare, as well as nanober-based sensors are sum-marized in Chapter 10. Numerous applications of micro- and nanobers and nano-particles for healthcare and drug delivery, as well as the physical mechanismsinvolved, are discussed in Chapter 11. All references are combined in the end of thebook chapters in a strictly alphabetic order. References in the text with coinciding namesof the rst author and the publication year are distinguished by an additional sufx addedto the year, e.g. Smith et al. (2011a) and Smith et al. (2012b). In the list of references

x Preface

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these two works can be separated by several others due to the alphabetic order ofthe initials or/and the second etc. co-authors names. Moreover, in the list of referencesSmith et al. (2012b) can even precede Smith et al. (2011a) if the former is Smith A.B.,and the latter is Smith C.D.The book allows for selective reading and Chapters 1, 2, 611 can be read stand-alone.

On the other hand, reading about the modeling aspects of melt- and solution blowing inChapter 4 and electrospinning in Chapter 5 imply understanding of the general quasi-one-dimensional equations described in Chapter 3. The book contains a wide range ofreferences to the relevant existing literature, albeit the description of all the subjectstreated in the book is practically self-contained, covered in depth and in sufcient detail.This book is written for the benet of senior-year undergraduate students, graduate

students (as a text book), researchers, engineers, and consultants and practitioners inindustry (as a reference book). The scope of the book is related to the growing number ofspecialists in non-Newtonian uid mechanics, rheology, electrohydrodynamics andapplied mathematics, materials scientists and engineers, textile and nonwoven engineers,nanotechnologists, micro- and nanoscale engineers, design engineers, sustainabilityengineers, energy engineers, chemical engineers, biotechnologists, bioengineers, bio-medical engineers, environmental scientists and engineers, life scientists, physicists,chemists, food scientists and engineers, etc. Readers with basic knowledge of materialsscience and engineering, physics, chemistry and mathematics will be able follow thecontents of the book.Special thanks are directed to our families, Liliya, Naomi, Shirley and Leonid Yarin,

Atefeh, Roxana and Neda Pourdeyhimi, and Sridhar, Sundar and Susithra. Without theirencouragement and help this book could not have appeared.

Preface xi

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1 Introduction

The rst chapter is devoted to the traditional methods of ber forming, which are used toproduce macroscopic bers. Since the novel methods used to form micro- and nanobersdescribed in this monograph have branched from the traditional methods, an introductioninto the history of manmade bers is instructive and fully appropriate (Section 1.1).There is a brief discussion of such traditional extrusion methods of ber forming as meltspinning (Section 1.2), dry spinning (Section 1.3), wet spinning (Section 1.4) and theintegrated process of spunbonding, which is used to form nonwoven ber webs(Section 1.5). Melt and dry spinning are closely related to the electrospinning used toproduce nanobers, so the discussion of these traditional methods allows a rst glimpseof electrospinning, covered in Chapter 5. One of the key elements of spunbondingis pulling polymer laments by fast co-owing air, which is known as meltblowing.Meltblowing, and its offshoot solution blowing, are also used to form micro- andnanobers, as detailed in Chapter 4. In a sense, Section 1.5 serves as an introduction tothe nonwoven nanober mats discussed later. Section 1.2 also contains some elements ofquasi-one-dimensional theory; namely, its application to the draw resonance instabilityof melt spinning. In its more involved form a similar quasi-one-dimensional approachis applied in Chapters 36 to describe processes characteristic of melt- and solutionblowing and electrospinning used to form micro- and nanobers.

1.1 History and outlook

The term ber originates from the French word bre, from Latin bra a ber, lament,of uncertain origin, perhaps related to Latin lum thread, or from the root ndere tosplit (Online Etimology Dictionary 2013). For centuries, the use of bers was limited tonatural materials such as cotton and linen, which had inherent problems with wrinkling.Silk was difcult to produce and was often too delicate. Wool was strong and abundant,but would shrink and was irritating next to the skin, and would not last long, as it was afood source for moths.The idea of forming manmade bers dates back to Robert Hooke and was expressed in

1664. In 1713, Ren Antoine de Raumur produced the rst spun glass bers and in 1735suggested forming bers from liquid varnish. The initial progress paced in quanta ofabout 100 years, and in 1883 Sir Joseph Swan issued a solution of nitrocellulose in acetic


acid into a bath lled with alcohol, and thus realized the rst wet spinning process, whichformed long continuous bers (Lewin 2007).The invention of rayon extends back to 1855 in England, when Georges Audemars, a

Swiss chemist, discovered how to make cellulose nitrate. In 1884 Count Hilairede Chardonnet invented a method of forming bers from regenerated cellulose. In1889, the introduction of fabrics made of articial silk at the Paris Exhibition receiveda lot of attention, and in 1891 Chardonnet established the rst company in Besanon,France, producing the so-called Chardonnet silk bers. After it was found that cellulose issoluble in aqueous solutions containing copper and ammonia, mass production ofcuprammonium rayon bers was started in Germany in 1899. The rst rayon ber wasintroduced as articial silk partly because of its luster and its continuous lamentnature. Viscose rayon bers were introduced by Ch. F. Cross, E.J. Bevan and C. Beadle in1893 and commercialized in England in 1905. The American Viscose Company, formedby S. Courtaulds and Co., Ltd., began production of rayon in 1910 in the USA.The discovery of the origins of cellulose acetate is attributed to A.D. Little of Boston in

1893. Acetate was rst introduced during 19041910, by two brothers, Camille andHenri Dreyfus in Basel, Switzerland (Morris 1989), making acetate motion picture lm.The rst commercial textile uses for acetate in ber form are attributed to the CelaneseCompany in 1924. Manmade cellulosics are a major player in the ber market today andare expected to continue due to their unique properties in terms of strength, exibility andabsorbency.Nylon bers were the rst truly synthetic bers that were industrially produced in

1939, thanks to the group led by W.H. Carothers. In 1931 Carothers reported onresearch at the DuPont Company on a polymer macromolecule called nylon 6,6. By1938, P. Schlack of the I.G. Farben Company in Germany, polymerized caprolactam andcreated a different form of the polymer, identied simply as nylon 6. Nylon was the rstcommercially successful synthetic polymer. As the rst synthetic ber, nylon wasdesigned to replace articial silk. Nylon led to the global synthetic ber revolution.Unlike rayon and acetate, which were derived from renewable cellulose stock, nylon wassynthesized completely from petrochemicals. This rst discovery led to the eld ofmacromolecules and the new world of synthetic bers. Nylon consists of repeatingunits linked by amide bonds and is frequently referred to as polyamide (PA). It is athermoplastic, silky material, rst used commercially in a nylon-bristled toothbrush(1938), and then for ladys stockings (nylons; 1940), after being introduced as a fabricat the 1939 New YorkWorlds Fair. Nylon stockings were shown in February 1939 at theSan Francisco Exposition. The USA entered World War II in December 1941 and allproduction of nylon was dedicated for military use; nylon replaced silk in parachutes andak vests, and found many other military uses.That was the origin of all the modern manmade macroscopic synthetic bers and

modern textile industry. Polyesters commercialization in 1953 was accompanied by theintroduction of triacetate. Today, polyester is the king of all synthetic bers and is foundin almost all apparel and many other applications. Polyesters have been developed withspecial shapes, ber nishes, dyes and pigments, and consequently, offer the greatestlevel of control over the performance attributes important to the industries they serve.

