Effect of reactant spatial distribution in the [Formula Presented] reaction kinetics in one dimension with Coulomb interaction

The effect of nonequilibrium charge screening in the kinetics of the one-dimensional, diffusion-controlled [Formula Presented] reaction between charged reactants in solids and liquids is studied. The incorrectness of the static, Debye-Hückel theory is shown. Our microscopic formalism is based on the Kirkwood superposition approximation for three-particle densities and the self-consistent treatment of the electrostatic interactions defined by the nonuniform spatial distribution of similar and dissimilar reactants treated in terms of the relevant joint correlation functions. Special attention is paid to the pattern formation due to a reaction-induced non-Poissonian fluctuation spectrum of reactant densities. This reflects a formation of loose domains containing similar reactants only. The effect of asymmetry in reactant mobilities ([Formula Presented], [Formula Presented]) contrasting the traditional symmetric case, i.e., equal diffusion coefficients ([Formula Presented]), is studied. In the asymmetric case concentration decay is predicted to be accelerated, [Formula Presented], [Formula Presented], as compared to the well-established critical exponent for fluctuation-controlled kinetics in the symmetric case, [Formula Presented], and/or the prediction of the standard chemical kinetics, [Formula Presented]. Results for the concentration decay and growth under permanent particle source are compared with results of the mesoscopic theory.