Theory of compartmentalised free-radical polymerisation reactions. Part 3

Abstract

An explicit analytic solution has been obtained for the time-dependent Smith–Ewart equations for the case where the rate of formation of new radicals is zero, as would be the case if the rate of the radical-generating reaction in a compartmentalised free-radical polymerisation reaction were suddenly reduced to zero. The decay characteristics of the reaction are determined by a set of “relaxation times”. The nature of these relaxation times does not depend upon the nature of the locus-population distribution from which the reaction decays, although the way in which the locus populations themselves decay does depend upon the initial distribution.

The general theory is applied to three special cases: (1) that of decay from a Stockmayer–O'Toole distribution of locus populations; (2) that of decay from a Poisson distribution of locus populations; and (3) that of decay from a homogeneous distribution of locus populations. Special treatment is necessary for the case where the reaction system is such that radicals cannot be lost from reaction loci by reactions which are kinetically first order in radical concentration in the locus.

The theory has been used to analyse results which have been reported previously by other workers for the decay of emulsion polymerisation following the cessation of the generation of new radicals.