Introduction to polymer molecular weight and Membrane Osmometry

1. TOPIC
Molecular Weight Of Polymers
 Introduction
 Membrane Osmometry
By: Kudzai Hamish Ruzvidzo
Harare Institute of Technology
EPT121 Analytical Polymer Chemistry
0719121469

2. Introduction
• Polymers are long chain molecules produced by linking small repeat units (monomers)
together
• There are many ways to link different types of monomer to form polymers
• Polymers exhibit very different physical properties compared to the monomers, dependent
on the length of the polymer chains
• The presence of small amounts of very long or very short chains can have drastic effects on
properties of the material

3. Molecular Weight
• Repetitive units make up a polymer.
• These repetitive units were originally the monomer molecules.
• When polymer chains form their lengths and thus their weights differ.
• It is important to be able to characterize the polymer structure.
• Determining the weight-average molecular weight or the number-average
molecular weight is a part of any polymer characterization.

4. “Molecular weight of a polymer is defined as sum of the atomic weight of each of
the atoms in the molecules, which is present in the polymer”.

5. Average molecular weights
• Number average molecular weight:
• Weight average molecular weight
• Viscocity average molecular weight
M
M
n
i i
i
n
n



M
M M
M
w
i i
i
i i
i i
w
w
n
n
 




2
a
ii
a
ii
v
n
n
1
1
M
M
M










 

6. Average molecular weights
• Z-average molecular weight
(Z = zentrifuge/centrifuge)
• Polydispersity
– If PDI = 1, the polymer is monodisperse
ni = Number of molecules with molecular weight Mi
wi = weight fraction with molecular weight Mi
a = constant, depends on polymer/solvent combination
2
3
M
M
M
ii
ii
z
n
n


M
M
w
n
PDI 
 A monodisperse, or uniform, polymer
is composed of molecules of the
same mass
 Nearly all natural polymers are
monodisperse

7. Molecular weight and dispersion
Syntetic polymers always show a distribution in molecular
weights.
number average :
weight average:
(ni and wi are number and weight fractions, respectively, of
molecules with molar mass Mi)
The polydispersity index is given by Mw /Mn


i
ii
n
n
Mn
M



 
ii
iii
i
ii
w
Mn
MMn
w
Mw
M

8. Molecular weight and dispersion -
an example:
Here are:
10 chains of 100 molecular weight
20 chains of 500 molecular weight
40 chains of 1000 molecular weight
5 chains of 10000 molecular weight
1347
5402010
)100005()100040()50020()10010(
Mn 



5390
)100005()100040()50020()10010(
)100005()100040()50020()10010(
M
2222
w 



4
M
M
sityPolydisper
n
w


9. Number-average molecular weight
• The number average molecular weight is not too difficult to
understand.
• It is just the total weight of all the polymer molecules in a sample,
divided by the total number of polymer molecules in a sample
Where,
n = Moles of molecules (n1 + n2 + n3 + ----------ni) i.e. weight (w)/molecular weight (M)
w = Weight of individual molecules (w1 + w2 + w3 + ---------wi)
M = Molecular weight of each molecules
niMi wi
Mn= =
ni wi/Mi
 
 

10. Molecular Weight
The Number Average
Molecular
Weight ( ) is the total
weight of the polymer
molecules divided by the
total number
of polymer molecules.

11. Weight average Molecular
Weight
The Weight Average Molecular
Weight ( ) takes into account
that the larger molecules contain a
much higher amount of the
molecular mass of the polymer.
The Weight Average Molecular
Weight is almost always higher
than the Number Average
Molecular Weight ( ).

12. Consider a polymer, which contains four molecular weight polymers in
different numbers and weight

13. Calculation

14. Calculation

15. Degree of polymerisation (DP)
Number of repeating unit in a polymer called as degree of polymerisation (DP). DP provides the
indirect method of expressing the molecular weight and the relation is as follows;
M = DP x m
Where, M is the molecular weight of polymer, DP is the degree of polymerisation and m is the
molecular weight of the monomer
Each of these averages can be related to the corresponding molecular weight average by the
following two equations;
Mn = (DP)n.m
Mw = (DP)w.m
2
i i i i
n w
i i i
n (DP) n (DP)
(DP) = and(DP) =
n n (DP)
 
 

16. Properties
When making polymers, the goal is to make a material with the
ideal properties.
The longer the molecules (or the higher the molecular weight)
the higher the entanglement forces:
• Longer hair is harder to get untangled than shorter hair

