The kinetics of cationic polymerization is studied theoretically
in accordance with a three-state mechanism which consists of two successive equilibria: the
ionization/ion collapse equilibrium
between covalent species and ion pairs, and the subsequent
dissociation/association equilibrium between
ion pairs and free ions. The number- and weight-average degrees of
polymerization and the polydispersity
index (PDI),
P̄
w/P̄
n, are
derived. The molecular weight distribution of the polymer
generated from this
mechanism is generally broader than that of polymers formed via a
two-state mechanism, i.e. with only
one equilibrium either between covalent species and ion pairs or
between covalent species and free ions.
Under this general mechanism, the exchange rate parameter, β, is
more complicated than that of two-state mechanisms and is a combination of the corresponding exchange rate
parameters for these two
mechanisms. The molecular weight distribution becomes narrower if
dissociation is reduced by adding
common counterions to the reaction system. Excess common ions lead
to a two-state polymerization
with covalent species and ion pairs only. On the other hand, if
dissociation is very strong, the PDI is
predominantly given by the rate of the ionization/ion collapse
equilibrium unless the dissociation/association equilibrium is very much slower than the former
one.