Analysis of molecular weight of polymers

Asst.Prof.Dr. Jatuphorn Wootthikanokkhan

Division of Materials Technology, School of Energy and Materials, King Mongkut’s University of Technology Thonburi,

Thailand

Polymer contains molecules with a variety of chain length

• Diversity in terms of molecular weight is an inherent

characteristic of the natural polymers

• For synthetic polymers, this is attributed to many factors

including uncontrollable terminations

Disproportionation

Combination

น ำ้หนักโมเลกลุพอลเิมอร์ จะสัมพนัธ์โดยตรงกบัควำมหนืด Effect of molecular weight on Newtonian viscosity

M.P. Stevens, Polymer Chemistry, 1991

จุดวกิฤต (Mc) เก่ียวขอ้งกบัการเก่ียวพนักนั

(entanglement) ของโมเลกลุพอลิเมอร์

Once molecular weight of polymer exceed a critical value (Mc), entanglement

between chains occur

Effects of Molecular Weight

• Higher Mw increases tensile strength

– Tension force cause polymers to align and reduce the number of

entanglements. If the polymer has many entanglements, the force

would be greater.

• Higher Mw increases toughness

– Toughness is increased with longer polymer chains because energy is transmitted down chain

• Higher Mw increases melting temperature – Melting point is a measure of the amount of energy necessary to

have molecules slide freely past one anotherใ

– If the polymer has many entanglements, the energy required would be greater.

กำรวดัค่ำดชันีกำรไหล Melt Flow Indexer

• ใชน้ ้าหนกั กดอดัพอลิเมอร์ ณ อุณหภมิูตามท่ีก าหนด

• Melt flow index (MFI) = น ้าหนกัตวัอยา่งท่ีไหลออก ในเวลา 10 นาที

• หน่วย เป็น (กรัม/10 นาที)

14/08/55 Dr. Jatuphorn Wootthikanokkhan, KMUTT

สภำวะในกำรทดสอบ MFI ตำมมำตรฐำน ASTM Test conditions for some plastics (ASTM D 1238)

Condition Temperature ( C) Total load (g) Materials A 125 325 PE B 125 2,160 PE D 190 325 Nylon. PE E 190 2,160 Nylon, PE F 190 21,600 Nylon, PE G 200 5,000 PS L 230 2,160 PP

14/08/55 Dr. Jatuphorn Wootthikanokkhan, KMUTT

Factors affecting result from MFI test

• Preheat time (Cylinder should be preheated to ensure uniform temperature)

• Moisture (Moisture in the plastic deviate the MFI

• Packing (Plastic should be pack properly be pushing the rod to expel the entrapped

air)

• Volume of the sample (keep constant for a good reporducibility)

• Type of Melt Indexer ( L/D of cylinder and Die, Die shape)

• Type of sample (No cross-comparison between different plastics)

ขอ้จ ากดัของเทคนิค MFI

• ค่าท่ีได ้สมัพนัธ์กบัความหนืดและน ้าหนกัโมเลกลุ แต่ไม่ใช่ค่าเฉล่ียน ้าหนกัโมเลกลุท่ีแทจ้ริง

• ค่าท่ีได ้บ่งบอกถึงความยากง่าย ในกระบวนการผลิตข้ึนรูป • ควรใชเ้ปรียบเทียบพอลิเมอร์ ชนิดเดียวกนัเท่านั้น

Mn MFI (g/10min)

100,000 10.0

150,000 0.30

250,000 0.05

Results from MFI test of polystyrene at 200 ºC

ความสามารถในการผลติ Ethylene Octene Copolymer 2 เกรด ทีม่คีา่ MFI ตา่งกนั

Effect of MFI and die temperature on polymer process-ability

145 C 125-135 C

115 C Low MFI polymer cannot be extruded,

regardless of the processing temperature Higher MFI polymer can be

extruded at a suitable temperature

Un-melted polymer Degradation at the die zone

Calculations of Average Molecular Weight of Polymer

Polydispersity index = Mw/Mn

(L.H. Sperling, Introduction to physical polymer science, 1992, John Wiley & Sons, NY)

Some k- and a- constants ทีม่า J. Brandrup and E.H. Immergut, Eds., Polymer Handbook, 2 nd ed., Wiley-Interscience, NY, 1975

kaพอลิเมอร ์ ตวัท ำละลำย อณุหภมิู ( C) k x 103 a

ซสิ พอลบิวิตะไดอนี เบนซนี 30 33.7 0.715

ไอโซแทคตคิ พอลพิรอพลินี คลอโรแนพธาลนี 139 21.5 0.67

พอลเิอธลิอะครเิลต อะซโิตน 25 51 0.59

พอลเิมธลิเมธาครเิลต อะซโิตน 20 5.5 0.73

พอลไิวนิลอะซเิทต เบนซนี 30 22 0.65

พอลสิไตรนี บวิธาโนน 25 39 0.58

พอลไิสตรนี ไซโคลเฮกเซน (-solvent) 34.5 84.6 0.50

พอลเิตตระไฮโดรฟิวแรน โทลอูนี 28 25.1 0.78

เฮกเซน (-solvent) 31.8 206 0.49

Effects of polydispersity

• Broader MWD decreases tensile strength – Broad MWD represents polymer with many shorter

molecules which are not as entangled and slide easily.

