ChE541_Molecular Weight Measurements

Direct Measurements Of Average Molecular Weights

Mn and Mw can be measured directly without knowing the full MWD; not Mz

Primary versus Secondary methods

Membrane Intrinsic Osmometry viscosity ( NM ) GPC / SEC Light scattering ( WM )

Ultracentrifugation ( ZM ) for biological polymers

Polymer Characterization • SIZE

Length, radius, characteristic dimension MW and MWD

• SHAPE

Coil, sphere, rod • CONFORMATION

Extended, compacted, cross-linked • CONSTITUTION

Functional groups, branches, distribution of blocks in copolymers

MW Characterization Techniques MN methods

Boiling point elevation Freezing point depression Vapour pressure change information on

Osmotic pressure change solution End-group analysis thermodynamics

MW methods

Light scattering Sedimentation, centrifugation

MV methods

Viscometry MWD methods

Chromatographic techniques Size exclusion chromatography (SEC) Gel permeation chromatography (GPC)

PRACTICAL ASPECTS OF MW MEASUREMENTS MN METHODS A) End-group analysis

MW is determined by chemical analysis of reactive functionalities in polymer e.g. polyester, titration of alkali

Major drawbacks: precision of the analysis;

restricted to MW ≤ 10,000 g/mol; assumptions about structure

Condensation polymers

B) Colligative methods

Rely on colligative solution properties; depend on the number of dissolved solute molecules and not on their sizes

Depend on the lowering of the chemical potential

of a solvent by introduction of a solute

Solution thermodynamics

Property measured Technique

Vapour pressure reduction VPO Lowering of freezing point Cryoscopy Elevation of boiling point Ebulliometry Osmotic pressure Membrane

osmometry

MT R =

cπ

] ... + c A + c A + M1 [ T R =

c2

32n

π

Membrane osmometry Osmotic pressure π = h ρ g µo

A (T,P) = µA (T, P+π, xA) Ideal solutions Van’t Hoff Equation Non-ideal solutions Virial equation

Practical range of MW's :

30,000 - 1,000,000

membrane smallest π permeability

Membranes “open” versus “fine” membranes cellophane / PTFE γ-rays

Instrumentation - Static - Dynamic

Osmotic Pressure

• In ideal solutions

expressed as

RTcm

37

Molar concentration

RTMV

m

Mass concentration

RTM

c

38

Molecular Weight Determination

Membrane Osmometry:

Dh = 0

Semipermeable membrane membrane. Allows passage of solvent molecules

39


Membrane Osmometry:

Dh > 0

M

RTcAcA

MRT

c c

0

2

32 .....1

Dh×g×

Non ideal

solution Mass

concentration

40


Membrane Osmometry – Numerical Application:

Plot of /c against c at 310 K in toluene for poly(vinyl acetate). What is Mn?

M

RTcAcA

MRT

c c

0

2

32 .....1

41


Membrane Osmometry – Numerical Application:

M

RTcAcA

MRT

c c

0

2

32 .....1

M

RTkgJ

c c

1

0.2.16

M = 8.31 (J.mol1.K1) 310 (K) / 16.2 (J.kg1) = 159 kg.mol1

42


Membrane Osmometry:

slope = RT A2

M

RTcAcA

MRT

c c

0

2

32 .....1

43


Membrane Osmometry:

slope = RT A2 = 0?

M

RTcAcA

MRT

c c

0

2

32 .....1

theta-solvent.

poly(methyl methacrylate)

toluene

acetone

acetonitrile

44

What does an ideal polymer

solution mean?

In a good solvent, the polymer want to maximize polymer-solvent contacts, the coil

is expanded and the bonds are strained. A2 > 0

In a poor solvent, the polymer wants to minimize polymer-solvent contact, the coil

is compact and the bonds are strained. A2 < 0

M

BAB

V

vA

2

2

ˆ

2

1

Ideal polymer solution

• What does it mean?

– In a qsolvent, the forces that try to collapse or expand the polymer coil cancel each other.

– Consequently, the polymer adopts its ideal conformation, that of a random coil.

– A polymer solution in a qsolvent is said to be ideal.

