polymers notes from class

The following equations have to be applied in order to calculate the number average molecular weight ( Mn ), the weight average molecular weight ( Mw ) and the polydispersity index ( PDI ) :
_
Mn = ΣNiMi / ΣNi
_
Mw = ΣWiMi/ ΣWi = ΣNiMi2 / ΣNiMi _ _
PDI = Mw / Mn
The molecular weight of polystyrene repeat unit (CH – CH2 )n is M = 104 C6H5

Using the input data of the 4 monodisperse fractions, we create the following table:

Sample
Wt/m
Ni
Mi
NiMi
Wt.fraction
MiWi
Mw
W
2.5/104
0.024
40,000
960
0.038
40000x0.038
1520
X
5.0/104
0.048
75,000
3600
0.141
75000x0.141
10575
Y
6.5/104
0.0625
150,000
9375
0.367
150000x0.367
55050
Z
3.5/104
0.033
350,000
11550
0.453
350000x0.453
158550
total(Σ)

0.1675

25485

225695

_
Mn = 25,485 / 0.1675 = 152,149 g/mol
_
Mw = 225,695 g/mol

PDI = 225,695/152,149 = 1.48

The repeat unit of poly(acrylamide) is the following :

( CH2 – CH )n and Molar mass = 71 g/mol CO – NH2 The average polymerization degree PD = 5,000,000/ 71= 70,422

The repeat unit of Nylon 6 poly(ε-caprolactame ) is the following :

{ NH – (CH2)5 – CO }n and M = 113 g/mol

PD = 60,000 / 113 = 531

The repeat unit of Nylon 6,6 ( polyhexamethyleneadipate ) is :

{ OC(O) – (CH2)4 – CO – NH – (CH2)6 – NH } and M = 226 g/mol

PD = 60,000 / 214 = 265

-a) The polymer formed by the polycondensation of 2 moles of terephtalic acid and 2 moles ethyleneglycol is poly(ethyleneterephtalate) with the following repeat unit :
{ OC – C6H4 – C(O)O – CH2 – CH2 – O }n and M = 192/2 = 96 -b) The average number polymerization degree “X” at an reaction extent P = 0.9 is :
X = 1/(1-P) = 1/ (1-0.9) = 10
Mn = X*M = 10 x 96= 960 g/mol
Mw = Mn (1 + P) = 960 ( 1 + 0.9 ) = 1824 g/mol

-c) For an reaction extent P = 0.995 , the values are :
X = 1 / (1-0.995) = 200
Mn = 200 x 96 = 19200 g/mol
Mw = 19200 ( 1 + 0.995 ) = 38304 g/mol

-d) N0 = initial number of moles diol/diacid = 2.0