Percolation in Cluster-Cluster Aggregation Processes

Abstract

Numerical simulations of Diffusion-Limited and Reaction-Limited Cluster-Cluster Aggregation processes of identical particles are performed in a two-dimensional box. It is shown that, for concentrations larger than a characteristic gel concentration, the morphology of the resulting spanning cluster at the gel time $t_g$ exhibits a crossover length $L_c$ between percolation ($l>L_c$) and aggregation ($l<L_c$). $L_c$ vanishes when increasing $c$, and, at a critical concentration value $c_p$ (where $L_c \rightarrow 0$) the entire spanning cluster scales as the percolating cluster obtained by standard percolation. Even if for $c>c_p$ the long-range correlations are similar to that of percolation, the vanishing links in the structure suggest that an homogeneous regime appears at small scales.