che541_molecular weight measurements
DESCRIPTION
Polymer sciTRANSCRIPT
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
Molecular Weight Determination
Membrane Osmometry:
Dh > 0
M
RTcAcA
MRT
c c
0
2
32 .....1
Dh×g×
Non ideal
solution Mass
concentration
40
Molecular Weight Determination
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
Molecular Weight Determination
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
43
Molecular Weight Determination
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
Molecular Weight Determination
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/
q
oI
rIR
r = distance to detector
52
Molecular Weight Determination
Light scattering: Multiple Centres
q
(scattered light)
V
NR 2
4
48
q
)cos1( 2
2/
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
Molecular Weight Determination
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).
Molecular Weight Determination
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
Molecular Weight Determination
Light Scattering
57
Light scattering - Internal Interferences:
For higher angles there is a big difference between the two path lengths destructive interferences
q
Molecular Weight Determination
Light Scattering
58
q
q
Large angles: destructive interferences Small angles: less affected by destructive interferences
cAPMR
Kc
w
22)(
1
59
Molecular Weight Determination Light Scattering
Light scattering - Interferences:
Small molecules
polymers Scattering Intensity
Note P(0 1
Molecular Weight Determination
Light Scattering
Variation of Pq with molecular weight and angle for PS
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.L1 = 1 wt%).
62
22
2
2
)2/(sin3
161
)(
1GR
P q
q
63
Molecular Weight Determination Light Scattering
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
Molecular Weight Determination
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
Molecular Weight Determination
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
Molecular Weight Determination
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
67
Molecular Weight Determination
Light scattering – Zimm plot:
.....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
Molecular Weight Determination
Light scattering – Zimm plot:
.....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
Molecular Weight Determination
Light scattering – Zimm plot:
Zimm plot of poly(vinyl acetate) in butanone at 25 oC
What is Mw?
70
Molecular Weight Determination
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
Molecular Weight Determination
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
Molecular Weight Determination
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
9 9
Molecular Weight Determination
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
Molecular Weight Determination Experimental Viscometry:
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
Molecular Weight Determination Experimental Viscometry:
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
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
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
25
Gel Permeation Chromatography
• 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
26
Gel Permeation Chromatography
• Nature of packing
– Porous solids
• Figure from Allcock and Lampe
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
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
Gel Permeation Chromatography
Remember smaller molecules
take more time to pass through
columns
Higher retention volumes (RV)
Columns specific to particular
MW ranges
Gel Permeation Chromatography
• 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
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
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
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.
36
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.
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
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
38
i
iii
MM
][
][loglog
Found from calibration curve Found from measurement
or MHS
40
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.
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
42
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
Polyethylene Triple Detection Data
Light scattering
clearly shows this is
a complex material
From Agilent Technologies
RI
Viscometer
RALLS
LALLS
Molecular Weight Determination Light Scattering
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
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
• Wyatt, Brookhaven – MALLS – RI – (viscometer). – “Absolute method” – Use extrapolation to q = 0 for each
slice
')(
q
qqR
RP
48
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.
49
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
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
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.
• 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
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
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
57
Estimation of Branching
• GPC/Viscometry
– Curvature in log MW vs Log IV curves.
– Gives a viscosity branching factor g/
Lin
Brg][
][/
58
Estimation of Branching
• 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 ),(/
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:
65
)(
Zero Shear Viscosity and MW
67
Rudin and Chee Macromolecules
(1973), 6, 613-624
Bottom Line
Polymer melt
behaviour relates
to M.
68
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.
69
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 )(
70
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
72
Estimation of Branching
• 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