Transition between flocculation and percolation of a diffusion-limited cluster-cluster aggregation process using three-dimensional Monte Carlo simulation

By Monte Carlo simulation we study the sol-gel transition of the diffusion-limited cluster aggregation process. We clearly show the absence of a critical concentration for gel formation and the existence of a well-defined gel time (${\mathit{t}}_{\mathit{g}}$) with a power dependence on the volume fraction (${\mathrm{\phi }}_0$): ${\mathit{t}}_{\mathit{g}}$∝${\mathrm{\phi }}_0^{\mathrm{-}2.85}$. We point out three main regimes of growth depending on the degree of overlap between the aggregates. In the very early stage when the aggregates have no overlap, the observed system behavior is in very good agreement with the predictions from the mean-field theory (flocculation regime). Close to the gel point there is a strong overlap between the aggregates and many critical quantities follow the same laws as those predicted by percolation theory. There is a smooth crossover between the two limiting situations due to a gradual interpenetration of the aggregates during the growth process. All throughout the growth process we found that networks built up by a dynamic random collision process have the same space filling properties as networks formed by a random distribution of matter.