2 1 Introduction


The other important types of bers and ber products include berboard, made out ofwood bers (dating back to 1897), berglass (1937) and ber optics (1956).Today, ber spinning is a commercial process to produce thin polymeric laments

that are used by a myriad of industries. Filaments can be produced from synthetic,manmade or natural polymers, usually by the process of extrusion. Extrusion is the processof forcing the rawmaterials in their liquid state through tiny orices and solidifying them toform bers. In their initial state the raw materials are solid. If they are thermoplasticpolymers they are heated or melted, while if they are nonthermoplastic, they are dissolvedin a suitable solvent.While we now take these processes for granted, it is interesting to notethat their history only extends back about a century, and rayon was the rst manmadeber introduced only 160 years ago. Today, manmade bers are found in almost everyapplication, ranging from apparel and home furnishings, to automotive industry andmedicine. The introduction of manmade and synthetic bers has led to the introductionof many high-performance products touching many different industries. It is hard toimagine what we would have used for these applications today without access to theseinnovations.The birth of nanobers is related to the patent by Formhals (1934), in which electro-

spinning of cellulose acetate bers was proposed. Electrically driven jets were in focusmuch earlier (Zeleny 1914, 1917), however, these were jets of inelastic Newtonianliquids, which are prone to capillary instability and cannot be used to form longcylindrical laments. Only the presence of viscoelasticity in the solutions used byFormhals allowed him to form bers. Moreover, these were nanobers, since thepresence of the electric forces results in dramatic reduction of the ber cross-sectionaldiameter due to the so-called electrically driven bending instability found much later byReneker et al. (2000). The nanoscale of the bers was actually considered to be adrawback in the time of Formhals, since they could not be used in the textile industry.As a result, they did not stir up toomuch interest, and only occasional publications relatedto the electrically driven jets of polymer solutions and melts, and the bers formed fromthem appeared in the 60 years after Fromhals work (Baumgarten 1971, Larrondo andManley 1981a, 1981b, 1981c). However, the situation had radically changed after thework of D.H. Renekers group in the 1990s (Doshi and Reneker 1995, Reneker and Chun1996). This was the time of nanotechnology, new applications of nanobers wereimmediately recognized and the number of publications devoted to nanober formingstarted to increase exponentially. This process continues today and is described in thetechnical sections of this book.The works on traditional and novel methods of ber forming encompass

synthetic chemistry, polymer physics, non-Newtonian uid mechanics, electro-hydrodynamics, applied mathematics and materials science, and require the concertedefforts of specialists from distant elds. The need for a comprehensive monographencompassing different aspects of ber-forming processes materialized rst in theseminal monograph by Ziabicki (1976). With interest in nanobers growing, severalmonographs exclusively devoted to electrospinning were published. Ramakrishna et al.(2005) covered the rapidly widening biomedical applications of electrospun nanobermats. Filatov et al. (2007) described the work of Petryanov-Sokolovs group in the Soviet

1.1 History and outlook 3


Union, which resulted in electrospun lters for protection from radioactive aerosols.Wendorff et al. (2012) discussed in depth the aspects of electrospinning related tomaterials science.The existing and rapidly extending processes for forming micro- and nanobers include

meltblowing, electrospinning, solution blowing and several other methods. The bers areformed from petroleum-derived and biopolymers. The scientic foundations of ber-forming processes and their practical implementations are rooted in polymer physics,rheology, non-Newtonian hydrodynamics, electrohydrodynamics, aerodynamics andapplied mathematics, while their applications extend to lters, membranes, electrodes,coatings, nanouidics, communications (optical bers), sensors, biomedical scaffolds anddrug delivery, as well as various military-oriented aspects. The present monograph aimsfor a comprehensive in-depth description of all these aspects.

1.2 Melt spinning

The basic principle of ber extrusion involves feeding pellets or granules of the solidpolymer into an extruder. The pellets are compressed, heated and melted by an extrusionscrew, then fed to a spinning pump and into the spinneret. The polymer is passed throughthe extruder and then a lter, to a manifold, and is distributed to one or more spinningpositions (Hensen 1997).The spinneret is the main component in determining ber shape and size after

extrusion. It may contain one to several hundreds of capillaries for lament spinning.In the case of spunbond systems, discussed in more detail in Section 1.5, there areas many as 6000 capillaries per meter. These tiny openings are very sensitive toimpurities, damage and corrosion. When warranted, the spinneret can be made fromvery expensive, corrosion-resistant metals for example, for extruding uoropolymerssuch as peruoroalkoxy polymer resin (PFA) and polyvinylidene diuoride (PVDF), aswell as other exotic polymers such as polyphenylene sulde (PPS). The polymer liquidfeeding them must be carefully ltered, and should not leave residue on the face of thespinneret, as this would lead to breaks and drips. Most polymers have lubricants, anti-oxidants and other additives compounded into them to overcome challenges due topolymer degradation, and spinning breaks and drips. Maintenance is also critical, andspinnerets must be removed and cleaned on a regular basis to prevent clogging.Thus, the term extrusion in the ber industry refers to the process of forming polymeric

laments by forcing the uid through a spinneret, and spinning is the collective term usedfor the extrusion and solidication of the laments produced.An important element is ber drawing following the extrusion. Drawing results in the

desired properties in the nal product and in a decreased ber diameter, increasedmolecular orientation, increased tensile properties and a reduction in strain to failure.The extent to which bers can be drawn depends on the properties of the materials beingextruded. Fibers are drawn as much as eight times their original length to form bers withthe desired properties.

4 1 Introduction


It is interesting to note also that some polymers such as polyester (PET) require a highber spinning speed to form crystallinity. At about 3200mmin1 PETstarts to show signsof crystal orientation. Fibers spun at low speed shrink extensively if exposed to heat. ForPET, therefore, bers are extruded at much higher speeds 4000 to 10 000 m min1 toovercome the issues with shrinkage.There are several methods for forming bers from molten state or from solution: melt,

dry, wet and gel spinning. These are briey described in this and the following sections.In melt spinning, the ber-forming polymer is melted and extruded through the spinneret,stretched and directly solidied by cooling (Figure 1.1) and then drawn to achieve higherdegrees of orientation and crystallization. Examples are polypropylene, polyester andnylon, among others. Melt spinning is by far the most widespread system globally.Continuous laments, as well as discontinuous crimped bers (also referred to as staplebers), are globally available. The process for forming continuous laments is somewhatdifferent from those for producing staple bers. Staple bers are produced in continuous

PolymerChips

FeedHopper

ColdAir

MeltSpinningMelter/

Extruder

Bobbin

Stretching

(a) (b)

Melt Spinning Polymer from Chip

TwistingandWinding

d0

d0, T0, V0

dL, TL, VL

d, T, V

x 1

2

3

L

Figure 1.1 (a) Melt spinning (Fiber Source, 2013). (b) Schematic of an individual molten threadline inmelt spinning process: 1 spinneret, 2 molten threadline, which cools down due to convectiveheat transfer to the surrounding gas and solidies, 3 winding bobbin. Ziabicki (1976). Courtesyof John Wiley and Sons.

1.2 Melt spinning 5


form in large tows, which are then crimped, heat set and cut into the desired staplelengths. These staple bers are then blended with other bers (natural as well asmanmade or synthetic bers) and are formed into a yarn. Most textile yarns are madefrom blends of various staple bers; the yarn spinning technology is quite well developedand produces incredibly interesting and desirable textures and properties. Filaments aresometimes textured to form bulk or stretch in post-processing. Many of the facilities haveintegrated polymer synthesis and ber formation that is, the most widespread processesfor staple (discontinuous) ber production couple synthesis and ber extrusion, andthereby control costs.Molten threadlines in the melt spinning process are free liquid jets pulled by a winding

bobbin to form solidied bers (Figure 1.1b). These molten threadlines are subjected toseveral instabilities and perturbation-amplication phenomena, which can make theresulting bers nonuniform. One of these instabilities, the so-called draw resonance,was discovered in the seminal works of Matovich and Pearson (1969) and Pearson andMatovich (1969), and below we discuss the elementary theory of this phenomenon.Consider an isothermal straight liquid threadline that is issued from a spinneret hole

of radius a0 with velocity V0. The longitudinal axis along the threadline axis is denoted x.It is reckoned from the spinneret hole where x = 0. The threadline has a circular cross-section and tapers due to the pulling force transmitted from a winding bobbin located atx = L. The winding velocity imposed by the bobbin on the threadline at x = L is V1;however, the cross-sectional radius at that point is to be determined.To formulate the mass and momentum balance and derive the corresponding

quasi-one-dimensional equations, we consider an innitesimally short slice of the thread-line of length dx located close to cross-section x. The liquid mass currently contained inthis slice is equal to a2dx, where is the liquid density and a(x,t) is the cross-sectionalradius, which depends on x and time t. During the time interval dt, this mass can change,due to the liquid inux through the cross-section x, which is a2V jxdt, and the outowthrough the cross-section x+dx, which is a2V jxdxdt, where V(x,t) is the longitudinalvelocity in the threadline. The mass balance reads

