Theory of compartmentalised free-radical polymerisation reactions. Part 4

Abstract

Approximate explicit analytic solutions are given for ĩ, the average number of radicals per reaction locus, and nr, the number of reaction loci per unit volume containing r radicals, as functions of time, t, for the case of a seeded emulsion polymerisation reaction in which radicals enter the reaction loci from a contiguous external phase at a constant rate and in which radicals are lost from reaction loci by processes which are kinetically of second order in radical concentration within the loci as well as by processes which are first order. The approximation is valid provided that the dominant radical-loss mechanism is not second order. The approximation predicts that the nr always form a time-dependent Poisson distribution with respect to the r. The parameter, θ(t), of the distribution at any instant is also equal to the value of ĩ at that instant. θ(t) is a function of t defined by the differential equation dθ//dt=σ–kθ–χθ2 subject to an appropriate initial condition. In this differntial equation, σ is the average rate of entry of radicals into a single locus, k characterises the rate of loss of radical activity by first-order processes, and χ characterises the rate of loss of radical activity by second-order processes.