Pattern formation and unusual A + B → 0 reaction kinetics between charged reactants in low dimensions

The effect of non-equilibrium charge screening in the kinetics of the one-dimensional, diffusion-controlled A + B → 0 reaction between charged reactants in solids and liquids is studied. Incorrectness of static, Debye-Huckel 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 (D_A = 0, D_B > 0) contrasting the traditional symmetric case, i.e. equal diffusion coefficients, (D_A = D_B) is studied. In the asymmetric case concentration decay is predicted to be accelerated, n(t) ∝ t^-α, α = 1/3 as compared to the well-established critical exponent for fluctuation-controlled kinetics in the symmetric case, α = 1/4 and/or the prediction of the standard chemical kinetics, α = 1/2 . Results for the present microscopic theory are compared with the mesoscopic theory.