General solution to the Smith–Ewart equation for emulsion polymerization kinetics

Abstract

Using matrix methods, complete time-dependent solutions are derived for the Smith–Ewart equations describing polymerization in emulsion systems with a constant number of polymerizing loci, where the mechanisms of free radical entry, exit and termination all operate simultaneously. The results, which are valid for any system where the average number of free radicals per particle is < ∼ 0.6, reduce to previous, more restricted, solutions under the appropriate limits.