Page 402 - Elements of Chemical Reaction Engineering Ebook

SSC. 7.3 Polymerization 373
I The number-average chain length, Equation (7-47), can be rearranged as

(EM.
1)
= pn = 820 structural (monomer) units
The number-average molecular weight is

=
a,, M, = a20 x 2s = 20,500
p,,
Recalling Equation (7-50) and rearranging, we have
WACL=pw=- Z j2P. = Z jz(Pj/CPj)
CJPj Z.i(PjfZPj) (E7-4.2)
- Zj2Y - ,
736 O0O = 897.5 monomer units.
. Zjy 820
The mass average molecular weight is
X?w = MMpw = 25 X 897.5 = 22,434

The variance is;
2
a$ = - rl) = 736,000 - (820)2
b G

= 63,600
u,, = 252.2 (E7-,4.3)

The polydispersity index D is

(E7-4.4)

Flory Statistics of the Molecular Weight Distributtion. "he solution to the
complete set (j = 1 to j = 100,OOO) of coupled-nonlinear ordinary differential
equations needed to calculate the distribution is an enormous undertaking even
with the fastest computers. However, we can use probability theory to estimate
the distribution. This theory was developed by Nobel laureate Paul Hory. 'We
have shown that for step polymerization and for free radical polymerization in
which termination is by disproportionation the mole fraction of polymer with
chain length j is

Rory mole fraction
distribution yj = (1 -p)pj-' (7-2!7)
In terms of the polymer concentration

The number average molecular weight