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 Osmometry (MN )

Intrinsic viscosity GPC / SEC

Light scattering ( MW ) Ultracentrifugation ( M Z ) 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 Osmotic pressure change End-group analysis

information on solution 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

Membrane osmometry Osmotic pressure π=hρg µoA (T,P) = µA (T, P+π, xA)

Ideal solutions

π

RT = c M

Van’t Hoff Equation

Non-ideal solutions

π c

= R T[

1 Mn

+ A2 c + A3 c 2 + ... ] Virial equation

Practical range of MW's : 30,000

membrane permeability

-

1,000,000

smallest π

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

Instrumentation - Static - Dynamic

Osmotic Pressure • In ideal solutions expressed as

  cm RT Molar concentration

m  RT MV Mass concentration

c  RT M 37

Molecular Weight Determination Membrane Osmometry:

Dh = 0

Semipermeable membrane membrane. Allows passage of solvent molecules

38

Molecular Weight Determination  RT  1  2  RT   A2c  A3c  ..... c  0 c M M  Non ideal solution

Mass concentration

Dh > 0

  Dh×g×

Membrane Osmometry:

39

Molecular Weight Determination Membrane Osmometry – Numerical Application: Plot of /c against c at 310 K in toluene for poly(vinyl acetate). What is Mn?

 RT  1  2  RT   A2c  A3c  ..... c  0 c M M 

40

Molecular Weight Determination Membrane Osmometry – Numerical Application:

 RT  1   RT   A2c  A3c 2  ..... c   0 c M M 

 RT 1 c   16 . 2 J . kg  0 c M

M = 8.31 (J.mol1.K1)  310 (K) / 16.2 (J.kg1) = 159 kg.mol1

41

Molecular Weight Determination Membrane Osmometry:

 RT  1  2  RT   A2c  A3c  ..... c  0 c M M 

slope = RT  A2

42

Molecular Weight Determination Membrane Osmometry:

poly(methyl methacrylate)

 RT  1   RT   A2c  A3c 2  ..... c   0 c M M 

toluene

acetone

acetonitrile slope = RT  A2 = 0?

theta-solvent. 43

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 2 1  vˆB A2     AB  2  VM

In a poor solvent, the polymer wants to minimize polymer-solvent contact, the coil is compact and the bonds are strained. A2 < 0 44

Ideal polymer solution • What does it mean? – In a qsolvent, 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 qsolvent 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. 2 ˆ 1 v   B A2     AB  2  VM

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

I θ 2 = Rθ r Io R90 Rayleigh ratio

Molecular Weight Determination (scattered light) Light Scattering Iq/ 8 4 2  4 2  (1  cos 2 q ) I0  r

q r = distance to detector

/

2

Iq r Rq  I o (1  cos 2 q ) Light scattering from a single centre:

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

51

Molecular Weight Determination (scattered light)

Light scattering: Multiple Centres q

/

Iq r Rq  2 I o (1  cos q )  dn  2 n   dc   K N A4 2

8  2 N  Rq  4    V  4

Rq is called the Rayleigh (scattering) ratio.

2

2

2 o

“System/sample constant” 52

Variables • Io light intensity at source. • I/ light intensity measured at detector. Instrument factors  q angle of detector from incident direction • r distance from scattering cell to detector   wavelength. • NA avagadro’s number • no refractive index Sample factors   excess polarizability • dn/dc refractive index increment.

Molecular Weight Determination Light Scattering • Bottom line for M analysis After rearrangement of terms for 

Rq  KcM Applies in situation with no interference (external or internal). So Rq can be equated with M OK For gas phase scattering

c = mass concentration M = molar mass

Molecular Weight Determination Light Scattering For polymers “Zimm equation” in solution

Kc 1   2 A2c Rq M

– 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 55

Example • The excess Rayleigh ratio Rq 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)

Rq x 105(cm-1)

0.5034

0.239

1.0068

0.440

1.5102

0.606

2.0136

0.790

2.517

0.902

Kc 1   2 A2c Rq M

56

Molecular Weight Determination Light Scattering

q

Light scattering - Internal Interferences: For higher angles there is a big difference between the two path lengths  destructive interferences 57

Molecular Weight Determination Light Scattering q

q

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

Kc 1   2 A2c Rq M w P(q ) 58

Molecular Weight Determination Light Scattering Light scattering - Interferences: Scattering Intensity

Small molecules polymers

Note P(0  1

59

Molecular Weight Determination Light Scattering

Variation of Pq with molecular weight and angle for PS

Disymmetry Factor for Different Types of Polymer Molecules

X axis R/

61

Molecular Weight Determination 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.L1 = 1 wt%).