• Broader MWD decreases impact strength – Shorter chain do not transmitted as much energy

during impact

• Broader MWD decreases melting point – Broad MWD represents polymer with many shorter

molecules which are not as entangled and melt sooner

– Broader MWD yield an easier processed polymer

Methods of determining polymer molecular weight

Method Type Molar mass range (g/mol)

Average value

Membrane osmometry A 104 – 105 Mn

End group analysis E < 104 Mn

Light scattering A 103 - 107 Mw

Viscometry R 102 -107 Mv

Size exclusion

chromatography (SEC) or GPC

R 102 -107 Mn, Mv, Mw, PDI

Molecular weight analysis techniques

• A = Absolute method (polymer Mw is directly calculated from the experimental data, without additional information on the chemical structure of the polymer.

• E = Equivalent method (chemical structure of polymer

must be known for a calculation of polymer Mw).

• R = Reference method (data must be calibrated with samples of known Mw)

Light scattering (LS) technique

• The basis of the LS is the measurement of intensity of scattered light, I() at various angle

• From the I(o) and I(), Rayleigh ratio [R()] at various angle can be calculated using the following equation;

R() = I() r2 / I(o) V

where

V = scattering volume

r = distance between detector and sample cell

I()

I(o)

D

Light scattering (LS) technique

• Rayleigh ratio is related to molecular weight of polymer through the below equation;

kc/R() = 1/(Mw) P() + 2A2C

where

k = an optical constant (related to RI of solvent, of incident light, and concentration).

P() = particle scattering function or form factor (which is equal to 1 at very low angle (), ~ 0 – 2°)

R() = R() solution - R() solvent

A2 = second varial coefficient, describing polymer - solvent interactions.

Light scattering (LS) technique

• Low angle lasers light scattering (LALLS) use He-Ne lasers

as a light source.

• This high intensity of the lasers permits scattering to be

measured at a much smaller angle than conventional LS

• Usually < 7 º (Jeng et al., J.Appli Polym Sci., 49(1993)1359)

• The equation can be re-written as

kc/R() = 1/(Mw) + 2A2C

Multiple Angle Laser Light Scattering (MALLS) technique

By measuring the I() at

various polymer solution

concentration (c),

a Zimm plot can be obtained.

From the Zimm plot, by performing “double extrapolation” ( = 0) and

c = 0, Y-intercept of the Zimm plot is equal to 1/ Mw

kc/R() = 1/(Mw) P() + 2A2C

Size Exclusion Chromatography (SEC)

(Gel Permeation Chromatography, [GPC] )

GPC apparatus

1. Injection port

2. Column(s)

3. Detector

4. Collector flask

5. Chart recorder

6. Solvent reservoir 7. Pump with pressure gauge

GPC solvent and injection system

• THF is normally used for the non-aqueous phase GPC. Sometime non UV grade THF is used if the UV detector was used

• Polymer sample prepared in a solution (0.1 -0.2 % g/ml)

• The sample must be filtered before injection

• Typical injection volume ~ 0.1 L

• Flow rate ~ 1 ml/min

Detectors

• UV visible spectrometer (measure the absorption of eluted polymer solution), A = elc – Suitable grade of solvent must be used

• Differential refractometer (detect differences in RI between pure solvent and polymer solution)

GPC columns

• Column packing material is

basically small porous beads.

Generally made from crosslinked

PS

• Pore diameter ranged between 10 – 107 ºA

Column packing materials

ผูผ้ลิต ช่ือกำรค้ำวสัดท่ีุเป็น packing

วสัดท่ีุใช้

Polymer Laboratories PL gel Styrene-divinylbenzene copolymer

Waters Styragel Styrene-divinylbenzene copolymer

Shodex Asahipak GF HQ Highly crosslinked poly(vinyl alcohol) *

Protein KW Silica *

Chitopak KQ Chitosan *

(Ref: H. Pasch and B. Trathnigg in HPCL of Polymers, Springer1999)

GPC experiment and GPC chromatogram (From L.H. Sperling in Introduction to Physical Polymer Science, John Wiley & Sons, 1992),

Resolution is affected by

the column characteristics and the flow rate

www.viscotek.com/images/Theory/separate.jpg

Typical GPC chromatogram (plot of retention volume vs signal strength [conc])

Reco

rded

sig

nal str

en

gth

Retention volume (ml)

