Percolation in cluster-cluster aggregation processes

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 ${\mathit{t}}_{\mathit{g}}$ exhibits a crossover length ${\mathit{I}}_{\mathit{c}}$ between percolation (l>${\mathit{L}}_{\mathit{c}}$) and aggregation (l<${\mathit{L}}_{\mathit{c}}$). ${\mathit{L}}_{\mathit{c}}$ vanishes when increasing c, and, at a critical concentration value ${\mathit{c}}_{\mathit{p}}$≃0.5 (where ${\mathit{L}}_{\mathit{c}}$→0) the entire spanning cluster scales as the percolating cluster obtained by standard percolation. Even if for 0.5<c<0.8 the long-range correlations seem to be similar to that of percolation, the scaling mass analysis and the vanishing links in the structure suggest that a homogeneous regime appears at small scales. © 1996 The American Physical Society.