Monte Carlo simulation of particle aggregation and gelation: I. Growth, structure and size distribution of the clusters

Lattice and off-lattice Monte Carlo simulations of diffusion-limited cluster aggregation and gelation were done over a broad range of concentrations. The large-scale structure and the size distribution of the clusters are characterized by a crossover at a characteristic size ($m_{\rm c}$). For $m < m_{\rm c}$, they are the same as obtained in a dilute DLCA process and for $m \gg m_{\rm c}$ they are the same as obtained in a static percolation process. $m_{\rm c}$ is determined by the overlap of the clusters and decreases with increasing particle concentration. The growth rate of large clusters is a universal function of time reduced by the gel time. The large-scale structural and temporal properties are the same for lattice and off-lattice simulations. The average degree of connectivity per particle in the gels formed in off-lattice simulations is independent of the concentration, but its distribution depends on the concentration