The kinetics of the bimolecular A+B→0 reaction in condensed matter: Effects of non-equilibrium charge screening

The kinetics of the bimolecular A + B→0 reaction between charged reactants is studied in two dimensions, i.e., on a surface. The theory is based on the Kirkwood superposition approximation for three-particle densities and the self-consistent treatment of the electrostatic interactions defined by the non-uniform spatial distribution of similar and dissimilar reactants. Special attention is paid to pattern formation and many-particle effects arising from reaction-induced formation of loose domains containing similar reactants only. It is shown that the critical exponent a characterizing the algebraic concentration decay law, n(r) ∝ t^-α, differs strongly between symmetric (D_A = D_B) and asymmetric (D_A = 0) reactant mobilities. This effect is abnormal from the point of view of standard chemical kinetics. It arises directly from the specific spatial distribution in the system as in "raisins A in a dough B." At long reaction times the asymptotics of the interaction potentials is of non-equilibrium type at large relative distances. The accumulation kinetics in the presence of a permanent source is studied. Results of the microscopic formalism are compared with a previous mesoscopic theory.