Non-ideal diffusion effects, short-range ordering, and unsteady-state effects strongly influence Brownian aggregation...

Brownian aggregation rates are determined for concentrated dispersions of interacting particles with Brownian dynamics (BD) simulations and various theoretical models. Using simulation results as benchmarks, the predictions of the classical Fuchs-Smoluchowski (FS) model are shown to be quite inaccurate for concentrated dispersions. A new aggregation model is presented which provides significantly improved predictions. This model is developed on the basis of the fundamental measure theory (FMT) which is a rigorous "liquid-state" dynamic density-functional theory (DDFT) approach. It provides a major improvement of the FS model by considering short-range ordering, non-ideal diffusion, and unsteady-state effects. These were recently shown by the authors to play important roles in Brownian aggregation of hard spheres at high concentrations. Two types of interparticle interaction potentials are examined, the purely attractive van der Waals potential and the DLVO potential which includes van der Waals attraction and electrostatic double layer repulsion. For dispersions of particles with purely attractive interactions, the FS model underpredicts the aggregation rates by up to 1000 fold. In the presence of strong interparticle repulsive forces, its predictions are in fair agreement with the BD simulation results for dilute systems with particle volume fractions ϕ < < 0.1. In contrast, the predictions of the new FM-DDFT based model compare favorably with the BD simulation results, in both cases, up to ϕ = 0.3. A new quantitative measure for colloidal dispersion stability, different from the classical FS stability ratio, is proposed on the basis of aggregation half-times. Hence, a better mechanistic understanding of Brownian aggregation is obtained for concentrated dispersions of particles with either attractive or repulsive interactions, or both.