Recovering boundaries for partly diffusion-controlled reaction kinetics

Abstract

Abstract For chemical reactions in solution which are close to, but slower than the diffusion-controlled limit it is usual to describe the reaction step using the radiation boundary condition, a simple parametrisation which treats first encounters and re-encounters identically. This paper introduces a new stochastic description of partly diffusion-controlled reactions which retains the diffusion equation, but attempts to model the way in which the reactivity of a pair grows back as a function of time since the last unreactive encounter. Analytic solutions for the new formalism are given for several important cases. The correction of the rate constant from the diffusion limit is shown to depend on the diffusion coefficient in an entirely different way from the usual parametrisation using the radiation boundary condition. The theory is applied to the reaction between the solvated electron and oxygen in aqueous solution.