– Ideality is reflected by a zero second virial coefficient,

– i.e. A2 = 0.

45

Virial Coeffients

• Give an idea of the non-ideality of the

polymer/solvent system.

• Most important is A2.

• A2 can be related to polymer solubility

characteristics in particular solvents.

M

BAB

V

vA

2

2

ˆ

2

1

MW methods

Light scattering Rayleigh scattering / Debye (1944) Mathematically very complex

R90 Rayleigh ratio

r II = R 2

o

θθ


Light Scattering

51

Light scattering from a single centre:

q )cos1(8 22

24

4

0

/

q

q rI

I

(scattered light)

http://math.ucr.edu/home/baez/physics/General/BlueSk

y/blue_sky.html

)cos1( 2

2/

qq

q

oI

rIR

r = distance to detector

http://math.ucr.edu/home/baez/physics/General/BlueSky/blue_sky.html

http://math.ucr.edu/home/baez/physics/General/BlueSky/blue_sky.html

52


Light scattering: Multiple Centres

q

(scattered light)

V

NR 2

4

48

q

)cos1( 2

2/

qq

q

oI

rIR

Rq is called the Rayleigh (scattering) ratio.

4

2

222

A

o

N

dc

dnn

K

“System/sample constant”

Variables

• Io light intensity at source.

• I/ light intensity measured at detector.

q angle of detector from incident direction

• r distance from scattering cell to detector

wavelength.

• NA avagadro’s number

• no refractive index

excess polarizability

• dn/dc refractive index increment.

Instrument factors

Sample factors

KcMR q


Light Scattering

• Bottom line for M analysis c = mass concentration

M = molar mass

So Rq can be equated with M

OK For gas phase scattering

After rearrangement of

terms for

Applies in situation with no interference (external or internal).


Light Scattering

– Only true for relatively small molecules

– Applies in situation with no__internal interference____________

• polymers having a polymer coil size < /20 (~25 nm for = 500 nm).

• Low angle light scattering

• At bigger angles if the polymer coil size is > /20, then one must deal with internal interferences and non-ideal solutions

cAMR

Kc22

1

q

55

For polymers “Zimm equation” in solution

Example

• The excess Rayleigh ratio Rq of cellulose acetate in dioxane was measured as a function of concentration by Low Angle Light Scattering measurements. Data are given in the Table. If the RI of dioxane is 1.4199, refractive index increment for CA in dioxane is 6.297 x 10-2 cm3/g and the wavelength of light was 6328 A, calculate the MW and second virial coefficient

C x 103 (g cm-3) Rq x 105(cm-1)

0.5034 0.239

1.0068 0.440

1.5102 0.606

2.0136 0.790

2.517 0.902

56

cAMR

Kc22

1

q


Light Scattering

57

Light scattering - Internal Interferences:

For higher angles there is a big difference between the two path lengths destructive interferences

q


Light Scattering

58

q

q

Large angles: destructive interferences Small angles: less affected by destructive interferences

cAPMR

Kc

w

22)(

1

qq

59

Molecular Weight Determination Light Scattering

Light scattering - Interferences:

Small molecules

polymers Scattering Intensity

Note P(0 1


Light Scattering

Variation of Pq with molecular weight and angle for PS

Disymmetry Factor for Different Types

of Polymer Molecules

61

X axis

R/


Light Scattering

• P(q) is the form factor which depends on the size and shape of the molecule

• The form factor of polymer coils was derived by Debye in 1947.

– It handles the intra-particle interferences needs to work with low polymer concentration (c < 10 g.L1 = 1 wt%).

62

22

2

2

)2/(sin3

161

)(

1GR

P q

q

63


Light scattering – Radius of Gyration: RG

G

Mi

point Mi along the chain at ri distance from G

G: Center of mass of the polymer coil

ri

i

iG rn

R22 1


Light Scattering

• The ratio Kc/Rq depends on polymer concentration (c) and the angle of observation (q).

• In practice, one prepares a set of solutions at different polymer concentrations.