D a2dx a2V j

xdt a2V j

xdxdt 1:1

Using the Taylor series, we see that

a2V jx a2V jxdx a2V x dx 1:2

and thus Eq. (1.1) reduces to the following differential mass balance, or following theuid mechanical terminology, continuity equation:

a2

t Va

2

x 0 1:3

In the momentum balance, we neglect inertial forces, surface tension and gravity, andaccount for only the internal normal stresses acting in the threadline cross-sections andassumed to be dominant. Denote normal stress as xx, and thus the corresponding force

6 1 Introduction


acting in cross-section x of the innitesimal threadline slice under consideration wouldbe xxa2jx. Accounting for the force acting at the cross-section x+dx of the slice, weform the momentum balance in the following form

xxa2jx xxa2jxdx 0 1:4

which means that

xxa2

x 0 1:5

In the elementary model we are dealing with, we assume that liquid in the threadline isNewtonian uid and is characterized by a single rheological parameter, viscosity (seeLoitsyanskii 1966, Landau and Lifshitz 1987, Batchelor 2002). Polymer melts used inmelt spinning, as well as polymer solutions used in dry and wet spinning, can hardly betreated as viscous Newtonian liquids, since they develop signicant and even dominantelastic stresses in strong elongational ows. Such uids are viscoelastic. Viscoelasticityis introduced in Chapter 2 and accounted for when considering different types of polymerjet ows and ber-forming processes relevant to manufacturing of micro- and nanobersin Chapters 35. The simplied rheological model of Newtonian uids employed herewould be directly relevant to the formation of optical bers (see Sections 6.6 and 6.7 inChapter 6). Molten glasses are Newtonian liquids, albeit their viscosities are strongfunctions of temperature. Here, for simplicity, we consider an isothermal case and thusviscosity = const.For the incompressible Newtonian uids

xx pxx 1:6yy p yy 1:7

where p is pressure, yy is the radial normal stress in the threadline cross-section, and xxand yy are the normal deviatoric stresses corresponding to xx and yy, respectively.Since the outer surface of the threadline can practically always be considered as

unloaded because all the tractions imposed by air or surface tension effects are negligiblysmall in comparison with the inner stresses in the liquid, yy = 0 practically everywhere inthe cross-section (Yarin 1993), and thus Eq. (1.7) yields p = yy. The latter allowstransformation of Eq. (1.6) to the following form

xx xx yy 1:8

For Newtonian uids,

xx 2 Vx ; yy Vx

1:9

and thus using Eq. (1.8) we arrive at

xx 3 Vx 1:10

1.2 Melt spinning 7


where the factor 3 is called the Trouton viscosity (Yarin 1993).Substituting Eq. (1.10) into Eq. (1.5), we transform the momentum balance to the

following form

x

a2Vx

0 1:11

The continuity and momentum balance equations (1.3) and (1.11) form a closedsystem of the two quasi-one-dimensional equations required to determine two unknownfunctions, the radius and velocity distributions a(x,t) and V(x,t). These equations repre-sent the simplest version of the quasi-one-dimensional equations of the dynamics of freeliquid jets (3.1) and (3.2) discussed in Section 3.1 in Chapter 3.Render Eqs. (1.3) and (1.11) using the following scales: L for x, a0E

1/2 for a and V1for V. Here E= V1/V0 denotes the draw ratio, which is the governing parameter ofthis problem. The continuity and momentum balance equations (1.3) and (1.11) in thedimensionless form do not change.In the case of melt spinning, solutions of the dimensionless system of Eqs. (1.3) and

(1.11) are subjected to the following dimensionless boundary conditions:

x 0 : a E1=2; V E1 1:12x 1 : V 1 1:13

In steady state, the time derivative in Eq. (1.3) vanishes and the steady-state solutions asand Vs depend only on x:

as E 1x =2; Vs E x1 1:14

Since the draw ratio E is always larger than 1, Eqs. (1.14) describe tapering of thethreadline from the cross-sectional radius a0 to a smaller value a1= a0E

1/2 at the windingbobbin, whereas velocity is increasing from V0 to V1. To form smaller bers, one isinterested in increasing the draw ratio E. This, however, is subject to a severe limitationrelated to the instability of the steady-state solution (1.14). Indeed, consider smallperturbations


x 0: 0; 0 1:18x 1: 0 1:19

Excluding from the system of equations (1.16) and (1.17), we reduce it to a singleequation for :

2x2

E 1x 2

xt 0 1:20

with the corresponding equation relating to .Solving Eq. (1.20) for , one can nd the corresponding as

2 2E1x

ln E

t

2ln E

x

t 1:21

The solutions for and are subject to the boundary conditions (1.19). As a result, wend the following distribution of the radius perturbation:

exp t F x ; F x x0exp

E1

ln E

d 1:22

where is the dummy variable, and the eigenvalue satises the following characteristicequation:

F 1 10E1F d

1:23

Solutions of Eq. (1.23) are sought on the complex plane.The investigation of the characteristic equation (1.23) shows that in the range

1 < E < 20.22 it possesses only the solutions with a negative real part r. Therefore, theperturbations (1.22) decay in time as exp jrjt , and the steady-state solution for themolten threadline (1.14) appears to be stable. At E = 20.22 the nondecaying smalloscillations set in, which corresponds to the solution of Eq. (1.23), = 0.693i, where iis the imaginary unit. Mathematically speaking, this is a classical Hopf bifurcation. At20.22 < E < 49.98 the solutions of Eq. (1.23) represent a pair of complex conjugatesolutions with a positive real part r. The corresponding linear perturbations grow in timeas exp(rt), and the draw resonance sets in (Pearson and Matovich 1969, Pearson 1985).Some of the relevant eigenvalues found from Eq. (1.23) are listed in Table 1.1, where idenotes the imaginary part of .At E > 20.22, the instability of the steady-state solution (1.14) results in a bifurcation to

a new solution. Under the xed boundary conditions (1.18) and (1.19), the nonlinearsolutions of the continuity and momentum balance equations (1.3) and (1.11) can befound either by the asymptotic method of multiple scales or numerically (Yarin 1993,Yarin et al. 1999). The solutions represent the self-sustained oscillations (the so-calledlimit-cycle solution) illustrated by the numerical results depicted in Figure 1.2. The berradius at the winding bobbin a(1,t) becomes a periodic function of time, with the

1.2 Melt spinning 9


amplitude variation in the range 0.5 to 7.5 (see Figure 1.2b). Therefore, formation ofuniform bers at E > 20.22 is impossible, and the draw resonance instability severelyrestricts the increase of the winding speed, the other parameters being xed.Donnelly and Weinberger (1975) conducted model experiments with isothermal

spinning of Newtonian liquids, intended to verify experimentally the existence of thedraw resonance instability. This work represents signicant fundamental interest,since it excluded all complicating effects related to the heat transfer at the threadlinesurface, the elasticity of the polymer melt and solidication. In these experiments ahighly viscous silicon oil threadline was drawn by a winding bobbin, from which itwas immediately scraped by a doctor blade located close to the bobbin surface. Theexperiments by Donnelly and Weinberger (1975) showed that the draw resonance setsin as soon as the draw ratio E reaches a value close to 20, in full agreement with thetheory. Similar data were obtained by Ishihara and Kase (1976), who employed anotherliquid, polyethylene terephthalate (PET), with approximately Newtonian behavior. Intheir case the threadline solidied on contact with the winding bobbin, which wassubmerged in cold water.In the general case, perturbations can be also introduced at both ends of molten

threadlines due to oscillations of metering pumps, equipment vibratitons and blowingof air for ber cooling. Then, the question of the threadline sensitivity to the imposedperturbations arises. To illustrate that, consider the case where only perturbations of theinitial threadline radius are present, for example, due to the die swell affected by theoscillations of the metering pump. In this case x = 0 approximately corresponds to the endof the die swell (the length of the die swell is negligible compared to the length ofthe threadline). Then, the linearized boundary conditions that replace the boundaryconditions (1.18) and (1.19) become

x 0: 0 sin t; 0 1:24x 1: 0 1:25

where 0 and are the dimensionless perturbation amplitude and frequency,respectively.

