Page 184 - Introduction to chemical reaction engineering and kinetics

166 Chapter 7: Homogeneous Reaction Mechanisms and Rate Laws

styrene monomer and butadiene monomer to produce SBR type of synthetic rubber).
These may both be classified broadly into chain-reaction polymerization and step-
reaction (condensation) polymerization. We consider a simple model of each, by way
of introduction to the subject, but the literature on polymerization and polymerization
kinetics is very extensive (see, e.g., Billmeyer, 1984). Many polymerization reactions
are catalytic.

7.3.1 Chain-Reaction Polymerization
Chain-reaction mechanisms differ according to the nature of the reactive intermedi-
ate in the propagation steps, such as free radicals, ions, or coordination compounds.
These give rise to radical-addition polymerization, ionic-addition (cationic or anionic)
polymerization, etc. In Example 7-4 below, we use a simple model for radical-addition
polymerization.
As for any chain reaction, radical-addition polymerization consists of three main
types of steps: initiation, propagation, and termination. Initiation may be achieved by
various methods: from the monomer thermally or photochemically, or by use of a free-
radical initiator, a relatively unstable compound, such as a peroxide, that decomposes
thermally to give free radicals (Example 7-4 below). The rate of initiation (rinit) can be
determined experimentally by labeling the initiator radioactively or by use of a “scav-
enger” to react with the radicals produced by the initiator; the rate is then the rate of
consumption of the initiator. Propagation differs from previous consideration of linear
chains in that there is no recycling of a chain carrier; polymers may grow by addition
of monomer units in successive steps. Like initiation, termination may occur in vari-
ous ways: combination of polymer radicals, disproportionation of polymer radicals, or
radical transfer from polymer to monomer.

Suppose the chain-reaction mechanism for radical-addition polymerization of a monomer
M (e.g., CH,CHCl), which involves an initiator I (e.g., benzoyl peroxide), at low concen-
tration, is as follows (Hill, 1977, p. 124):
initiation: 1%2R* (1)
R’ + M&P; (2)

propagation: P; + M%pI m
q+M%pf 0-9)
. . *
Y-l + M%P; (W
. . .
termination: P’k + P; AP,+, k,e= 1,2,... (3)
in which it is assumed that rate constant k, is the same for all propagation steps, and k, is
the same for all termination steps; Pk+e is the polymer product; and PF, r = 1,2, . . . , is a
radical, the growing polymer chain.
(a) By applying the stationary-state hypothesis (SSH) to each radical species (including
R’), derive the rate law for the rate of disappearance of monomer, (-Q), for the
mechanism above, in terms of the concentrations of I and M, andf, the efficiency
of utilization of the R’ radicals;f is the fraction of R’ formed in (1) that results in
initiating chains in (2).