Page 405 - Elements of Chemical Reaction Engineering Ebook

376 Nonelementary Reaction Kinetics Chap. 7

Propagation:

Chain transfer to solvent:

Rj+S ’ k*s ’ P,+S-

Transfer to monomer:
Batch reactor R,+M km > P,+R,
calculations
The corresponding combined batch reactor mole balances and rate laws are:
For the initiator:

dA- = k,AB - k-iA-B+ - k,A-M
dt

For the live polymer:
”3 Live

L
For the dead polymer:

dP .
-I = k,SRj + k,,MRj
dt
In theory one could solve this,coupled set of differential equations. However,
“Houston, we have a this process is very tedious and almost insurmountable if one were to carry it
Problem!” through for molecular weights of tens of thousands of Daltons, even with the
-Ap~llO 13
fastest of computers. Fortunately, for some polymerization reactions there is a
way out of this dilemma.

Some Approximations. To solve this set of coupled ODES we need to make
some approximations, There are a number of approximations that could be
made, but we are going to make ones that allow us to obtain solutions that pro-
vide insight on how the live polymerization chains grow and dead polymer
chains form. First We neglect the termination terms (k6SRj and kmRjA4) with
respect to propagation terms in the mole balances. This assumption is an excel-
.
lent one as long as the monomer concentration remains greater than the live
polymer concentration.
For this point there are several assumptions that we can make. We could
assume that the initiator (I = A-) reacts slowly to form R, (such is the case in
Problem P7-22).