• The light scattered by each polymer solution is monitored at different observation angles

.....32

1

)(

1 2

32 cAcAMPR

cK

wqq

64

Light scattering – Non ideal solutions:

Zimm Plot!

65


Light scattering – Zimm plot:

.....32

1

)(

1 2

32 cAcAMPR

cK

wqq

sin2(q/2) + bc

qR

cK C (#6) C (#5) C (#4) C (#3) C (#2) C (#1)

q1 q2 q3 q4 q5 q6 q7

66



.....32

1

)(

1 2

32 cAcAMPR

cK

wqq

sin2(q/2) + bC

qR

cK C (#6) C (#5) C (#4) C (#3) C (#2) C (#1)

q1 q2 q3 q4 q5 q6 q7

67



.....32

1

)(

1 2

32 cAcAMPR

cK

wqq

sin2(q/2) + bc

qR

cK

q1 q2 q3 q4 q5 q6 q7

C (#6) C (#5) C (#4) C (#3) C (#2) C (#1) C 0

w

GM

RR

cK 1....)2/(sin

3

161 22

2

2

q

q

slope = 162RG2/(Mw 32

1/Mw

68



.....32

1

)(

1 2

32 cAcAMPR

cK

wqq

sin2(q/2) + bc

qR

cK

q 0, q1 q2 q3 q4 q5 q6 q7

C (#6) C (#5) C (#4) C (#3) C (#2) C (#1) C 0

Slope = 2A2

1/Mw

69



Zimm plot of poly(vinyl acetate) in butanone at 25 oC

What is Mw?

70


Light scattering – Numerical Application: What is Mw?

Mw1 = 0.8 106 mol.g1 Mw = 1.25 106 g.mol1

slope = 162RG2/(Mw 32

Multi Angle LS

Zimm Plot • Very useful for determining multiple pieces of

info – Mw

– Rg

– A2

• BUT. – Very laborious !!!

– Very sensitive to dust etc.

– Time consuming.

• Used for fundamental studies rather than as a quality control or routine research tool.

MV methods

Viscosity of dilute polymer solutions higher than that of pure solvent

A polymer solution has a higher viscosity than the solvent, because:

Solvent trapped in-between the coils can not attain the velocities which the liquid would have

- polymer coil has the same effect on the

viscosity of the mixture as a sphere

Viscosity increase depends on T, nature of solvent and polymer, C, and the sizes of polymer molecules

- Mv depends to some extent on the solvent

used

2

Dilute Solution Viscosity

• Viscosity is the quantity that describes a fluid's resistance to flow.

• Viscosity of polymer solutions depends on – Concentration

– Solvent

– Temperature

– Molecular weight

• Can be used to determine molecular weights

– Viscosity Average MW

2

3 3


Viscometry:

capillary

V hydrodynamic volume

The concept of the equivalent hydrodynamic sphere:

Solvent molecules located inside the polymer coil move almost in

unison, like polymer beads, as though the solvent molecules were

bound to the polymer.

Viscometer

4

Molecular Weight Measurement Viscometry

• Secondary method

• A polymer solution has a higher viscosity than pure solvent.

– Solvent trapped in coils cannot attain velocities of free solvent

4

http://www.pslc.ws/welcome/tour/macrog/vis.htm



5

Viscosity Relationships

5

Adx

dvF

Newton

Ql

Ptr

8

4

Einstein. viscosity increase for spheres in liquid

)5.21( o

o solvent viscosity volume fraction of dissolved species

Poiseuille. Viscosity of a liquid in a tube related to flow time

r =radius l = length t = time P =pressure drop Q = volume exiting in t

Not really considered for polymer

solution

6 6

individual polymer coils

overlap concentration entanglements

Effect of Polymer Concentration

Simple relationships only apply to low concentrations

7 7


Viscometry:

hydrodynamic volume

M

cVN hAP )5.21(

0

)5.21( o

Volume fraction of solute

5.21

0

c = mass

concentration

8

Intrinsic Viscosity

8

M

VN

c

hAc

5.21lim

0

0

0

How do we relate viscosity to MW ?

http://www.ias.ac.in/initiat/sci_ed/resources

/chemistry/Viscosity.pdf Link now on Learn

“Intrinsic Viscosity”

