Kinetic Behavior of Aggregation—Fragmentation Process with Annihilation

The kinetic behavior of an aggregation-fragmentation-annihilation system with two distinct species is studied. We propose that the aggregation reaction occurs only between two clusters of the same species, and the irreversible annihilation reaction occurs only between two clusters of different species, meanwhile there exists the fragmentation reaction of a cluster into two smaller clusters for either species. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates and obtain the asymptotic descriptions of the cluster-mass distribution. In the case of the same initial concentrations of two species, the scaling descriptions for the cluster-mass distributions of the two species are found to break down completely. It is also observed that the kinetic behaviors of distinct species are quite complicated for the case of different initial concentrations of the two species. The clusters of larger initial concentration species (heavy species) possess peculiar scaling properties, while the cluster-mass distribution of light species has not scaling behavior. The exponents describing the scaling behavior for heavy species strongly depend on its fragmentation rate and initial monomer concentrations of two kinds of reactants.

Breakdown of Scaling in Aggregation-Fragmentation- Annihilation Process of n-Species Systems

The kinetic behaviors of aggregation-fragmentation-annihilation processes of three n-species systems arestudied in this paper. Aggregation reaction occurs only between the same species but irreversible annihilation reactionoccurs between two different species, and meanwhile the fragmentation reaction coexists. Based on the mean-field theory,we investigate the rate equations of the processes and obtain the asymptotic descriptions of the cluster-mass distributionsfor the symmetrical cases. We find that the fragmentation reaction may lead to the complete breakdown of the standardscaling description for the cluster-mass distribution of each species contrast to the scaling behavior of aggregation-annihilation processes without fragmentation.In our joint annihilation model, we also observe that the kinetic behaviorsof distinct species are quite complicated for the case with different initial concentrations. The cluster-mass distributionof heavy species with the largest initial concentration possesses peculiar scaling properties, while that of light species hasnot scaling behavior.