Relating colloidal particle interactions to gel structure using Brownian dynamics simulations and the Fuchs stability ratio

Brownian dynamics simulations of aggregation of hard-sphere dispersions at intermediate volume fractions (∼3–10 vol%) have been performed. A long-range activation energy for aggregation was incorporated. The bonds formed were irreversible and flexible. Cluster growth rate and fractal properties of the gel matrix could be related to particle interactions by using a Fuchs stability ratio $W_F.$ Although this approach is expected to apply only to the very early stages of gelation, $W_F$ was shown to be a useful parameter, especially for predicting gel matrix parameters like the fractal dimensionality $D_f$ (which is a measure of the compactness of the clusters in the intermediate or fractal length scale regime) and the correlation length ξ (which is a measure of the average gel pore size). The number of aggregates, $N_{\mathrm{agg}},$ was found to be a convenient measure of the stage of aggregation for the range of volume fractions and interactions studied. For high values of $W_F,$ the value of $D_f$ was more generic (i.e., less dependent of $W_F$ or φ). In addition, the fractal parameters were less dependent on $W_F$ at higher φ. These observations can be explained by the limited formation of (diffusion-kinetics type) depletion zones in the presence of repulsive barriers compared to purely attractive systems.