17. Properties
• Increasing the molecular weight of the material increases
many of the properties of the material by increasing the
entanglement of the molecules.
A higher molecular weight:
•Increases the chemical resistance - to a point
– It takes more damage to the main chains of the molecules
before it will affect the strength of the material
– The big loophole to this is if you have a chemical
that is very similar to the chemical makeup of the
main chain, it will dissolve it much more easily
»Like Dissolves Like

18. Properties
A higher molecular weight:
•Increases how far the material can stretch before rupturing
(ductility)
– The higher degree of entanglement allows the material to
be pulled further before the chains break

19. Properties
A higher molecular weight:
•Increases the impact resistance of the material
–The higher degree of entanglement means that in order to
rupture, more polymer bonds need to be broken, this means
that the polymer can absorb more energy before failing.

20. Properties
A higher molecular weight:
•Increases the weather resistance of the material
– Same type of reasoning behind the increase in chemical
resistance, the chains are longer, so they can withstand
more damage before the mechanical properties will start to
diminish

21. Properties
A higher molecular weight:
•Increases the viscosity of the material – makes it harder to
process the material using conventional methods
–The longer the chains, the harder it is to get them to flow
» More tangled

22. Important Facts
• Weight- average molecular weight is larger or equal to number-
average molecular weight.
• Weight- average molecular weight and molecular weight
distributions are determined from ultracentrifuge sedimentation,
diffusion and light scattering.
• Number-average molecular weight and molecular weight
distributions are determined from osmotic pressure and intrinsic
viscosity determinations.
• Optical properties are best reflected in the weight-average
molecular weight, while strength properties are best reflected in
number-average molecular weight.

23. Determination of Molecular Weight

26. Membrane Osmometry
Lecture
Tutorial

27. OSMOMETRY
Osmotic measurements use a semipermeable
membrane through which the solvent can freely pass
but which excludes polymer molecules.
 If this membrane separates two compartments, one
filled with pure solvent and the other with a polymer
solution, the activity of the solvent in the two
compartments is different.
 A membrane osmometer is a device used to indirectly
measure the number average molecular weight Mn of
a polymer sample.
 One chamber contains pure solvent and the other
chamber contains a solution in which the solute is a
polymer with an unknown Mn
 The osmotic pressure of the solvent across the
semipermeable membrane is measured by the
membrane osmometer.
 This osmotic pressure measurement is used to
calculate Mn for the sample.
The operating principle of a membrane
osmometer. Water (below) is connected
to the solution to be measured (above) via
a membrane that lets water through.

28. Osmotic Pressure Definition
• The pressure that needs to be applied to a solution to stop the movement of a solvent into
it, when the solution and solvent (such as water) are separated by a semipermeable
membrane that only allows the solvent to pass through.
• In other words, although the semipermeable membrane would normally allow the solvent
to pass through it, osmotic pressure prevents the solvent from passing through.

29. Membrane osmometer: Basic operation
• A low concentration solution is created
by adding a small amount of polymer to
a solvent.
• This solution is separated from pure
solvent by a semipermeable membrane.
• Solute cannot cross the semipermeable
membrane but the solvent is able to
cross the membrane.
• Solvent flows across the membrane to
dilute the solution.
• The pressure required to stop the flow
across the membrane is called the
osmotic pressure.
• The osmotic pressure is measured and
used to calculate Mn
• In an ideally dilute solution, van ‘t Hoff’s
law of osmotic pressure can be used to
calculate Mn from osmotic pressure.
 In practice, the osmotic pressure produced by an ideally dilute solution would be too small to be accurately measured.
 For accurate Mn measurements, solutions are not ideally dilute and a virial equation is used to account for deviations from
ideal behavior and allow the calculation of Mn

30.  Osmotic pressure is a colligative property, which means that it is proportional to the
concentration of solute.
 The van’t Hoff equation is often presented in introductory chemistry for calculating
osmotic pressure (Π) from the moles of solute (nsolute) that occupy a given volume (V)
and the absolute temperature (T) of the solution

31. CORPORATE TRAINING AND PLANNING
Working Principle

32. Osmometric measurement
• Pure solvent and a dilute solution of
polymer in the same solvent are
placed on opposite sides of a semi-
permeable membrane
• Membrane will allow the solvent to
pass through but will retain the
polymer molecules in solution
• In equilibrium the difference in the
heights of the solvent and solution in
capillaries can be used to calculate
the osmotic pressure

