Determination of molecular weight of polymers by ostwald viscometry

1. Determination of molecular weight
of polymers by viscometry
Presented by:
Udhay Kiron
13305017

2. Contents
• Introduction
• Determination of molecular weight
• Polymer solutions
• Viscometry
• References

3. Introduction
• In simple compounds there is some
definiteness about the molecular weight,
hence we can say the simple compounds
have fixed molecular weight.
• Example Hydrogen: 2
Ethylene: 28
• Since a polymer sample is a mixture of
molecules of same chemical type with
different molecular weight it is expressed in
terms of an average value.

4. Number Average and Weight Average Molecular
Weight
The molecular weight of polymers
a. Some natural polymer (monodisperse) :
All polymer molecules have same molecular weights.
b. Synthetic polymers (polydisperse) :
The molecular weights of polymers are distributed
c. Mechanical properties are influenced by molecular weight
much lower molecular weight ; poor mechanical property
much higher molecular weight ; too tough to process
optimum molecular weight ; 105 -106 for vinyl polymer, 15,000
- 20,000 for polar functional group containing
polymer (polyamide)

5. Determination of molecular weight
a. Absolute method :
mass spectrometry
colligative property
end group analysis
light scattering
ultracentrifugation.
b. Relative method : solution viscosity
c. Fractionation method : GPC

6. Definition of average molecular weight
a. number average molecular weight ( Mn )
Mn=
 i i
Ni
(colligative property and end group analysis)
b. weight average molecular weight ( Mw)
Mw=
WiMi
(light scattering)
N M
Wi

7. Definition of average molecular weight
c. z average molecular weight ( MZ )
M Z=
NiMi
(ultracentrifugation)
2
d. general equation of average molecular weight :
M =
( a=0 , Mn a=1 , Mw a=2 , Mz )
e. Mz > Mw > Mn
NiMi
3
NiMi
a+1
NiMi
a

8. Polydispersity index : width of distribution
polydispersity index (PI) = Mw / Mn ≥ 1

9. Example of molecular weight calculation
a. 9 moles, molecular weight ( Mw) = 30,000
5 moles, molecular weight ( Mw) = 50,000
Mn=
(9 mol x 30,000 g/mol) + (5 mol x 50,000 g/mol)
9 mol + 5 mol
= 37,000 g/mol
Mw =
9 mol(30,000 g/mol)2 + 5 mol(50,000 g/mol)2
9 mol(30,000 g/mol) + 5 mol(50,000 g/mol)
= 40,000 g/mol

10. Example of molecular weight calculation
b. 9 grams, molecular weight ( Mw ) = 30,000
5 grams, molecular weight ( Mw ) = 50,000
9 g + 5 g
Mn = 35,000 g/mol =
(9 g/30,000 g/mol) + (5 g/50,000 g/mol)
Mw =
(9 g/30,000 g/mol) + (5 g/50,000 g/mol)
9 g + 5 g
= 37,000 g/mol

11. Polymer Solutions
A. Process of polymer dissolution : two step
First step : The solvent diffuses into polymer masses to make
a swollen polymer gel
Second step : Swollen polymer gel breaks up to solution

12. Polymer Solutions
B. Thermodynamics of solubility :
Gibb's free energy relationship
G =H - TS
ΔG < 0 : spontaneously dissolve T and ΔS are always positive for
dissolving process.
Conditions to be negative ΔG,
ΔH must be negative or smaller than TΔS.

13. C. Hydrodynamic volume of polymer molecules in solution
depend on the following:
a. polymer-polymer interaction
b. solvent-solvent interaction
c. polymer-solvent interaction
d. polymer structure ( branched or not )
e. brownian motion
r = end-to-end distance
s = radius of gyration
Figure : Coil molecular shape
r 2 = ro
22
s2= so
22
 = (r2)1/2
(ro
2)1/2
The greater the value of α, the ‘better’
the solvent
α = 1, 'ideal' statistical coil.

14. Polymer Solutions
D. theta(θ) temperature and theta(θ) solvent
The lowest temperature at which α=1 : theta(θ) temperature blink
The solvent satisfied this condition : theta(θ) solvent point
E. Flory-Fox equation :
The relationship among hydrodynamic volumes,
intrinsic viscosity and molecular weight
[η] : intrinsic viscosity
M : average molecular weight
 : Flory constant (3×1024/mol)
r : end-to-end distance
[η] =
(r2)3/2
M

15. Polymer Solutions
F. Mark-Howink-Sakurada equation
: The relationship between intrinsic viscosity and molecular weight
[η] : intrinsic viscosity
K , a : constant for specific polymer and solvent
M : average molecular weight
[η] = KMa
G. Important properties of polymer solution : solution viscosity
a. paint spraying and brushing
b. fiber spinning

