Fluctuating Bond Aggregation: a Numerical Simulation of Neutrally-Reacted Silica Gels

Numerical simulations of gel formation using the newly developed Fluctuating Bond Aggregation (FBA) algorithm are presented. This algorithm allows possible cluster deformations during aggregation by considering a tuning bond flexibility parameter $F$. Three-dimensional computer simulations show that for large $F$, there is a well-defined threshold value of concentration $c$ below which the realization of all intra-aggregate bond possibilities prevents the formation of a gelling network. For $c>c_{\rm g}$, a true sol-gel transition occurs at a characteristic time $t_{\rm g}$, i.e. an infinite cluster (self connected through the boundary conditions) appears. In contrast to the diffusion limited cluster-cluster aggregation (DLCA) model, $t_{\rm g}$ does not increase as the box size increases. Comparison between numerical results and measurements of the gelation time of silica gels prepared in container of various sizes suggests that gelation without addition of catalyst (neutrally-reacted) and under base catalyzed conditions corresponds to large and small $F$, respectively. Moreover, for large $F$ values, we calculate scattering intensity curves for FBA gels and find that they agree with experimental SANS data for neutrally-reacted silica aerogels