33. Osmometric measurement
• Van’t Hoff equation for the osmotic pressure of an ideal, dilute
solution:
p = osmotic pressure
c = concentration
R = gas constant 8.314 J/mol/K
T = temperature (K)
= number average molecular weight (g/mol)
g = gravitational constant 9.80665 m/s2
ρ = solvent density
p 
RT
c
nM
p
c
RT
n

M
Mn
ghp 

34. Osmometric measurement
• Van’t Hoff equation is for ideal, dilute solutions. In real solutions the equation will be
following:
• For the determination of molecular weight, 4-6 pressure measurements with different
concentrations are required. When solutions are dilute enough, p/c can be obtained by
extrapolation of c to 0. Average molecular weight can be calculated from:
• Polymer concentration is g/dm3 and p/c in J/kg
p
c
RT
Bc Cc
n
   
M
2
.... B, C are virial coefficients
lim
c nc
RT


0
p
M

35. Osmometric measurement: determining π/c
PS in toluene
PS in acetone
c (g/dm3)

36. Worked Example

39. 0
20
40
60
80
100
120
140
160
180
0 2 4 6 8
π/c(m2s-2)
c (kg/m3)

41. Membrane osmometry gives number average molecular weight.
A2 is positive so the interaction between polystyrene and xylene
is favorable (xylene is a good solvent for polystyrene) at this
temperature.

42. Worked example 2
b) At 20o
C, the osmotic pressure of a polycarbonate was measured in chloro-
benzene solution with the following results: [12]
Concentration (g/L) 1.95 2.93 3.91 5.86
Osmotic pressure
(cm chlorobenzene)
0.20 0.36 0.53 0.98
[Solvent density = 1.10g/cm3
; polymer density = 1.20g/cm3
]
Estimate:
a) polymer molecular weight,
b) second virial coefficient A2

43. Solution
Osmotic pressure, π = ρgh
Where ρ = solvent density = 1.10𝑔/𝑐𝑚3 =1100𝑘𝑔/𝑚3
g = gravitational constant = 9.8𝑚/𝑠2
h = osmotic head (in metres)
R = 8.314𝑘𝑔𝑚2
𝑠2
𝑚𝑜𝑙−1
𝐾−1
𝑇 = 20 + 273 = 293𝐾
Also taking note that:
1𝑔
𝐿
= 1𝑘𝑔/𝑚3

44. Concentration, c
(𝑘𝑔/𝑚3)
1.95 2.93 3.91 5.86
Osmotic head, h
(𝑚)
0.002 0.0036 0.0053 0.0098
Osmotic Pressure, π
i.e. 𝜋 = 𝜌𝑔ℎ (Pa)
21.56 38.81 57.13 105.64
𝜋
𝑐
(𝑚2/𝑠2) 11.06 13.25 14.61 18.03
Thus plotting a graph of
𝜋
𝑐
𝑣𝑠 𝑐, gives:

45. y = 1.7454x + 7.8448
0
2
4
6
8
10
12
14
16
18
20
0 2 4 6
π/c(m2s-2)
c (kg/m3)

46. • From the graph, y-intercept = 7.8𝑚2
𝑠−2
• But, 7.8 =
𝑅𝑇
𝑀𝑛
𝑠𝑜 𝑀𝑛 =
𝑅𝑇
7.8𝑚2 𝑠−2
=
8.314𝑘𝑔𝑚2 𝑠2 𝑚𝑜𝑙−1 𝐾−1 ×293𝐾
7.8𝑚2 𝑠−2
= 312.31𝑘𝑔/𝑚𝑜𝑙
= 𝟑𝟏𝟐𝟑𝟏𝟎𝒈/𝒎𝒐𝒍

47. A2 = gradient =
𝑦2−𝑦1
𝑥2−𝑥1
=
18.03−14.61 𝑚2 𝑠−2
5.86−3.91 𝑘𝑔𝑚−3
= 𝟏. 𝟕𝟓𝒎 𝟓 𝒔−𝟐 𝒌𝒈−𝟏

48. Osmometric measurement: challenges
• Simple experimental procedure, but can be very time consuming
• Performance of the membrane can be a problem
• Membrane can let some smaller polymer molecules through and this will result in an
artificially-higher Mn value
• Thus, the method is considered accurate for molecular weights above 20,000 g/mol
• The practical range of molecular weights that can be measured by membrane osmometry is
approximately 30000 to one million
• For measurements of Mn less than 30000 another technique known as vapour-phase
osmometry is more suitable