1. Polymer Properties
Exercise 1

2. Structure
Draw the different stereoregular polymer structures that can be obtained.

3. 1a)
Stereoregularity of PP:

4. 1b)
No stereoregularity differences in polymer.

5. 1c)
Also Syndiotactic
Also Isotactic

6. 1d)

7. Avarage molecular weights
Equations for number average and weight average molecular weights as well as polydispersity index are defined as follows:
where Mi molecular weight of molecules i
ni number of molecules with molecular weight i
wi mass of the molecules with molecular weight i

8. 2
A sample of polystyrene is composed of a series of fractions of different sized molecules (total mass 10 g).
Calculate the number average and weight average molecular weights of this sample as well as the PDI.
How would adding styrene oligomer change the average molecular weights? Added amount is 5wt.% of polymer mass and M=1000g/mol.
Table 1. PS fractions.
Fraction
weight fraction
Molecular weight
[g/mol] A
0.130
11000 B
0.300
14000 C
0.400
17000 D
0.170
21000

9. 2a)
Determine the number of moles in each fraction. Assume that the sample is 10 g in the beginning. Number of moles of the fraction is ni = wi / Mi.
fraction wi
[g] Mi
[g/mol] ni
[mmol] A
1.30
11000
0.118 B
3.00
14000
0.214 C
4.00
17000
0.235 D
1.70
21000
0.0810
wi = 10.0 g
ni = mmol

10. 2a) Number average molecular weight: Weight average molecular weight:
Polydispersity index:

11. 2b)
When 5.0 wt-% of styrene oligomer (fraction E) is added, the total mass and number of moles increase as follow:
fraction wi
[g] Mi
[g/mol] ni
[mmol] A
1.30
11000
0.118 B
3.00
14000
0.214 C
4.00
17000
0.235 D
1.70
21000
0.0810 E
0.50
1000
wi = 10.5 g
ni = 1.10 mmol

12. 2b) number average molecular weight weight average molecular weight
Polydispersity index

13. 3 Viscosity relative viscosity:
Relative viscosity increment (or specific viscosity):
Reduced viscosity (or viscosity number):
 Inherent viscosity:
Mark-Houwink equation:
Intrinsic viscosity [] can be defined:

14. Polystyrene concentration [mg/ml]3)
Viscosity of atactic polystyrene was measured in dilute solutions and the results are presented in table 2.
Determine the viscosity average molecular weight for the sample . Mark-Houwink constants are k =  ml/g and a =
Table 2. Efflux times for polystyrene samples. Solvent toluene. T =25°C.
Polystyrene concentration [mg/ml]
efflux time
[t/s]
110.0
5.0
123.5
10.0
138.0
15.0
153.6
20.0
170.2
25.0
187.9

15. 3) Calculate the required viscosity parameters:
Draw inh and red as function of concentration. c
[mg/ml]
efflux time
[t/s] r
= t/t0
sp
= (t-t0)/t0
inh
=ln(r)/c
red
= sp/c
110.0
5.0
123.5
1.123
0.123
0.0232
0.0246
10.0
138.0
1.255
0.255
0.0227
0.0255
15.0
153.6
1.396
0.396
0.0222
0.0264
20.0
170.2
1.547
0.547
0.0218
0.0274
25.0
187.9
1.708
0.708
0.0214
0.0283

16. 3) [] is obtained from the plot from the crossing of y-axis:
and the average from these is [] = ml/g.
Viscosity average molecular weight from Mark-Houwink equation:
Note! Due to empirical coefficients k ja a. the equation gives the molecular weight without unit. In literature k = 0.007…0.01 and a = 0.69…0.78  accuracy of the calculation is not particularly good.

17. 4) Light scattering
Both weight average molecular weight Mw and second virial coefficient A2 can be determined from graph when Kc/R(q) is plotted as a function of concentration:
1/Mw is the cross point on y-axis and A2 is half of the linear coefficient.

18. 4)
From the plot:
And second virial coefficient: