NONUNIVERSALITY AND BREAKDOWN OF SCALING IN 2-SPECIES AGGREGATION WITH ANNIHILATION

We study the kinetics of a simple model of aggregation with two distinct monomeric species in which irreversible bonding occurs only between like species and annihilation occurs between unlike species. In the mean-field approximation we find an unexpected kinetic behaviour which depends crucially on the ratio of reaction rates. For a relatively simple model of constant reaction rates, we investigate the corresponding rate equations and derive exact expressions for the exponents describing the kinetics of the model. It is observed that the kinetic behaviours of distinct species are quite different and that corresponding scaling exponents are also generally nonuniversal. Analytical solutions of the rate equations show that a modified scaling description, with different sets of exponents for light and heavy species, exists in systems with sufficiently weak annihilation; in systems with strong annihilation, the scaling for the cluster-mass distribution of the light species completely breaks down. A model with constant reaction rates of fusion and sum-kernel reaction rates of annihilation is also studied.