Flocculation and percolation in reversible cluster-cluster aggregation

Off-lattice dynamic Monte-Carlo simulations were done of reversible cluster-cluster aggregation for spheres that form rigid bonds at contact. The equilibrium properties were found to be determined by the life time of encounters between two particles (t(e)). t(e) is a function not only of the probability to form or break a bond, but also of the elementary step size of the Brownian motion of the particles. In the flocculation regime the fractal dimension of the clusters is d(f)=2.0 and the size distribution has a power law decay with exponent tau=1.5. At larger values of t(e) transient gels are formed. Close to the percolation threshold the clusters have a fractal dimension d(f)=2.7 and the power law exponent of the size distribution is tau=2.1. The transition between flocculation and percolation occurs at a characteristic weight average aggregation number that decreases with increasing volume fraction.