Bimolecular annihilation reactions with immobile reactants: Unequal reactant concentrations

We study the bimolecular annihilation reaction A + B→0 with immobile reactants interacting via exchange. We extend our previous analyses to the case of unequal concentrations of A and B particles. A comparison between the direct simulation of the reaction process and an analytical approach, which is based on Kirkwood's superposition approximation, shows reasonable agreement, although deviations are larger than in the case of equal A and B concentrations. Interestingly, the asymptotic decay forms for the particle concentrations (when formulated in terms of a suitable reaction length) parallel those encountered in diffusion-limited reactions. Here the diffusion length l _D = (Dt)^1/2 gets replaced by the reaction radius ξ= 1n t. We discuss implications of this finding for a qualitative (but quite accurate) picture of the temporal evolution behavior.