3

3

4Gcoil RV

Note

http://www.ias.ac.in/initiat/sci_ed/resources/chemistry/Viscosity.pdf

http://www.ias.ac.in/initiat/sci_ed/resources/chemistry/Viscosity.pdf

9 9


Viscometry - Definitions:

Real Viscosity is expressed in Pa.s Relative viscosity Specific viscosity Reduced viscosity Intrinsic viscosity

o

r

o

osp

o

osp

cc

1

o

o

oc

sp

oc cc

1limlim][

Note: units for IV are reciprocal concentration

Molecular Weight Measurement

F Varies depending on the solvent

2.1 x 1023 Chanda

Radius

Depends on M

and solvent

11

Intrinsic Viscosity and Molecular Weight

11

aKM

Mark-Houwink-Sakurada equation. Generally 0.5 < a < 0.8.

For q solvent a = 0.5

Good solvent

33

3

4Phh MkRV 3 = Flory exponent = 1.5 in theta solvent

= 1.8 in good solvent

12

Intrinsic Viscosity and Molecular Weight Distribution

12

a

vMK

Viscosity average molecular weight

13

Viscosity Average Molecular Weight

• Definition of the

viscosity-average

molecular weight:

aa

ii

a

ii

a

iiv Mw

MN

MNM

1

11

13

14 14

Molecular Weight Determination Experimental Viscometry

Step #1: Polymer solution is placed in tube A.

Step #2: Tube D is blocked and the polymer

solution is sucked into bulb C above the

mark A.

Step #3: Tube D is unblocked. The solution starts

to flow and the time it takes the solution

to flow between mark A and mark B is

measured.

Timing mark A

mark B

Hagen-Poiseuille equation: η = K t

CLASSIC METHOD. Nowadays automated available

Flow

Capillary

15 15

Molecular Weight Determination Experimental Viscometry:

mark A

mark B

Concentration

(g.L1

Time

(s)

c0 = 0 to

c1 t1

c2 t2

c3 t3

c4 t4

o

o

o

o

o

o

t

tt

cKt

KtKt

cc

111

(solvent)

16 16


mark A

mark B

o

o

o

o

o

o

t

tt

cKt

KtKt

cc

111

o

o

c

1

c, g.dL1

17 17


a

v

o

o

cMK

c

1lim][

0

o

o

c

1

c, g.L1

ckc

H

o

o 2][][1

Huggins equation: Accounts for deviations from linearity at higher c

Modern Method

http://www.malvern.com/LabEng/technolog

y/dilute_solution_viscosity_theory/dilute_so

lution_viscosity_theory.htm

Use pressure drop

differences

Ql

Ptr

8

4

http://www.malvern.com/LabEng/technology/dilute_solution_viscosity_theory/dilute_solution_viscosity_theory.htm



19

Viscometry Notes

• A given polymer sample has only 1 or – May have more than one – Because “a” varies with solvent

• The broader the MWD the more may vary with solvent.

• What happens with branched polymers and copolymers? – Copolymer composition and microstructure has an effect

on polymer-solvent interactions – Branching gives a more compact structure for a given MW.

• For a given MW, viscosity will be lower for branched compared to linear (see later for GPC).

19

NM WM

vM

vM

20

Example

• The data shown were obtained for polystyrene dissolved in cyclohexane, when viscosity measurements were made at the q temperature of 308K.

• Solvent flow time = 100 s

20

c (g cm-3) t (s)

0.001 109.5

0.002 120

0.003 135

0.004 144

Determine the average MW if K = 8.6 x 10-2 Ans 1.1M

21

Example

• The following data were obtained for the intrinsic viscosity of polystyrene fractions in C2H4 Cl2 at 22oC using LS as the measurement of MW. Evaluate the MHS constants.

21

[] (cm3/g)

260 278 142 138 12.2 4.05

Mw X 10-4

178 157 56.2 48.0 1.55 0.308

Measuring Polymer Molecular Weight Gel Permeation Chromatography

What about distributions???

23

Gel Permeation Chromatography

• Previous methods give molecular weight averages.

