Aerogelation process simulation by a cluster-cluster aggregation algorithm

A ballistically-limited cluster-cluster aggregation (BLCA) model was developed to simulate aerogelation processes. In the model, the clusters move along linear paths, in random directions, in a finite box. When two aggregates contact each other, they are combined irreversibly to form a larger aggregate. As expected, the simulations show that the aggregation time is much shorter than that obtained with diffusion-limited cluster-cluster aggregation (DLCA) models. The minimum concentration, c(g), required for gel formation scales as LD-3, where L is the length of the sides of the box and D is the fractal dimension of the aggregates (D approximate to 1.95). For a concentration c larger than c(g), the mean free path of the aggregating clusters, [lambda], scales as c(-1.1). The pair correlation function g(r) and its Fourier transform S(q) were determined for the single large aggregates formed at the end of the simulations. These functions indicate that there is a characteristic length xi which scales as c(1/(D-3)). As observed previously for the DLCA model, there is a discrepancy between the fractal dimensions obtained from g(r) and S(q).