1 16 2 2 1 sin ( q / 2 )  R G 2 P(q ) 3 2

62

Molecular Weight Determination Light Scattering Light scattering – Radius of Gyration: RG Mi

ri

G: Center of mass of the polymer coil

2 G

R

G

point Mi along the chain at ri distance from G

1 2  ri  n i 63

Molecular Weight Determination Light Scattering Light scattering – Non ideal solutions:

K c Rq

 1  1 2     2 A2c  3 A3c  ..... P(q )  M w 

• The ratio Kc/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

 Zimm Plot! 64

Molecular Weight Determination

 1  K c 1 2     2 A2c  3 A3c  ..... Rq P(q )  M w 

Light scattering – Zimm plot:

q1

q2

q3

q4

q5

K c Rq

q6 q7 C (#6) C (#5) C (#4) C (#3) C (#2)

C (#1)

sin2(q/2) + bc 65

Molecular Weight Determination

 1  K c 1 2     2 A2c  3 A3c  ..... Rq P(q )  M w 

Light scattering – Zimm plot:

q1

q2

q3

q4

q5

K c Rq

q6 q7 C (#6) C (#5) C (#4)

C (#3) C (#2) C (#1)

sin2(q/2) + bC 66

Molecular Weight Determination

K c

Light scattering – Zimm plot:

Rq q1

q2

 1  1 2     2 A2c  3 A3c  ..... P(q )  M w  q3

q4

q5 q6 q7

K c

C (#6)

Rq

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

1/Mw slope = 162RG2/(Mw 32

 1 K  c  16 2 2 2   1  sin ( q / 2 ) R  .... G 2 Rq 3   Mw sin2(q/2) + bc 67

Molecular Weight Determination Light scattering – Zimm plot:

K c Rq

q  0,

q1 q2 q3

 1  1 2     2 A2c  3 A3c  ..... P(q )  M w  q4 q5

q6

K c Rq

q7 C (#6) C (#5) C (#4) C (#3)

Slope = 2A2

C (#2) C (#1) C0

1/Mw sin2(q/2) + bc 68

Molecular Weight Determination

Light scattering – Zimm plot: Zimm plot of poly(vinyl acetate) in butanone at 25 oC

What is Mw?

69

Molecular Weight Determination Light scattering – Numerical Application: What is Mw?

Mw1 = 0.8  106 mol.g1  Mw = 1.25  106 g.mol1

slope = 162RG2/(Mw 32

70

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

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

Molecular Weight Determination Viscometry: 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.

capillary

Viscometer

V hydrodynamic volume 3

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 http://www.pslc.ws/welcome/tour/macrog/vis .htm 4

Viscosity Relationships Newton

dv F  A dx

Einstein. viscosity increase for spheres in liquid Poiseuille. Viscosity of a liquid in a tube related to flow time

Not really considered for polymer solution

  o (1  2.5 )



r Pt 4

8Ql

o  solvent viscosity   volume fraction of dissolved species

r =radius l = length t = time P =pressure drop Q = volume exiting in t 5

Effect of Polymer Concentration

individual polymer coils

overlap concentration

entanglements

Simple relationships only apply to low concentrations 6

Molecular Weight Determination

Viscometry:

  o (1  2.5 )   (1  2.5 ) 0     1  2.5  0 

hydrodynamic volume

Volume fraction of solute

N AcVh P  M c = mass concentration

77

Intrinsic Viscosity How do we relate viscosity to MW ?

