Cluster size distribution in chemically controlled cluster–cluster aggregation

Abstract

The dynamics of the cluster–cluster aggregation process is investigated through the time dependent cluster size distribution function using Monte Carlo simulations, scaling theory, and the Smoluchowski coagulation equation. Depending on such factors as the chemical reactivity, kinetic energy, mass, etc. of the aggregates the coagulation of two clusters may or may not take place. These effects are simulated by assuming that the probability that two clusters of sizes i and j irreversibly stick together is proportional to (ij)σ. Our results show that for constant small sticking probability cluster size distribution and its moments asymptotically scale with the same exponents as for the case when the sticking probability is unity. In the early stages, coagulation is slow and the process is chemically controlled. However, for finite sticking probability, as the aggregation process develops in time the chance that two clusters join permanently increases with the surface of the cluster and there is a crossover from chemically controlled to diffusion-limited aggregation. The effect of a finite σ is similar to the exponent γ for the mass dependent diffusion coefficient. There exists a critical value, σc, above which for a given γ the cluster size distribution changes from a bell shaped curve to a monotonically decreasing function of s, in agreement with various experiments. The simulations are found to agree with the dynamic scaling theory, but a reasonable approach to include the effect of sticking probability within the Smoluchowski equation fails to produce results that agree with the simulations.