Kinetic behavior of aggregation processes with complete annihilation.

Abstract

The kinetic behavior of an aggregation-annihilation process of an n-species (n> or =2) system is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species and an irreversible complete annihilation reaction occurs between any two different species. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions for the cluster-mass distributions. We find that the cluster-mass distribution of each species satisfies a modified scaling law, which reduces to the standard scaling law in some special cases. The scaling exponents of the system may strongly depend on the reaction rates for most cases; however, for the case with all the aggregation rates twice the annihilation rate, these exponents depend only on the initial concentrations. All the species annihilate each other completely except in the case in which at least one aggregation rate is less than twice the annihilation rate.