Table 1.1 Spectrum (1.23) of the linear stability problem. Reprinted withpermission from Yarin et al. (1999). Copyright 1999, AIP Publishing LLC.

E r i

19 0.0111 0.73120.22 0 0.69321 0.00495 0.672325 0.01918 0.586928 0.0258 0.536930 0.029 0.50835 0.0349 0.4497

10 1 Introduction


To nd the response of the threadline radius at the winding bobbin at x = 1 to theperturbations of the initial radius at x = 0, in the linearized approximation one shouldagain solve the linearized problem (1.20) for the radius perturbation and calculate thecorresponding from Eq. (1.21). After that, the boundary conditions (1.24) and (1.25)are applied. The resulting distribution of the perturbation of the threadline cross-sectionalradius reads

0.5

0.4

0.3

0.2

0.1

00 2 4

1

2

3

6a

V

8 10(a)

6

7

5

4

3

2

1

02900 2920 2940 2960 2980 3000 3020 3040 3060

t(b)

a (1

,t)

Figure 1.2 The phase plane describing the threadline midlength x = 0.5. The limit-cycle behavior (drawresonance) at: (1) E = 28, (2) E = 50 and (3) E = 100. (b) The ber radius at the winding bobbina(1,t) as a function of time, corresponding to E = 100. Reprinted with permission fromYarin et al.(1999). Copyright 1999, AIP Publishing LLC.

1.2 Melt spinning 11


x; t 0 sint 1 1 E B1 Si x B2 Ci x

B21 B22

ln E

( )

0 cost 1 E B1 Ci x B2 Si x

B21 B22

ln E

( ) 1:26

where

Si Si

ln E

Si E

ln E

1:27

Ci Ci

ln E

Ci E

ln E

1:28

cos cos

ln E

cos E

ln E

1:29

sin sin

ln E

sin E

ln E

1:30

In the above equations, Si(.) and Ci(.) denote the sine and cosine integral functions(Abramowitz and Stegun 1972). In addition, the following notations are used

B1 cos Ci ln E Si 1:31

B2 sin Si ln E Ci 1:32

Ci x CiE 1x

ln E

Ci E

ln E

1:33

Si x SiE 1x

ln E

Si E

ln E

1:34

The amplitude-frequency characteristic of the threadline is of interest in the applications.It is dened as

A 20

2=0

1; t 2dt 1:35

It is calculated using Eq. (1.26) and the result is shown in Figure 1.3 by curve 2, whichcorresponds to the isothermal case considered in detail in this section. The resultcorresponds to the sub-critical case of E < 16, where the draw resonance instabilitydoes not appear, and the dominant role is played by the externally excited perturbations.In the nonisothermal case, threadline cooling results in a signicant increase in liquidviscosity (see Section 6.6 in Chapter 6), which suppresses radius uctuations at thewinding bobbin, as is shown by curve 1 in Figure 1.3.The fully nonlinear analysis of the dynamics of molten threadlines subjected to

external perturbations at E > 20.22 reveals a nontrivial interplay of the self-sustained

12 1 Introduction


oscillations corresponding to the draw resonance instability with the imposed excitation.The boundary conditions that replace (1.12) and (1.13) read

x 0: a E1=2 1 cost ; V E1 1:36x 1: V 1 1:37

with the dimensionless parameter being responsible for the perturbation amplitude(0=E

1/2).

Yarin et al. (1999) solved Eqs. (1.3) and (1.11) numerically and showed that at thedraw ratio E 30 the nonlinear interplay between the propensity to the draw resonanceinstability and the external excitation in the form of Eq. (1.36) results in quasi-periodicor chaotic variation of the ber cross-section at the winding bobbin. The route to chaosmay be smooth, via period doubling, or explosive, via abrupt disappearance of quasi-periodic solutions; as a result a strange attractor sets in. The irregular variation of theber diameter corresponding to a strange attractor is illustrated in Figures 1.4 and 1.5.These results point at the possibility that optical bers drawn from molten glass may beperturbed nonperiodically. The experimental data of Tyushkevich et al. (1970) andreferences therein show that this, indeed, may take place in glass ber drawing. Theystate, . . .that a change of thickness of glass ber length-wise is a random process . . .and the corresponding correlation function decays exponentially. Draw resonance,being a periodic process, certainly cannot be responsible for this picture. A possiblesource for the random unevenness of drawn bers may be random noise entering athreadline. This, however, should lead to random perturbations at any winding velocity(at any draw ratio E), which is not the case; they are seen at the bers drawn only athigh enough speed (Burgman 1970), which agrees with the predictions of the theoryoutlined above.Note that melt spinning of hollow bers is of interest in relation to fabrication

of optical bers and glass capillaries. Stability and sensitivity study of spinning of

0.5 1.5 2.5

1

2

A

0

100

200

Figure 1.3 The amplitude-frequency characteristic of a threadline with perturbations of the cross-sectionalradius at the die exit in the subcritical case of E = 16. (1) Non-isothermal case, (2) isothermal case,which corresponds to Eq. (1.26). Yarin (1993). Courtesy of Pearson Education.



1.00

0.1

0.2V

0.3

0.4

2.0 3.0a

4.0 5.0

100000

0.5

1.0

1.5

2.0

a (1

,t)

2.5

3.0

3.5

12000 14000 16000t

18000 20000

(a)

(b)

Figure 1.4 Irregular ber shape at = 0.13, = 1 and E = 30. (a) The Poincar map sampled at x = 0.5. (b) Theber cross-sectional radius a(1,t) at the winding bobbin corresponding to a strange attractor.Reprinted with permission from Yarin et al. (1999). Copyright 1999, AIP Publishing LLC.

14 1 Introduction


isothermal drawing of hollow bers was published by Yarin et al. (1994). The resultsrevealed that drawing of hollow bers is also subjected to the draw resonance instabilityand the threshold value of the draw ratio is the same as the one found in the presentsection, E = 20.22.

00

0.2

0.4

0.6

2.0 4.0a

6.0 8.0

V

(a)

100000

0.5

1.0

1.5

2.0

a (1

,t)

2.5

3.0

3.5

4.0

12000 14000 16000t

18000 20000(b)

Figure 1.5 Irregular ber shape at = 0.13, = 1 and E = 30. (a) The Poincar map sampled at x = 0.5. (b) Theber cross-sectional radius a(1,t) at the winding bobbin corresponding to a strange attractor.Reprinted with permission from Yarin et al. (1999). Copyright 1999, AIP Publishing LLC.



