Page 395 - Elements of Chemical Reaction Engineering Ebook

366 Nonelementary Reaction Kinetics Chap. 7

Net rate of In general, the net rate of disappearance of live polymer chains with j
disappearance of monomer units (i.e., length j) for (j 2 2) is
radicals of chain
I m 1
length j
- rj = k,M(Rj - Rj- 1) + (k, + kd) Rj R,
i= I
t k,MR, + kcCRj -I- k,SR,

At this point one could use the techniques developed in Chapter 6 on multiple
reactions to follow polymerization process. However, by using the PSSH, ‘we
can manipulate the rate law into a form that allows closed-form solutions for a
number of polymerization reactions.
First, we let R* be the total concentration of the radicals Rj:

R*= CRj (7-33)
j= 1
and k, be the termination constant,k, = (k, + kd). Next we sum Equation
(7-32) over all free-radical chain lengths fromj = 2 toj = m, and then add
the resvlt to Equation (7-31) to get
m
-rj
1 = -ri + ~,(R*>z
j= 1
The total rate of termination is just

(7-34)

m
-5
Using the PSSH for all free radicals, that is, 1 = 0, the total free-radical
If1
concentration solves to

Total
free radical (7-35)
concentration

We now use this result in writing the net rate of monomer consumption.
As a first approximation we will neglect the monomer consumed by monomer
chain transfer. The net rate of monomer consumption, -rM, is the rate of con-
sumption by the initiator plus the rate of consumption by all the radicals Rj in
each of the propagation steps (rp).

m
-rM = -ri + -rp = -ri + k,M 2 Rj
j=l