1    0  2.5 N AVh     c lim 0  c  0  M “Intrinsic Viscosity” http://www.ias.ac.in/initiat/sci_ed/resources /chemistry/Viscosity.pdf Link now on Learn

Note

4 Vcoil    RG3 3 8

Molecular Weight Determination Viscometry - Definitions: Real Viscosity is expressed in Pa.s Relative viscosity

Specific viscosity

Reduced viscosity

Intrinsic viscosity

 r  o   o  sp  o

 sp 1   o  c c o

 sp

1   o [ ]  lim  lim c o c c o c o

Note: units for IV are reciprocal concentration

9

Molecular Weight Measurement

Radius Depends on M and solvent

F Varies depending on the solvent

2.1 x 1023

Chanda

Intrinsic Viscosity and Molecular Weight 4 Vh    Rh3  k  M P3 3

3 = Flory exponent = 1.5 in theta solvent = 1.8 in good solvent

   KM

a

Mark-Houwink-Sakurada equation. Generally 0.5 < a < 0.8. Good solvent For q solvent a = 0.5 11

Intrinsic Viscosity and Molecular Weight Distribution

   K M

a v

Viscosity average molecular weight

12

Viscosity Average Molecular Weight • Definition of the viscosity-average molecular weight: 1 a

  N i M ia 1    M v   N M  i i  

 w M  i

1 a a i

13

Molecular Weight Determination Experimental Viscometry Timing mark A

Step #1: Step #2:

mark B

Step #3:

Flow Capillary

Polymer solution is placed in tube A. Tube D is blocked and the polymer solution is sucked into bulb C above the mark A. 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.

CLASSIC METHOD. Nowadays automated available

Hagen-Poiseuille equation: η = K  t 14

Molecular Weight Determination Experimental Viscometry:

mark A mark B

Concentration Time (g.L1 (s)

c0 = 0

to

c1

t1

c2

t2

c3

t3

c4

t4

(solvent)

1  o 1 Kt  Kto 1 t  to   c o c Kto c to 15

Molecular Weight Determination Experimental Viscometry:

1  o 1 Kt  Kto 1 t  to   c o c Kto c to

mark A mark B

1   o c o

c, g.dL1 16

Molecular Weight Determination Experimental Viscometry:

1   o c o

c, g.L1

a 1   o [ ]  lim KM v c 0 c  o

Huggins equation: Accounts for deviations from linearity at higher c

1   o  [ ]  k H [ ]2 c c o 17

Modern Method Use pressure drop differences



r 4 Pt 8Ql

http://www.malvern.com/LabEng/technolog y/dilute_solution_viscosity_theory/dilute_so lution_viscosity_theory.htm

Viscometry Notes • A given polymer sample has only 1 M N or M W – May have more than one M v – Because “a” varies with solvent

• The broader the MWD the more M v 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

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 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 20

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. [] (cm3/g)

260

278

142

138

12.2

4.05

Mw X 10-4

178

157

56.2

48.0

1.55

0.308

21

Measuring Polymer Molecular Weight Gel Permeation Chromatography

What about distributions???

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

Molecular weight • SEC: schematic diagram

24

Gel Permeation Chromatography •

http://www.malvern.com/LabEng/technology/gel_permeation_chromatography_t heory/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

Gel Permeation Chromatography • Nature of packing – Porous solids

• Figure from Allcock and Lampe

26

Gel Permeation Chromatography • 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

What are these?

27

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

High MW

Low MW

MW related to the time (volume) required to reach the detector 28

Gel Permeation Chromatography Remember smaller molecules take more time to pass through columns

Higher retention volumes (RV) Columns specific to particular MW ranges

29

Gel Permeation Chromatography • Columnmaterials – Depend on mobile phase – Relates to polymer solubility

Polymer Laboratories Column manufacturer

Gel Permeation Chromatography Conventional Calibration

http://www.malvern.com/LabEng/technology/gel_permeation_chromatography _theory/conventional_calibration_gpc_theory.htm

31

Gel Permeation Chromatography • 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

Gel Permeation Chromatography Mi comes from calibration with Elution Volume

hi

Software breaks chosen area for integration into slices based on fixed time intervals Note: known concentration of sample not necessary for analysis.