Basic steps in obtaining MWD curve from a chromatogram

(Ref: H. Pasch and B. Trathnigg in HPCL of Polymers, Springer1999)

(1)

(2) (3)

(4)

(Calibration curve)

Narrow molecular weight calibration curve

(H. Pasch and B. Trathnigg, HPLC of Polymers, Springer, Berlin, 1999)

Polymer standards for establish a calibration curve

Polymers Suppliers Number of standards

Lowest Mw

Highest Mw

Polystyrene Polymer Laboratories 29 162 15,000,000

Polymer standard service 18 500 4,000,000

Water Corp. 20 400 20,000,000

PMMA Polymer Laboratories 20 500 1,500,000

Polymer standard service > 70 102 1,200,000

Water Corp. 10 1,000 15,000,000

Polyisoprene Polymer Laboratories 11 1,000 3,000,000

Water Corp. 10 1,000 3,000,000

Polybutadiene Polymer Laboratories 11 1,000 1,000,000

Polymer standard service 4 5,000 80,000

Polyethylene Polymer Laboratories 10 170 120,000

(ท่ีมำ H. Pasch and B. Trathnigg, HPLC of Polymers, Springer, Berlin, 1999)

Note: there are many more, see the reference

Universal calibration

[]M hydrodynamic volume, regardless of the polymer type

Universal calibration

Universal calibration curve

Membrane Osmometer

(from M.P. Stevens in Polymer Chemistry, John Wiley & Sons, 1990, NY)

Osmotic pressure is related to molecular weight by the van’t Hoff equation

Plot of /c versus c for PMMA dissolved in three different solvents

; (a) toluene, (b) acetone and (c) acetonitrile

พอลิเมอร ์ ตวัท ำละลำย อณุหภมิู (องศำเซลเซียส)

(ซสิ) พอลบิวิตะไดอนี n-haptane (-1)

พอลเิอธลินี Biphenyl 125

พอลบิวิธลิอะครเิลต Benzene/methanol (52/48) 25

พอลสิไตรนี Cyclohexane 34

Toluene

Acetone

Acetonitrile

solvent ของพอลเิมอรช์นิดต่างๆ

The osmotic pressure data for cellulose tricaproate in DMF at three temperatures. The Flory -temperature was determined to be 41 ±1 °C

(from L.H. Sperling, Introduction to physical polymer science, 1992, John Wiley & Sons)

Schematic representation of a molecular coil. r = end-to-end distance, s = radius of gyration

Unpurturbed dimension (mean-square average)

Expansion factor

will be greater than 1 in a good solvent.

The lowest temperature at which = 1 is called the theta () temperature

and the solvent is then called a theta solvent.

The theta state is that in which the polymer is on the brink of becoming insoluble. The solvent is having a minimal solvation effect.

Viscometers

Some useful equations

Some useful equations

Poiseville’s equations

Some k- and a- constants ทีม่า J. Brandrup and E.H. Immergut, Eds., Polymer Handbook, 2 nd ed., Wiley-Interscience, NY, 1975

kaพอลิเมอร ์ ตวัท ำละลำย อณุหภมิู ( C) k x 103 a

ซสิ พอลบิวิตะไดอนี เบนซนี 30 33.7 0.715

ไอโซแทคตคิ พอลพิรอพลินี คลอโรแนพธาลนี 139 21.5 0.67

พอลเิอธลิอะครเิลต อะซโิตน 25 51 0.59

พอลเิมธลิเมธาครเิลต อะซโิตน 20 5.5 0.73

พอลไิวนิลอะซเิทต เบนซนี 30 22 0.65

พอลสิไตรนี บวิธาโนน 25 39 0.58

พอลไิสตรนี ไซโคลเฮกเซน (-solvent) 34.5 84.6 0.50

พอลเิตตระไฮโดรฟิวแรน โทลอูนี 28 25.1 0.78

เฮกเซน (-solvent) 31.8 206 0.49

Determination of k- and a- constants (from Introduction to physical polymer science, L.H. Sperling, 1992)

End-group analysis

Exercise 1. What is the DP of a sample of

polyester prepared from 4-hydroxy benzoic acid if the acid number determined with standard KOH solution is 11.2 ?

Note: Acid number = mg of base used to neutralize 1 g of the polymer

2. A 0.5 g sample of unsaturated polyester resin was reacted with excess acetic anhydride. Titration of the reaction mixture with 0.0102 M KOH required 8.17 ml to reach the end point. What is the number average molecular weight of the polyester? Would this method be suitable for determining any polyester?

• Determination of the amount of functional groups at the chain ends by using some techniques such as – Titration

– UV spectroscopy – Elemental analysis

แบบฝึกหดั

(260,000, 420,000)

Mw of each fractions Mole

50,000 1

100,000 4

200,000 5

500,000 3

700,000 1

Determine Mn, Mw and PDI using data from the table above