Gel formation by reversible cluster-cluster aggregation

Based on the reversible diffusion-limited cluster-cluster aggregation (DLCA) algorithm, a model for gel formation is proposed, where the interaction energy between particles is considered as a parameter. Unlike the irreversible DLCA models, which study only rigid motion of the clusters, the reversible DLCA model simulates explicitly the kinetics of the particles of the clusters, such as restructuring within the same cluster or breaking away from it. Precisely because of the decrease in the compactness of the clusters with interaction energy epsilon between the particles, our simulation reveals that the sol-gel transition point c(g) of the particle concentration decreases with increasing epsilon. The most important result of our study is that the value of c(g) is greater than zero and independent of the system size (i.e., the side length L of the two-dimensional square lattice) when the interaction energy epsilon is below 1.5. The zero-c(g) difficulty encountered by the irreversible DLCA models is therefore removed. In addition, the fractal dimension D of the clusters is found to decrease with epsilon and converge to the value obtained by irreversible DLCA models when epsilon goes to infinity.