Structure and kinetics of reaction-limited aggregation

Several different models are used to investigate reaction-limited cluster-cluster aggregation and the crossover from diffusion-limited to reaction-limited aggregation. The results obtained from these models are consistent with each other, if finite-size and finite-concentration effects are taken into account. For reaction-limited aggregation in three dimensions we find, in the case where the probability that two clusters will combine depends only on the time that they spend in contact with each other, that the mean cluster size S(t) increases exponentially with time t and that the cluster-size distribution $N_s$(t) (of clusters of size s at time t) decays as $N_s$(t)∼$s^{\mathrm{-}\tau }$ with τ having a value larger than 1.5. For the case where the probability that two clusters will combine depends only on the number of times they collide with each other, we find a power-law growth in the mean cluster size, S(t)∼$t^z$ with z∼2.0–2.5, and a cluster-size-distribution exponent τ close to 1.0. Our results indicate that the approach to asymptotic behavior may be quite slow and that the effective fractal dimensionality of the clusters depends both on the aggregation kinetics and on the extent of aggregation. We find that if the rate of bonding between two clusters depends on their collision frequency, then the exponent τ has a value close to 1 for the aggregation of small rigid clusters and close to 2 for the aggregation of large floppy clusters.