ar X iv : c on d - m at / 9 50 40 44 v 1 1 1 A pr 1 99 5 The Sol - Gel Process Simulated by Cluster - Cluster Aggregation
نویسنده
چکیده
The pair-correlation function g(r, t) and its Fourier transform, the structure factor S(q, t), are 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 ξ exhibits a crossover close to the gel time tg which depends on the volumic fraction c. In this model tg tends to infinity when the box size L tends to infinity. For systems of finite size, it is shown numerically that, when t < tg, the wave vector qm, at which S(q, t) has a maximum, decreases as S(qm, 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 n̄ is also investigated. Our numerical results are in qualitative agreement with small angle scattering experiments in several systems.
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