Page 403 - Elements of Chemical Reaction Engineering Ebook

374 Nonelementary Reaction Kinetics Chap. 7

m co
M,, = yi~j 2 yjjR
=
Termination other j= 1 j= 1
than by combination m
1
= Ms(l -p> jpJ-1 = M,(1 -p> -
]=1 (1 - P)2
and we see that the number average molecular weight is identical to that given
by Equation (7-26)

M, = X,M, = - (7-26)
+
-_.
1-P
The weight fraction of polymer of chain length j is

j= 1 j=l j= 1

u
Flory weight
fraction distribution wj = j(1 -p)2pj-l (7-56)

The weigk fraction is shown in Figure 7-7 as a function of chain length.
The weight average molecular weight is
W m

j=1 j= 1

I I
These equations will also apply for ARIA and BR2B polymers if the
monomers are fed in stoichiometric portions. Equations (7-54) through (7-56)
also can be used to obtain the distribution of concentration and molecular
weights for radical reactions where termination is by chain transfer or by dis-
proportionation if by p is given by Equation (7-43). However, they cannot be
used for termination by combination.
Figure 7-7 compares the molecular weight distribution for poly(hexame-
thylene adipamide) calculated from Flory's most probable distribution' [Equa-

P. J. Flory, Principles of Polymer Chemistry, Cornel1 University Press, Ithaca, N.Y.,
1953.