Predictive model for diffusion-limited aggregation kinetics of nanocolloids under high concentration.

Smoluchowski's equation for the rate of aggregation of colloidal particles under diffusion-limited conditions has set the basis for the interpretation of kinetics of aggregation phenomena. Nevertheless, its use is limited to sufficiently dilute conditions. In this work we propose a correction to Smoluchowski's equation by using a result derived by Richards ( J. Phys. Chem. 1986 , 85 , 3520 ) within the framework of trapping theory. This corrected aggregation kernel, which accounts for concentration dependence effects, has been implemented in a population-balance equations scheme and used to model the aggregation kinetics of colloidal particles undergoing diffusion-limited aggregation under concentrated conditions (up to a particle volume fraction of 30%). The predictions of population balance calculations have been validated by means of Brownian dynamic simulations. It was found that the corrected kernel can very well reproduce the results from Brownian dynamic simulations for all concentration values investigated, and is also able to accurately predict the time required by a suspension to reach the gel point. On the other hand, classical Smoluchowski's theory substantially underpredicts the rate of aggregation as well as the onset of gelation, with deviations becoming progressively more severe as the particle volume fraction increases.