Annihilation and Coagulation Reactions in Low-Dimensional Substrata: Effects of Probability of Reaction and Short Range Interactions

Abstract

We study the bimolecular coagulation A + A → A and annihilation A + A → 0 reactions with diffusion and probability p of reaction in one dimension and annihilation reaction with diffusion and short range interactions in two-dimensional fractal and nonfractal percolation clusters. In these cases there is no input of particles and the particle density Ρ decays as a function of time t. The effect of p and interactions become relevant at short times. In one dimension analytical approximations of the density for coagulation and annihilation reactions are found which agree very well with Monte Carlo results of Ρ(t) for all times and for small values of p. For percolation clusters and large values of the nearest-neighbor repulsive interaction Ubetween particles, we find that a simple mean-field approximation works at short times. The length of the interval where this approximation holds increases as U increases. For the case of repulsive nearest-neighbor with attractive next nearest-neighbor interactions we find an exponential decay of the density at short times. We also analyze the steady-state regime of annihilation and coagulation reactions ofimmobile reactants with reaction probability and input of particles in a one-dimensional lattice. Analytical approximations of the particle density and of the n-particle correlations are obtained. The limit of zero input rate is solved exactly. The analytical results were confirmed by Monte Carlo simulations.