Heat transfer with the surrounding gas is a factor in stabilizing draw resonance (Petrieand Denn 1976, Yarin 1993 and references therein). The corresponding experimental andtheoretical results show that when heat removal is sufciently rapid and the bersolidies before reaching the winding bobbin, the draw resonance instability can befully suppressed. This probably explains the fact that it is possible to exclude this type ofinstability in the industrial melt-spinning processes where the values of the draw ratio Eare on the scale of several hundred, and V1 is of the order of 10

4 m min1. In the case ofnonisothermal drawing of optical microcapillaries, an analysis of the draw resonanceinstability is given by Gospodinov and Yarin (1997).Given the fact that melt spinning is applied to polymer melts, the effect of the

elastic stresses on the draw resonance instability is of signicant importance. Inisothermal conditions for a number of polymers, threshold values of E < 20 werefound (sometimes as small as E 2) for destabilization due to the elastic stresses(see Weinberger et al. 1976). On the other hand, Chang and Denn (1979) observedsuppression of the draw resonance instability by elastic stresses. It is emphasizedthat the theoretical investigation of the draw resonance of viscoelastic polymericthreadlines initiated by the seminal work of Fisher and Denn (1976) (see also Hyun1978) is still far from over.An additional type of instability that affects melt spinning in practice is the

so-called melt fracture (Koopmans et al. 2010). Initially it manifests itself in theform of roughness, with multiple ripples appearing at the threadline and ber surface,called sharkskin melt fracture. A more developed instability of this type leads to theappearance of large-amplitude bending perturbations and undulations on the threadlineright after it leaves the spinneret hole (Figure 1.6). In the case of a fully developedmelt fracture, the extrudate transforms into a succession of chunks that practicallyare not connected to each other. Melt fracture sets in above a certain threshold of thepressure drop on a spinneret hole, i.e. above a certain extrusion velocity (Figure 1.6).The threshold value depends on liquid properties. The experimental data summarizedby Petrie and Denn (1976) shows that melt fracture is never observed in theextrusion of Newtonian liquids. Therefore, this type of instability is directly relatedto viscoelasticity of polymer melts. This phenomenon severely restricts the rate of melt

a) b) c)

d

2d

Figure 1.6 Melt fracture: (a) for the lowest extrusion speed the surface is smooth, (b) for the intermediate speedsome roughness appears, (c) at the highest speed a more developed melt fracture is observed.Reprinted with permission from Bertola et al. (2003). Copyright 2003, American Physical Society.

16 1 Introduction


spinning. A fully acceptable theory and explanation of melt fracture is still unavailable.However, all signs point to the emergence of self-sustained oscillations in polymer meltow inside the die (Drda and Wang 1995, Wang and Drda 1996, Yarin and Graham1998, Bertola et al. 2003, Koopmans et al. 2010).

1.3 Dry spinning

Dry spinning of sufciently concentrated polymer solutions is used in cases wherepolymers are not thermoplastics and cannot be effectively melted. If solvents are volatileenough, threadline precipitation and solidication is possible on the way from thespinneret hole to the winding bobbin, and this method is called dry spinning(Figure 1.7). Sometimes evaporation is facilitated with a stream of air or inert gasblown at threadline. The list of solvents appropriate for dry spinning includes alcohols,acetone, ether solvents and tetrahydrofuran (THF). Because there is no precipitatingliquid involved (see Section 1.4), the ber does not need to be dried and the solvent ismore easily recovered. Examples are acetate, triacetate, acrylic, modacrylic, spandex,etc. Dry spinning is typically conducted in a vertical connement, where polymersolution jets are surrounded by a stream of a high-temperature gas (e.g. air) that facilitatessolvent evaporation. Chardonnet silk bers, discussed in Section 1.1, were spun fromnitrocellulose solutions in a blend of alcohol and ether using dry spinning, which makesthe latter the ancestor of melt spinning described in Section 1.2, since the ber-formingand pulling systems are alike. On the other hand, the physical processes which take placein and around the liquid threadline in dry spinning of macroscopic bers are similar to

8

1

2

3

4

5

6

7

9

Figure 1.7 Schematic of dry spinning: (1) dosing pump, (2) spinneret, (3) liquid threadlines, (4) drying section,(5)(7) receiving pulleys, (8) hot air inlet, (9) hot air outlet. Ziabicki (1976). Courtesy of JohnWiley & Sons.

1.3 Dry spinning 17


those in solution blowing and electrospinning of polymer micro- and nanobers,discussed in detail, respectively, in Sections 4.8 and 4.9 in Chapter 4, and in severalsections in Chapter 5.

1.4 Wet or solvent spinning, gel spinning

Wet spinning is used to form bers from polymers that are not thermoplastics andthus cannot be spun as melts, and can be dissolved only in nonvolatile solvents.Then, polymer solutions are issued as jets into a precipitation bath lled with anonsolvent for a particular polymer. As a result of the binary diffusion of solventinto the bath, and nonsolvent into the threadlines, polymer precipitates and solidiedlaments are pulled out by the receiving pulleys (Figure 1.8). Wet spinning is appliedto polyamides (nylon 6 and nylon 6,6), as well as to process rigid-rod polymers, such asKevlar brand Aramid bers. In the latter case, sulfuric acid (H2SO4) is used as thesolvent, and water in the precipitation bath as the nonsolvent. The other examples areacrylic, rayon, etc.Combinations of wet and dry spinning are also possible, with part of the threadline being

in air, and another part in the precipitation bath. The part in air can be a polymer gel, whichis partially liquid. The nal solidication of the bers is achieved after solvent evaporationin air followed by precipitation in the bath. Such a process is called gel spinning.

1.5 Spunbonding

The spunbond process is an integrated system producing nonwoven webs of continuouslaments that are then bonded normally in a single step to form a strong and exiblefabric. While attempts have been made to produce laments from solution, the currentprocesses in place use a thermoplastic polymer resin to form the laments/fabrics. In itsstandard form, the spunbond process results in relatively large bers, more than 20 m indiameter.

2 3 46

1

7

8

10

95

Figure 1.8 Schematic of horizontal wet-spinning process. (1) polymer supply line, (2) spinneret, (3)threadlines, (4) precipitation bath, (5) false twist grooved rolls, (6) inlet for the nonsolvent, outletof the bath content (mixture of solvent and nonsolvent), (8) plastication bath, (9) and (10) dry-heatsetting cans. Ziabicki (1976). Courtesy of John Wiley & Sons.

18 1 Introduction


In the spunbond processes, when a polymer other than a polyolen is used, it isoften necessary to have drying and/or crystallizing (in the case of PET) of thepolymer chips. The polymer chips are delivered by extruders designed to processpolymers with a wide range of characteristics. The extruder barrel is heated and thehigh degree of compression of the polymer chips during processing also contributesto the generation of heat that results in melting of the polymer chips. The currentstandard processes can reach a maximum of 350 C this is sufcient for mostordinary polymers used in the formation of nonwoven fabrics today, ranging frompolyolen to polyester.The molten polymer exiting the extruder goes through a lter pack to remove solid

particulates and contamination with screen lters. It then ows into a gear pump thatmeters and delivers precise amounts of polymer to the spinpack. The spinpack iscontained in the spinbeam that in todays technology would cover the entire width ofthe machine. At the bottom of the spin beam resides a spinneret plate, normally with up to6000 holes m1. The molten polymer ows through the spinneret holes and formslaments upon solidication brought about by quenching. In current (modern) systems,the laments form a curtain, owing into an air gap where fast moving air provides a dragforce that pulls the laments away from the spinneret and reduces the ber diameter, butmore importantly leads to a much higher degree of molecular orientation in the structure.Upon drawing, the laments may be traveling at velocities exceeding 8000 m min1.Pulling polymer bers by high-speed co-owing air is characteristic of the meltblowingprocess considered in detail in Chapter 4.As the laments approach a moving collection belt, they slow down, and due to the

resulting bending instabilities, the laments intertwine and are laid on the moving belt.The lay-down is a critical element in the formation of the nal structure, as it controls thedegree of isotropy in the structure. The web is then normally bonded by two heated rolls(calendar), or sometimes other forms of bonding, such as hydroentangling or chemicalbonding, may also be employed.The features of the process that give spunbond fabrics their uniqueness lie in the

technologies used to extrude the laments and form the web. These aredescribed below, in a historical context; most of them are still in use in theiroriginal or somewhat modied form. The spunbond process emerged from lamentspinning and the early systems developed in the 1950s and 1960s relied on usingmultiple lament extrusion units placed in a row to form continuous webs. Eachextrusion unit was equipped with spinnerets containing a few hundred holes. Thebers, instead of being wound on a bobbin to form continuous lament yarn, werefed into a lay-down system to separate and place the laments on a moving belt.The early systems suffered from incomplete lament separation, causing ropeformation and spatial mass nonuniformity, as well as streaks caused by usingmultiple side-by-side systems to form a web. A number of techniques weredeveloped to deal with these inadequacies these included the use of lamentdistributors in various forms, and also the use of electrostatic charge to causelament separation. A good review of these early developments is found in thebook by Batra and Pourdeyhimi (2012).

