Exercise 1.2
KE-100.3410 Polymer properties
Exercise 1: Stereoregular polymers, average molecular
weights
Exercise 1.1
Draw the different stereoregular polymer structures that can be obtained
from the following monomers
a)
CH2=CH–CH3
b)
CH2=C(CH3)2
c)
CH3–CH=CH–C2H5
d)
CH3–CH=CH–CH=CH2
O
CH3 CH CH C2H5
e)
f)
CH3
A sample of polystyrene is composed of a series of fractions of
different sized molecules
a) Calculate the number average and weight average molecular
weights of this sample as well as the PDI.
b) How would adding styrene oligomer change the average
molecular weights? The added amount is 5 %wt of polymer
mass and M=1000g/mol.
Table 1. PS fractions.
Fraction
weight fraction
A
B
C
D
0.130
0.300
0.400
0.170
Molecular weight
[g/mol]
11000
14000
17000
21000
Exercise 1.3
The 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 M v . Mark-Houwink constants
are k = 0.00848 ml/g and a = 0.748.
Table 2. Efflux times for polystyrene samples. Solvent toluene, T =
25°C.
Polystyrene concentration
efflux time
[mg/ml]
[t/s]
0
110.0
5.0
123.5
10.0
138.0
15.0
153.6
20.0
170.2
25.0
187.9
where R() Rayleigh ratio, Mw weight average molecular weight, c
particle concentration (g/dm3), A2 second virial coefficient and K is a
function of the refractive index,
2 2 no2  dn 
K
 
N A 4  dc 
2
where no is the refractive index of the pure solvent, NA = 6,0231023
mol-1 Avogadro´s number,  wavelength, dn/dc specific refractive
increment of the dilute polymer solution.
For cellulose acetate, the Rayleigh ratio R() in dioxane with LALLS
measurement with different concentrations is:
c (g/m3)
5.034E+02
1.007E+03
1.510E+03
2.014E+03
2.517E+03
R() (m-1)
2.390E-04
4.400E-04
6.060E-04
7.900E-04
9.020E-04
Exercise 1.4
Low-Angle Laser Light-Scattering = LALLS (2o-10o) can be used to
determine the molecular weight of polymer particles even from very
dilute solutions using the Debye equation:
Kc
1

 2 A2 c
R( ) M w
Refractive index for dioxane is no = 1.4199, cellulose acetate solution
has dn/dc = 6.29710-2 cm3/g and the wavelength is  = 6328 Å.
Calculate the weight average molecular weight and the second virial
coefficient (A2).
Exercise 1.5*
Polymers A and B are monodisperse polystyrenes. The molecular
weight of Polymer A is three times the molecular weight of polymer B.
Polymer C is polydisperse PS with Mw=2.0105 g/mol. A mixture
containing 25g of polymer A, 50g of polymer B and 25g of polymer C
was measured with light scattering, and molecular weight obtained was
112500 g/mol. With osmotic pressure, the molecular weight was
determined to be 60000 g/mol. Estimate the number average molecular
weight Mn of the polymer C.
Exercise 1. 6*
The following measurements have been obtained for a polymer solution
at 25oC:
c (g/dL) h (cm of solvent)
0,32
0,70
0,66
1,82
1,00
3,10
1,40
5,44
1,90
9,30
Density of the solvent is 0.85 g/cm3.
a) Plot π/(RTc) as a function of concentration c.
b) Determine the average molecular weight for the polymer and
the second virial coefficient.