• Gel Permeation Chromatography (GPC).

– Gives molecular weight distributions

• Based on separation of polymer sizes by differential flow through a stationary bed of particles.

– “ SIZE EXCLUSION CHROMATOGRAPHY” (SEC)

23

24 24

Molecular weight

• SEC: schematic diagram

25


• http://www.malvern.com/LabEng/technology/gel_permeation_chromatography_theory/separations_theory.htm

– Small molecules held up more than large.

– Large molecules elute through to detectors more quickly.

– Detector responses are acquired with respect to time measured from injection of sample.

25

http://www.malvern.com/LabEng/technology/gel_permeation_chromatography_theory/separations_theory.htm

http://www.malvern.com/LabEng/technology/gel_permeation_chromatography_theory/separations_theory.htm

26


• Nature of packing

– Porous solids

• Figure from Allcock and Lampe


• Detectors

• Traditional concentration detectors

– Refractive Index

– UV

• Modern

– LS

– Viscometry

– IR (rare)

• How do we get MW information?

– Conventional calibration

– Universal calibration

– Multi detector calibration

27 27

What are these?

28

GPC Trace Conventional calibration is based on the use of one detector (concentration).

MW related to the time (volume) required to reach the detector

High MW Low MW

29


Remember smaller molecules

take more time to pass through

columns

Higher retention volumes (RV)

Columns specific to particular

MW ranges


• Column-materials

– Depend on mobile phase

– Relates to polymer solubility

Polymer

Laboratories

Column

manufacturer

31

Gel Permeation Chromatography Conventional Calibration

http://www.malvern.com/LabEng/technology/gel_permeation_chromatography

_theory/conventional_calibration_gpc_theory.htm

http://www.malvern.com/LabEng/technology/gel_permeation_chromatography_theory/conventional_calibration_gpc_theory.htm

http://www.malvern.com/LabEng/technology/gel_permeation_chromatography_theory/conventional_calibration_gpc_theory.htm


• Conventional

– Run multiple standards

– Prepare calibration curve

• For sample of unknown distribution

• M for each slice is based on RV and relationship with calibration line.

• Concentration of polymer for each slice is proportional to area (height) of slice.

32


Software breaks chosen area for

integration into slices based on fixed

time intervals

hi

Mi comes from

calibration with

Elution Volume

Note: known concentration of sample not

necessary for analysis.

35


• Conventional

– Run multiple standards

– Prepare calibration curve

• For sample of unknown distribution • M for each slice is based on RV and relationship with

calibration line.

• Concentration of each slice is proportional to area (height) of slice.

36


• Problems with conventional calibration

– Polymer standards are not available for every type of polymer.

– Separation is based on polymer hydrodynamic volumes (size when dissolved) not on molar masses.

– Hydrodynamic volumes are a function of polymer’s chemical structure and the degree of interaction there is between polymer and solvent

– Conventional gives MW values w.r.t. polymer standard used.

37

Intrinsic Viscosity

37

M

VN

c

Ac

5.21lim

0

0

0

How we relate intrinsic viscosity to MW.

Universal Calibration VNM A5.2][

38


• Universal calibration

– Use intrinsic viscosity along with RV to get molecular weight values.

• If system has IV detector then MW obtained by using UC and measured IV values

• Otherwise calculations necessary

38

i

iii

MM

][

][loglog

Found from calibration curve Found from measurement

or MHS

40


• Universal (conventional) calibration conversion to MW data.

• Two polymers ( x and y)

– with known MHS constants.

– Calculation of Mx from calibration based on My.

y

x

y

x

y

x

x Ma

a

K

K

aM log

)1(

)1(log

)1(

1log

Gives calibration line for second polymer based on first

41

GPC In line viscometer

• Alternative to traditional glass viscometers

– 4 capillary tubes

– Differential pressure transducers measure pressure drop across the bridge

– Pressure drop related to IV

http://www.malvern.com/LabEng/technolog

y/gel_permeation_chromatography_theory/

viscometer_detector_theory.htm

http://www.malvern.com/LabEng/technology/gel_permeation_chromatography_theory/viscometer_detector_theory.htm



42


Multi Detector Systems • GPC system same as for

conventional and UC except for the detectors.

