Kinetic modeling of aggregation and gel formation in quiescent dispersions of polymer colloids

In this work, a methodology suitable for the description of aggregation and gel formation processes of polymeric colloidal dispersions in quiescent conditions is presented. The modeling of aggregation is based on the use of populations balance equations to describe the time evolution of the aggregate distribution. Monte-Carlo simulations are used to generate the structural properties of individual aggregates, which are necessary to compute the average radius of gyration and hydrodynamic radius that are compared to the values measured using light scattering. The agreement between model predictions and measured sizes is good in both diffusion-limited and reaction-limited conditions. For the description of progress toward gel formation, the cumulatively occupied volume, a measure of the fraction of space occupied by the clusters, is defined. Due to the fractal nature of clusters, during the aggregation the system can reach a condition of space filling, after which the formation of gel is a result of the interconnection of the clusters. It is found that in diffusion-limited conditions the interconnection step is much faster than the preceding aggregation, while in reaction-limited conditions the aggregation and the interconnection are of comparable duration.