Sol-gel transition of reversible cluster-cluster aggregations

This paper investigates the sol-gel transition of reversible cluster-cluster aggregations in terms of numerical simulations. The temperature dependence of the sol-gel transition point $c_g$ is calculated by forming clusters with different particle concentrations for two-dimensional $\mathrm{}(d=2\mathrm{})\mathrm{}$ and three-dimensional $\mathrm{}(d=3\mathrm{})\mathrm{}$ systems. We present phase diagrams on sol-gel transitions from these calculations. The fractal dimension $D_f$ for $d=3\mathrm{}$ reversible cluster-cluster aggregations is calculated at the sol-gel transition point, which gives $D_f=2.4\mathrm{}\pm 0.1,$ apparently larger than that of diffusion-limited cluster-cluster aggregations. These results show good agreement with those obtained by small-angle x-ray scattering experiments.