1.5 Spunbonding 19


The origin of the modern systems stems from a few key developments. The rst isthe introduction of curtain spinning using a single spinneret block by Matsuki et al.(1974), assignee Asahi. To improve the formation (web uniformity) they chose to usehigh capacity extruders, which could supply polymer to a single spinneret blockthat extended across the collecting belt. Figure 1.9 shows a schematic of the equipment.The rectangular spinneret die would deliver a two-dimensional array of lamentscontinuously across the width of the machine. The so-called open systems offeredtoday by Hills, Neumag and others are all based on this early development.The next most signicant advance was due to a development by Kimberly Clark that

combined the quenching and lament draw functions in a full-width slot attenuator, apatent granted in 1982. Figure 1.10 shows a quench and draw box integrated withthe spinneret section into a single enclosure. This led to the development of technologiesknown today as closed systems. Such a system is offered by Reicol (Reifenhauser),the global leader in supplying such systems. The rst Reifenhauser system was intro-duced in 1989 and modied the full-width slot concept of Kimberly Clarks technology.The schematic of the system is shown in Figure 1.11. It integrates the spinneret blockwith the quenching and draw system into a single closed unit.The next major development relates to the use of bicomponent bers in the spunbond

process. The earliest patent discussing the manufacture of a bicomponent ber may wellhave been granted to DuPont in 1934. A series of subsequent developments followed.Hills (1992) patented the multicomponent spin pack in 1992.In the area of spunbond today, there are numerous commercial systems installed

around the globe. These naturally employ two dryer hoppers, each feeding a differentpolymer to two different extruders, followed by lter-packs, gear pumps and onto thespin block, containing the spinnerets. The spin packs used here are of special design; one

1320a

16

12

M

14b

L

14

10

11

15

14a

l

Figure 1.9 Schematic of the full-width slot attenuator-based system (Matsuki et al. 1974).

20 1 Introduction


is shown schematically in Figure 1.12. The designs are quite complex, but permit theextrusion of a variety of cross-sectional arrangements of two or more polymers in thelament. The rest of the process is essentially the same as a homocomponent system,with the usual draw and collection systems. The initial motivation for the use ofbicomponent bers was essentially due to the fact that bicomponent laments facilitatethermal bonding. For example, a lower melting-point sheath allows thermal bonding at alower temperature without melting the core, potentially resulting in improved perform-ance at a lower cost. This arrangement allows the exploitation of a higher-strength secondcomponent at a lower energy cost during bonding. However, the rationale for usingbicomponent laments in spunbond fabrics goes far beyond simply thermal bonding.Bicomponent structures are enablers that can help develop new generations of non-wovens with improvements in strength and softness, with ultrane bers, improvementin loft (crimped bers) in the fabric, etc. and even nonwovens with stretch and recovery.

2610

18

46

28

28

29

54

24

2040

34

36

25

38

Figure 1.10 Integrated spinneret, quenching and slot attenuator (Appel and Mormon 1982).

1.5 Spunbonding 21


314

12

13

1117

4 35a

5

1615

35 8

2

10

19

18

y1

yn

y2xn

y1

x2

x17

1II9

20

18

19

1918

6

Figure 1.11 The Reifenhauser system (Balk 1989).

16 17 19

18

1116

20

2316

10

12

2613

3230

3233

3332

332725

29

22

33

32

3238

28

383836 36

3636 36

36

1416

41

40

41

4115

1638

41

Figure 1.12 Spin pack for bicomponent bers (Hills 1992).

22 1 Introduction


1.6 References

Abramowitz, M., Stegun, I. A. (Editors), 1972. Handbook of Mathematical Functions. Dover,New York

Appel, D.W.,Mormon,M. T., 1982.Method for forming nonwoven webs. US Patent No. 4340563.Balk, H., 1989. Apparatus for making a spun eece from endless synthetic-resin lament. USPatent No. 4812112.

Batchelor, G. K., 2002. An Introduction to Fluid Dynamics. Cambridge University Press,Cambridge.

Batra, S. K., Pourdeyhimi, B., 2012. Introduction to Nonwovens, DEStech Publishing, Lancaster.Baumgarten, P. K., 1971. Electrostatic spinning of acrylic microbers. J. Colloid. Interface Sci. 36,7179.

Bertola, V.,Meulenbroek, B.,Wagner, C., Storm, C.,Morozov, A., van Saarloos,W., Bonn, D., 2003.Experimental evidence for an intrinsic route to polymer melt fracture phenomena: A nonlinearinstability of viscoelastic poiseuille ow. Phys. Rev. E 90, 114502.

Burgman, J. A., 1970. Liquid glass jets in the forming of continuous glass bers.Glass Technol. 11,110116.

Chang, J. C., Denn, M.M., 1979. An experimental study of isothermal spinning of a Newtonianand viscoelastic liquid. J. Non-Newton. Fluid Mech. 5, 369385.

Donnelly, R. J., Weinberger, C. B., 1975. Stability of isothermal ber spinning of a Newtonianuid. Ind. Eng. Chem. Fundam. 14, 334337.

Doshi, J., Reneker, D. H., 1995. Electrospinning process and applications of electrospun bers.J. Electrostatics 35, 151160.

Drda, P. P.,Wang, S. Q., 1995. Stick-slip transition of polymer melt/solid interfaces. Phys. Rev. Lett.75, 26982701.

Fiber Source, 2013. Available at http://www.bersource.com/f-tutor/techpag.htm. Accessed July27, 2013.

Filatov, Y., Budyka, A., Kirichenko, V., 2007. Electrospinning of Micro- and Nanobers.Fundamentals and Applications in Separation and Filtration Processes. Begell House,New York.

Fisher, R. J., Denn, M.M., 1976. A theory of isothermal melt spinning and draw resonance.AIChE J. 22, 236246.

Formhals, A., 1934. Process and apparatus for preparing articial threads. US Patent No. 1975504.Gospodinov, P., Yarin, A. L., 1997. Draw resonance of optical micro-capillaries in non isothermaldrawing. Int. J. Multiphase Flow 23, 967976.

Hensen, F. (Editor), 1997. Plastic Extrusion Technology. C.Hanser, Munich.Hills, W.H., 1992. Method of making plural component bers. US Patent No. 5162074.Hyun, J. C., 1978. Theory of draw resonance. Part II: Power-law and Maxwell uids. AIChE J. 24,423426.

Ishihara, H., Kase, S., 1976. Studies on melt spinning. VI. Simulation of draw resonance usingNewtonian and power law viscosities. J. Appl. Polym. Sci. 20, 169191.

Koopmans, R., Den Doelder, J., Molenaar, J., 2010. Polymer Melt Fracture. CRC Press, BocaRaton, FL.

Landau, L. D., Lifshitz, E.M., 1987. Fluid Mechanics. Pergamon Press, New York.Larrondo, L., Manley, R. S. J., 1981a. Electrostatic ber spinning from polymer melts.I. Experimental observations on ber formation and properties. J. Polym. Sci., Polym. Phys.Ed. 19, 909920.

1.6 References 23


Larrondo, L., Manley, R. S. J., 1981b. Electrostatic ber spinning from polymer melts. II.Examination of the ow eld in an electrically driven jet. J. Polym. Sci., Polym. Phys. Ed. 19,921932.

Larrondo, L., Manley, R. S. J., 1981c. Electrostatic ber spinning from polymer melts. III.Electrostatic deformation of a pendant drop of polymer melt. J. Polym. Sci., Polym. Phys. Ed.19, 933940.

Lewin, M. (Editor), 2007.Handbook of Fiber Chemistry. 3rd Edition. CRC Press, Boca Raton, FL.Loitsyanskii, L. G., 1966. Mechanics of Liquids and Gases. Pergamon Press, Oxford (the Englishtranslation of the 2nd Russian edition), and the 3rd Russian edition published by Nauka,Moscow, 1970.

