SOL-GEL PROCESS SIMULATION BY CLUSTER-CLUSTER AGGREGATION

The pair-correlation function, g(r , t), and its Fourier transform, the structure factor, S(q, t), were computed during the gelation process of identical spherical particles using the diffusion-limited cluster-cluster aggregation model in a box. This numerical analysis shows that the time evolution of the characteristic cluster size, xi, exhihits a crossover close to the gel time, t(g), which depends on the volumic fraction, c. In this model, t(g) tends to infinity when the hox size, L, tends to infinity. For systems of finite size, it is shown numerically that, when t < t(g), the wave vector, q(m), at which S(q, t) has a maximum, decreases as S(q(m), t)-1/D, where D is an apparent fractal dimension of clusters, as measured from the slope of S(q, t), The time evolution of the mean number of particles per cluster, ($) over bar n, was also investigated. Numerical results are in qualitative agreement with small-angle scattering experiments in several systems.