• Commercial systems have various options.

• Viscotek (Malvern) – LALLS (7o angle) – 90o = RALLS – Viscometer – RI – “Triple detection” methods

for MW determination

Polyethylene Triple Detection Data

Light scattering

clearly shows this is

a complex material

From Agilent Technologies

RI

Viscometer

RALLS

LALLS


Variation of Pq with molecular weight and angle for PS

44

Important for 7o LALLS Pq 1

GPC Triple Detection

• Calibration • Single standard

– Accurately known concentration

– Known dn/dc – Known M – Known IV

• Zimm equation assumed for ideal case

• Detector constants are found.

45

cAMR

Kc22

1

q

Kc

RM q

http://www.malvern.com/LabEng/technology/gel_permeation_chromatography_theory/triple_detection_gpc_theory.htm

For GPC ci is low



GPC Triple Detection

• Unknown sample

• Conc (c) of slice from RI response.

• M for slice from LS response using Zimm expression and detector constants

46

47


• Other systems • Use responses from multiple (or

dual) angle detection to estimate disymmetry factors.

• Use Zimm equation for Mw. • Can also use viscosity information

to estimate Rh

• Polymer Laboratories – RALLS – 45o

– Viscometer – RI

• Wyatt, Brookhaven – MALLS – RI – (viscometer). – “Absolute method” – Use extrapolation to q = 0 for each

slice

')(

q

qqR

RP

48


• Each system has advantages/disadvantages. • Conventional

– Simple equipment (cheapest). – Lengthy and careful calibration needed with multiple

standards. – Not so bad now. Companies sell multiple standard vials.

– Calibration is only true for polymers of same type as polymers for calibration.

• Universal – Simple equipment – Can be applied to different polymer types. – Multiple standard calibration needed.

49


• Multi detector

– Benefit

• one standard calibration (for detectors).

– not so time consuming as Conventional and Universal.

• Direct measurement of molecular weights.

• Can give branching information.

– Disadvantage

• one standard calibration for detectors

– If there is a problem with the standard that will carry over to all samples.

• Low M species give low LS response at low concentrations

Branching Structures • Polymers may have a wide variety

of branching structures depending on

how they have been made or

modified

• Dendrimers are special cases of

polymer that combined the structures

of star and hyperbranched polymers

• The branching can further be

characterised by the length of the

branch into long chain or short chain

branching

• Long chain branching affects the

size and density of polymer

molecules and is easier to measure

by GPC

Slide from

Agilent

• The effect of branching is to reduce the size and increase the density

of a polymer molecule at any given molecular weight in solution

• If we can measure the density or size of a branched molecule and

compare it to a linear molecule of similar chemistry, we might be able to

get information on the nature of the branching

Effect of Branching on Molecular Properties

Estimation of Branching

• Long chain branching has a significant effect on polymer properties. – E.g Polymer rheology (melt behavior), crystallinity.

• Long chain branching difficult to detect by spectroscopic methods if the concentration of branch points is low.

• How to assess branching levels? – Light scattering

– GPC/SEC

52

53


• Parameters for branched polymers measured relative to equivalent properties for linear.

• See “Branching Level Detection in Polymers”

Scorah M., R. Dhib and A. Penlidis. Encyclopedia of Chemical Processing. Taylor and Francis . 251.

• Branching factor (g) • Ratio of mean squared radius values for

branched and linear polymers with equivalent MW’s.

• Mean square radius

N

i

i

N

rs

1

22

l

b

S

S

g2

2

5.02sRg

Contraction factor

54


• Branching numbers

• Star shaped – f is functionality of

branch points

• Randomly branched (monodisperse). – Trifunctional

– mb = number average number of branch points per molecule

– tetrafunctional

2

53

ffg

5.05.0

39

4

71

bb mm

g

5.05.0

43

4

61

bb mm

g

Mark-Houwink Plots of Hyperbranched Polyesters

• Clear trend in Mark-Houwink plots

• Increased branching/decreased molecular size leads to a decrease in IV

Slide from Agilent

56

Branching Affects Solution Viscosity

57


• GPC/Viscometry

– Curvature in log MW vs Log IV curves.