Matovich, M.A., Pearson, J. R. A., 1969. Spinning a molten threadline. Steady-state viscous ows.Ind. and Eng. Chem. Fundam. 8, 512520.

Matsuki, M., Nishimura, S., Goto, M., 1974. Apparatus for producing non-woven eeces. USPatent No. 3802817.

Morris, P. J. T., 1989. The American Synthetic Rubber Research Program. Pennsylvania Press,Philadelphia, PA.

Online Etimology Dictionary, 2013. Available at http://www.etymonline.com/index.php?term=ber. Accessed July 27, 2013.

Pearson, J. R. A., 1985. Mechanics of Polymer Processing. Elsevier, London.Pearson, J. R. A., Matovich, M., 1969. Spinning a molten threadline. Stability. Ind. Eng. Chem.Fundam. 8, 605609.

Petrie, C. J. S., Denn, M.M., 1976. Instabilities in polymer processing. AIChE J. 22, 209236.Ramakrishna, S., Fujihara K., Teo, W. E., Lim, T. C., Ma, Z., 2005. An Introduction toElectrospinning and Nanobers. World Scientic, Singapore.

Reneker, D. H., Chun, I., 1996. Nanometer diameter bers of polymer, produced byelectrospinning. Nanotechnol. 7, 216223.

Reneker, D. H., Yarin, A. L., Fong, H., Koombhongse, S., 2000. Bending instability of electricallycharged liquid jets of polymer solutions in electospinning. J. Appl. Phys. 87, 45314547.

Tyushkevich, N. I., Krasko, A. S., Chepurkin, A.A., Shiman, O. P., Kozello, T. O., Ananich, N. A.,1970. Study of the unevenness of glas ber by statistical methods. Glass Ceram. 27, 9597.

Wang, S. Q., Drda, P. P., 1996. Superuid-like stick-slip transition in capillary ow of linearpolyethylene melts. I. General features. Macromol. 29, 26272631.

Weinberger, C.B., Cruz-Saenz, G. F., Donnelly, G. J., 1976. Onset of draw resonance during isothermalmelt spinning: a comparison between measurements and predictions. AIChE J. 22, 441448.

Wendorff, J. H., Agarwal, S., Greiner, A., 2012. Electrospinning. Wiley-VCH, Weinheim.Yarin, A. L., 1993. Free Liquid Jets and Films: Hydrodynamics and Rheology. Longman Scienticand Technical and John Wiley & Sons, Harlow, NY.

Yarin, A. L., Gospodinov, P., Gottlieb, O., Graham, M.D., 1999. Newtonian glass ber drawing:Chaotic variation of the cross-sectional radius. Phys. Fluids 11, 32013208.

Yarin, A. L., Gospodinov, P., Roussinov, V., 1994. Stability loss and sensitivity in hollow berdrawing. Phys. Fluids 6, 14541463.

Yarin, A. L., Graham, M.D., 1998. A model for slip at polymer/solid interfaces. J. Rheol. 42,14911504.

Zeleny, J., 1914. The electrical discharge from liquid points and a hydrostatic method of measuringthe electric intensity at their surfaces. Phys. Rev. 3, 6991.

Zeleny, J., 1917. Instability of electried liquid surfaces. Phys. Rev. 10, 16.Ziabicki, A. 1976. Fundamentals of Fibre Formation. John Wiley & Sons, London.

24 1 Introduction


2 Polymer physics and rheology

Several physical concepts that are of the utmost importance in ber-forming processesare described in this chapter. The basic physical model of a exible polymer macro-molecule as a random walk is outlined in Section 2.1. The elongational and shearrheometry of polymer solutions and melts, which elucidate the stress relation with strainsand strain rate, as well as stress relaxation is described in Section 2.2. The phenomeno-logical rheological constitutive equations appropriate for the description of viscoelasticpolymer solutions and melts are introduced in Section 2.3. The micromechanical foun-dations of the entropic elasticity responsible for viscoelasticity of polymer solutions andmelts are sketched out in Section 2.4. Solidication and crystallization are discussed inSections 2.5 and 2.6, respectively.

2.1 Polymer structure, macromolecular chains, Kuhn segment,persistence length

A linear polymer macromolecule can be represented as a succession of identical rigidsegments connected at arbitrary angles, i.e. freely jointed with each other (Flory 1969,de Gennes 1979, Doi and Edwards (1986). Such a macromolecule is comprised ofN segments, each of length b. The total length of a fully stretched macromolecule isthen L = Nb. The rigid segments are called Kuhn segments. A real macromolecular chainconsisting of n monomers is idealized as a random walk of N Kuhn segments, which arenot monomers, nor is N identical to the degree of polymerization n. If the number ofKuhn segments in a macromolecule is not large, i.e. N is close to 1, it is rather inexible,almost rod-like. On the other hand, if N >> 1, the macromolecule is very exible, and onlength scales that are signicant compared to b, but much smaller than L, it can be viewedas a exible string. Persistence length is another length scale that characterizes theresistance of segments of macromolecular chains to bending. It is of the same order ofmagnitude as the length of the Kuhn segments.

2.2 Elongational and shear rheometry

Rheological characterization of viscoelastic polymer solutions and melts used in ber-forming processes should include elongational and shear rheometry. In particular, not


only zero-shear viscosity and ow curves in simple shear ow should be measured tocharacterize rheological behavior of polymeric liquids, but also their elastic relaxationtime, since all such liquids are viscoelastic (see Section 2.3). Moreover, it is highlydesirable to measure the viscoelastic properties in the uniaxial elongational ows athigh strain rates, i.e. in the situations resembling those in ber-forming processes. Itshould be emphasized that rheological characterization of polymeric liquids in bothsimple shear and uniaxial elongational ows encompasses the most important types ofow kinematics, which are mixed in all other types of ows. In this context, elonga-tional rheometers based on uniaxial elongational ow resulting in self-thinning threads(discussed in Yarin 1993, Stelter et al. 1999, 2000, 2002, McKinley and Tripathi 2000,Wunderlich et al. 2000, Yarin et al. 2004, Reneker et al. 2007 and Tiwari et al. 2009)can be used to characterize spinnability (i.e. the ability to form bers) and to measurethe rheological parameters of polymer solutions, depending on the polymer type andconcentration. An elongational rheometer of this type consists of a stationary lowerplate and a moveable upper plate driven by a solenoid, a continuous light source and ahigh-speed video camera (see Figure 2.1). A droplet of the polymer solution of interestis placed in between the plates. Then the upper plate (spindle) is retracted upwardrapidly with the help of the solenoid, forming a cylindrical liquid thread. After the platemotion has ceased, the thread exhibits a uniaxial elongational ow driven by surfacetension that results in self-thinning of the thread. A high-speed digital camera (forexample, Redlake MotionPro) equipped with a 185-mm macro-lens records thethread self-thinning. An example of a thread-thinning video clip is shown inFigure 2.2. This variant of data acquisition is the most effective way to analyze self-thinning threads with sufcient accuracy.It should be emphasized that ow in the thread is directed from the center toward the

two end regions. This ow is driven by surface tension, since the capillary pressure in thethread is much higher than in the end regions. A detailed theory of such ow is given asan example in Section 2.3 (see Eqs. 2.312.39 there). The nal result, which is relevantfor measuring the elastic relaxation time reads

d d0 exp t3

2:1

Solenoid

Light source

High-speed CCD

Figure 2.1 Schematic of an elongational rheometer based on self-thinning threads of polymer solutions.Dotted lines below the solenoid show the initial uid conguration before the movement of the topplate. Tiwari et al. (2009), with kind permission of Springer Science-Business Media.

26 2 Polymer physics and rheology


where d = 2a is the cross-sectional diameter in the thread (a is the radius), with the initialvalue d0 at t = 0; t is time. Correspondingly, the elongational viscosity el, which is theratio of the normal axial stress to the rate of elongation, exponentially increases in time as

el 3d0

expt

3

2:2

where is the surface tension.An example of data acquired using an elongational rheometer with a self-thinning

thread is shown in Figure 2.3. Fitting Eq. (2.1) to the data, as shown in that gure, yieldsthe values of the elastic relaxation time . For polymer solutions relevant in formingnanobers using solution blowing and electrospinning (see Chapters 4 and 5, respec-tively), such an approach is demonstrated in Theron et al. (2004). The polymer solutionsthey studied are listed in Table 2.1, along with the rheological parameters measured.These include, zero shear viscosities and ow curves of these polymer solutions in

simple shear ow. For example, Figure 2.4 shows that poly(ethylene oxide), PEO, sol-utions revealed pronounced shear thinning. Relaxation times are in the range 1360 ms.Relaxation times of polycaprolactone, PCL, solutions could not be measured because ofthe high evaporation rates of the solvents, acetone and methylene chloride (MC). Note,also that surface tension measurements conducted with a pulsating bubble surfactometer

Figure 2.2 Self-thinning thread of 1000 ppm aqueous solution of polyacrylamide Praestol 2540. Severalsnapshots illustrate how the thread diameter decreases as time increases. Reprinted with permissionfrom Stelter et al. (2000). Copyright 2000, The Society of Rheology.

2.2 Elongational and shear rheometry 27


200

62.5125 ppm

250 ppm

500 ppm 1000 ppm

400 600 800t [ms]

1000 1200 1400 160000.01

0.1

1

d [

mm

]

Measured

Fitted

Figure 2.3 Diameter decrease of a liquid thread of an aqueous Praestol 2540 solution for the differentconcentrations listed in the graph. Reprinted with permission from Stelter et al. (2000).Copyright 2000, The Society of Rheology.

Table 2.1 Rheological properties of several polymer solutions: poly(ethylene oxide), PEO; poly(acrylic acid), PAA;poly(vinyl alcohol), PVA; polyurethane, PU; polycaprolactone, PCL. Solvents: tetrahydrofuran, THF; methylene chloride(dichloromethane, MC); dimethylformamide, DMF. Molecular weight is denoted Mw, polymer weight concentration,C, zero-shear viscosity, , and the elastic relaxation time, .

Polymer Mw [Da] Solvents C[%] [P] = [101 Pa.s] [ms]

PEO 6 105 Ethanol/water (40/60) 2 2.85 213 12 254 30 286 432 33

PEO 106 Ethanol/water (40/60) 2 15.9 1423 96 183

PEO 4 106 Ethanol/water (40/60) 1 42.5 2172 900 2983 3350 359

PEO 106 Water 2 5.7 4 106 1 26 128

PAA 2.5 105 Ethanol/water (40/60) 6 4.55 48.14.5 105 5 2.55 22.75

PVA 104 Ethanol/water (50/50) 6 3.55 29.6PU Tecoex THF/ethanol (50/50) 6 0.25

8 82 1.77PCL 8 104 Acetone 8 107

10 165 14 400

PCL 8 104 MC/DMF (75/25) 10 670 MC/DMF (40/60) 10 950



showed that surface tension is mainly a function of the solvent in the solutions and tends tobe less sensitive to variation in the polymer concentration. Therefore, the values of surfacetension can be taken as those of the solvents.Xu et al. (2003) designed an elongational rheometer, shown in Figure 2.5. The

rheometer was able to generate extensional ows mechanically and was applied topolymer solutions used in electrospinning. In their experiments, approximately 0.2 mlof polymer solution was placed in a reservoir located on the bottom plate of therheometer. A cylindrical tip mounted on a horizontal arm was dipped in the polymersolution initially. The arm could move vertically at a constant speed for a certain distance.

00

0.5

2%

3%

4%

4%3%C = 2%

1.0

1.5

Vis

cosi

ty [

Pa.

s]

2.0

2.5

3.0

3.5

500Shear rate [1/s]

1000 1500

Figure 2.4 Flow curves: shear viscosity versus shear rate. Plots for solutions of PEO (Mw = 6 105 Da)

in ethanol/water (40/60) at different weight concentrations. Reprinted from Theron et al. (2004),with permission from Elsevier.

High-speedcamera

Polymer fluidcolumn

Light sensor Stretchingarm

Linearsourceof light

Polymerdrop

Figure 2.5 Sketch of the elongational rheometer used by Xu et al. (2003) and Reneker et al. (2007). Reprintedfrom Reneker et al. (2007), with permission from Elsevier.



The motion stopped after a distance, chosen by the experimenter, where the horizontalarm ran in between the infrared emitter and the sensor pair and blocked the infraredemission. The tip picked up a portion of the polymer solution and moved 21 mm upwardat a constant speed of 350 mm s1. A polymer-solution thread was created betweenthe bottom plate and the tip. Self-thinning due to gravity of the thread then started. Thethreads were much longer than those in the rheometer sketched in Figure 2.1, thereforegravity rather than surface tension determined the self-thinning. A high-speed cameramonitored the decreasing diameter of this self-thinning thread. Two linear halogen lightswere adjusted to provide proper illumination to the lament and a dark background. Theliquid thread was outlined by the specular reection of two linear lights from its lateralsurface. The contour of the thread was seen as two bright lines on a dark background.Figure 2.6 shows the reections of the two linear light sources from the lateral surface ofthe liquid thread. The initial thread diameter d0 was recorded when the probe tip reachedits highest position at time t = 0. Polymer-solution threads with diameters as small as80 m could be accurately measured. The rheometer was mounted on a vibration-damped imaging bench. A special thread holder was designed to minimize its vibrationduring the self-thinning process.In the rheometer of Xu et al. (2003) shown in Figure 2.5, polymer threads thinned

mostly due to gravity, which resulted in the following expressions (Reneker et al. 2007):

d d0 exp t2

2:3

with the corresponding elongational viscosity being

el g0expt

2:4

where is the solution density, 0 the initial lament length, and g gravity acceleration.Figure 2.7 shows the entire thread during the stretching and self-thinning stages.

The cylindrical shape of the thread reects that a uniform elongational ow was

t = 0 ms t = 280 ms

600 micron 600 micron

Figure 2.6 Reections of two linear light sources from the lateral surface of the polymer solution thread.Reprinted from Reneker et al. (2007), with permission from Elsevier.



produced. At the middle part of the thread a pure extensional deformation was sustained.The diameter decrease was monitored at this position. The large strain was produced bythe long residence time of the thread during the thinning process. The time evolution of thethread diameter was studied for several aqueous solutions of PEO of different concen-trations. The results shown in Figure 2.8 reveal that the rate of thread thinning during theself-thinning process was higher for solutions with lower polymer concentrations.The relaxation time found by tting Eq. (2.3) to the experimental data is shown in

Figure 2.9. It can be seen that the relaxation time window suitable for electrospinningnanobers of PEO solutions is in the range 20 ms to 80 ms, which agrees with the data forPEO in Table 2.1 obtained using another rheometer. The logarithm of the relaxation timedecreases linearly with polymer concentration. The corresponding elongational viscos-ities of the aqueous solutions of PEO found using Eq. (2.4) are shown in Figure 2.10.They exponentially increase in time during the self-thinning stage. The gure also showsthat a low-concentration solution has a lower initial elongational viscosity. However, insuch solutions the viscosity increases at a much faster rate than in the high-concentrationsolutions. As a result, the low-concentration PEO solutions can reveal a higher elonga-tional viscosity than the high-concentration solutions at the latter stages of thinning. Notethat the threads were birefringent, which points to a high order of alignment of polymermacromolecules along the self-thinning threads (Xu et al. 2003).Han et al. (2008) introduced two additional approaches to elongational rheometry.

They worked with polymer solution jets stretched by electric forces, as in electrospinningused to form polymer nanobers (see Chapter 5). A digital video camera attached to an

Entire jet, during stretching

Entire jet, self thinning

Figure 2.7 The entire thread (jet) during stretching and self-thinning stages. Reprinted fromReneker et al. (2007), with permission from Elsevier.



optical microscope was used to record the prole of the transition zone between thepolymer droplet at the exit of a capillary with an

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