34

Gel Permeation Chromatography • 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.

35

Gel Permeation Chromatography • 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. 36

Intrinsic Viscosity

1    0  2.5 N AV     c lim 0  c  0  M How we relate intrinsic viscosity to MW.

Universal Calibration

[ ]M  2.5N AV 37

Gel Permeation Chromatography • 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

 M  [ ]i   log M i  log i  [ ]i 

Found from measurement or MHS

Found from calibration curve 38

39

Gel Permeation Chromatography • Universal (conventional) calibration conversion to MW data. • Two polymers ( x and y) – with known MHS constants. – Calculation of Mx from calibration based on My.

K y (a y  1) 1 log M x  log  log M y (ax  1) K x (ax  1)

Gives calibration line for second polymer based on first 40

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

41

Gel Permeation Chromatography 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 42

Polyethylene Triple Detection Data  Light

scattering clearly shows this is a complex material LALLS

RALLS Viscometer

RI

From Agilent Technologies

Molecular Weight Determination Light Scattering

Important for 7o LALLS Pq  1

Variation of Pq with molecular weight and angle for PS 44

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.

Kc 1   2 A2c Rq M For GPC ci is low

Rq M Kc http://www.malvern.com/LabEng/technology/gel_permeation_c hromatography_theory/triple_detection_gpc_theory.htm

45

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

Gel Permeation Chromatography • 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

Rq P(q )  Rq '

• Wyatt, Brookhaven – – – – –

MALLS RI (viscometer). “Absolute method” Use extrapolation to q = 0 for each slice

47

Gel Permeation Chromatography • 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. 48

Gel Permeation Chromatography • 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 49

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

Effect of Branching on Molecular Properties • •

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

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

Estimation of Branching • 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.

• Mean square radius s Rg  s

• Branching factor (g) •

ri 2   i 1 N N

Ratio of mean squared radius values for branched and linear polymers with equivalent MW’s.

2

2 0.5

g

S

2 b

S

2 l

Contraction factor 53

Estimation of Branching • Branching numbers • Star shaped – f is functionality of branch points

• Randomly branched (monodisperse). – Trifunctional – mb = number average number of branch points per molecule – tetrafunctional

3 5 g  2 f f  mb   g 3  1  7    mb   g 4  1  6  

0.5

0.5

4mb    9   4mb    3  

0.5

0.5

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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

Branching Affects Solution Viscosity

56

Estimation of Branching • GPC/Viscometry – Curvature in log MW vs Log IV curves. – Gives a viscosity branching factor g /

[ ]Br g  [ ]Lin /

57

Estimation of Branching • Calculation of g /

[ ]Br g  [ ]Lin /

g/  gx Branching factor

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

 b  g / (, M ) KM a “slice” molecular weight

mb  M 58

Finding mb Find g

g g /

x

 mb   g 3  1   7  

0.5

 4mb   9  

0.5

From g values use parameter estimation to find mb

59

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

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.

62

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. 

   Shear stress

Shear rate 64

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: 

 ( ) 

 



65

Polymer Rheology Zero shear viscosity

Newtonian

66

Zero Shear Viscosity and MW

Rudin and Chee Macromolecules (1973), 6, 613-624

Bottom Line Polymer melt behaviour relates to M.

67

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.

68

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

MV  k (M n )

c

69

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  MI   ( M ) W mass of polymer per unit time http://www.exxonmobilchemical.com/Public_Products/Polyethylene/Polyet hylene/NorthAmerica/Grades_and_Datasheets/HDPEXOM_IDESDataSheet.asp

70

Zero Shear Viscosity and branching

71

Estimation of Branching • Rheological properties – Melt behaviour

• Branching has two conflicting effects – Drops molecular sizes.

Zero shear viscosity

0 Br  g 0l a

• Lower MW Fewer entanglements. • Related to a critical chain length. • a = 1.

– Longer polymer chains • a = 3.4. 72

Summary: Molecular Weight Determination Methods

73