– Gives a viscosity branching factor g/

Lin

Brg][

][/

58


• Calculation of g/

Lin

Brg][

][/

xgg /

Branching factor

x is a structure factor which depends on the nature of branching 0.5 < x < 1.8

M

mb

“slice” molecular weight

a

b KMMg ),(/

Finding mb

59

5.05.0

39

4

71

bb mm

g

From g values use parameter estimation to find mb

xgg /

Find g

Mark-Houwink Plot

Downward curvature of the

plot at high molecular weight

indicative of branching

Branching Number and g Plot

• Branching number Bn and

branching frequency calculated

• Values are dependent on the

choice of branching model

62

Case Study (Painter and Coleman)

• Long Chain Branching in poly(chloroprene).

• Polychloroprene

– Difunctional monomer gives possibility of branching from vinyl sites on main chain.

– Branching favoured as monomer concentration drops.

– Can assess branching with conversion using SEC/viscosity method.

Polymer Rheology

• The science that deals with the way materials deform when forces are applied to them – The term is derived from the Greek words

– “ ρέω ” = to flow, and

– “ λόγoς ” = study

• Most commonly applied to the study of liquids and liquid-like materials – paint, blood, polymer solutions and molten plastics,

– materials that flow,

63

Polymer Rheology • Newtonian Fluids

– The simplest type of rheological behaviour for a material that can flow.

– For simple shear this type of behaviour is described by a linear relationship between the shear stress and the shear rate:

– Viscosity is simply the proportionality factor for shear stress with respect to shear rate.

64

Shear

stress

Shear

rate

Polymer Rheology

• For polymeric liquids (non Newtonian Fluids)

– the relationship between stress and strain rate is no longer linear

– cannot be described in terms of a single constant.

– Relate steady simple shear experiment in terms of a viscosity function defined as follows:

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)(

Polymer Rheology

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Zero shear viscosity

Newtonian

Zero Shear Viscosity and MW

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Rudin and Chee Macromolecules

(1973), 6, 613-624

Bottom Line

Polymer melt

behaviour relates

to M.

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Molecular Weight Related Measurements

• Industry – Rubber Mooney

Viscosity – Most important empirical test

in the rubber industry.

– Measures torque for a rotor embedded in softened rubber at specific T.

– Results for Mooney • 50ML 1+4 (100oC) • “50M” Mooney number • L = large rotor • 1 time (mins) for specimen to warm

up • Time of test (minutes) • 100oC temperature of test.

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Mooney Viscosity

• Empirical test

• Mooney number may be related to MW

– Eg for nitrile rubber – http://techcenter.lanxess.com/trp/americas/en/pr

oducts/types/index.jsp?pid=444

cnMkMV )(

http://techcenter.lanxess.com/trp/americas/en/products/types/index.jsp?pid=444

http://techcenter.lanxess.com/trp/americas/en/products/types/index.jsp?pid=444

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Molecular Weight Related Measurements

• Melt Flow index (MFI)

– Data from a capillary rheometer

– Ease of flow of a thermoplastic through capillary

– Fixed temperature and applied pressure (load)

– Measure throughput as mass of polymer per unit time http://www.exxonmobilchemical.com/Public_Products/Polyethylene/Polyet

hylene/NorthAmerica/Grades_and_Datasheets/HDPE-XOM_IDESDataSheet.asp

)( WMMI

http://www.exxonmobilchemical.com/Public_Products/Polyethylene/Polyethylene/NorthAmerica/Grades_and_Datasheets/HDPE-XOM_IDESDataSheet.asp




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Zero Shear Viscosity and branching

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• Rheological properties – Melt behaviour

• Branching has two conflicting effects – Drops molecular sizes.

• Lower MW Fewer entanglements.

• Related to a critical chain length.

• a = 1.

– Longer polymer chains • a = 3.4.

l

a

Br g 00

Zero shear viscosity

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Summary: Molecular Weight Determination Methods

ChE541_Molecular Weight Measurements

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