16. SOLUTION VISCOSITY AND
MOLECULAR SIZE
• The usefulness of solution viscosity as a
measure of polymer molecular weight has
been recognized ever since the early work of
Staudinger (1930).
• Solution viscosity is basically a measure of the
size or extension in space of polymer
molecules. It is empirically related to
molecular weight for linear polymers

17. • Viscosity is an internal property of a fluid that
offers resistance to flow.
• It is due to the internal friction of molecules
and mainly depends on the nature &
temperature of the liquid.
• Many methods are available for measuring
viscosity of polymer solution.
• Example Ostwald viscometry

18. Ostwald viscometry
• The Ostwald method is a simple method for the
measurement of viscosity, in which viscosity of
liquid is measured by comparing the viscosity of an
unknown liquid with that of liquid whose viscosity is
known. In this method viscosity of liquid is
measured by comparing the flow times of two
liquids of equal volumes using same viscometer.
• The molecular weight of the polymer is measured by
using viscometer and the molecular weight obtained
by this technique is called viscosity average
molecular weight.
• The molecular weight of the polymer solution is
very high so the viscosity of polymer solution is very
high compared to that of pure solvent.

19. • Consider two liquids are passing through a
capillary of same viscometer. Then the
coefficient of viscosity of liquid (η2) is given by
equation

20. Viscometry
IUPAC suggested the terminology of solution viscosities as following.
Relative viscosity :
 : solution viscosity
o: solvent viscosity
t : flow time of solution
t o: flow time of solvent
Specific viscosity :
Reduced viscosity :
Inherent viscosity :
Intrinsic viscosity :

rel = o
=
t
to
 - o =
t - to =
sp = rel - 1
o
to
rel =
sp = c
c
rel - 1
In rel
inh = c
[] = (
sp )c=o=(ηinh)C = 0
c

21. Mark-Houwink-Sakurada equation
[η] = KMa
log[η] = logK + alogMv
(K, a : viscosity-Molecular weight constant, )
Mw > Mv > Mn
Mv is closer to Mw than Mn

22. TABLE . Representative Viscosity-Molecular Weight Constants
Polymer
Polystyrene
(atactic)
Polyethylene
(low pressure)
Poly(vinyl chloride)
Polybutadiene
98% cis-1,4, 2% 1,2
97% trans-1,4, 3% 1,2
Polyacrylonitrile
Poly(methyl methacrylate-co-styrene)
30-70 mol%
71-29 mol%
Poly(ethylene terephthalate)
Nylon 66
Solvent
Cyclohexane
Cyclihexane
Benzene
Decalin
Benzyl alcohol
Cyclohexanone
Toluene
Toluene
DMFg
DMF
1-
Chlorobutane
1-
Chlorobutane
M-Cresol
M-Cresol
Temperature,
oC
35
50
25
135
155.4
20
30
30
25
25
30
30
25
25
Molecular Weight
Range  10-4
8-42
4-137
3-61
3-100
4-35
7-13
5-50
5-16
5-27
3-100
5-55
4.18-81
0.04-1.2
1.4-5
K 103
80
26.9
9.52
67.7
156
13.7
30.5
29.4
16.6
39.2
17.6
24.9
0.77
240
a
0.50
0.599
0.74
0.67
0.50
1.0
0.725
0.753
0.81
0.75
0.67
0.63
0.95
0.61

23. Image taken from Textbook of Polymer Science by Fred. W. BillMeyer

24. • For measuring intrinsic viscosity of polymer
sample, solutions of known concentrations are
prepared, the flow times of solvent ( ) and the
solutions ( ) are measured using viscometer.
• Double extrapolation plots of reduced viscosity
against concentration and inherent viscosity
against concentration is plotted by calculating
the corresponding reduced viscosity and inherent
viscosity. The intrinsic viscosity is given by the
common ordinate intercept of these graphs.

28. Determining the Intrinsic Viscosity of the Polymer- solvent system:
• Select the Polymer and Select the Solvent.
• Determine the Time of flow of the solvent (t0).
• Determine the time of flow of polymer-solvent system at different
concentrations.
• From the concentration and time of flow, the inherent viscosity and
reduced viscosity are calculated using the equations;
Inherent Viscosity = Reduced Viscosity =
• A graph is drawn by plotting reduced viscosity against concentration
and inherent viscosity against concentration.
• Intrinsic viscosity can be obtained by extrapolating the graph to zero
concentration.
• From the value of intrinsic viscosity, the viscosity average molecular
weight of the polymer can be calculated by using the equation.

29. References:
Books:
• Polymer Science by V R Gowarikar, N V Viswanathan, Jayadev
Sreedhar.
• Textbook of Polymer Science by Fred. W. BillMeyer.
Webliography:
• www.udel.edu/pchem/C446/Experiments/exp5.pdf
• www.ias.ac.in/initiat/sci_ed/resources/chemistry/Viscosity.pdf
• www.isasf.net/fileadmin/files/Docs/Colmar/Paper/T19.pdf
• en.wikipedia.org/wiki/Polymer
Image Source:
• t1.gstatic.com/images