Effect of an external electric field on the diffusion-influenced geminate reversible reaction of a neutral particle and a charged particle in three dimensions. III. Ground-state ABCD reaction

Abstract

In the presence of an external electric field, the ground-state A+B(q)<->C(q)+D diffusion-influenced reversible reaction for a geminate pair, a neutral and a charged particle, is investigated in three dimensions. The probability density functions, the rates of reactions, and the survival probabilities of individual particles are analytically derived in the Laplace domain in terms of series solutions. The long-time kinetics of probability density functions and rates of reactions in rescaled forms shows a kinetic transition behavior from a t(-3∕2) power law to a t(-3∕2)e(t) increase when the condition D1F1 (2)≤D2F2 (2), which depends on the diffusivities of particles and the external electric fields, changes to D1F1 (2)>D2F2 (2). In the transition region D1F1 (2)=D2F2 (2), the long-time behavior also shows a t(-3∕2) power law decay but with a different value of the prefactor. The rescaled survival probabilities only exhibit an exponentially increasing behavior at long times with no dependence on the various values of parameters.