The sol to gel transition in irreversible particulate systems

A review of the process by which irreversible aggregation of solid particles creates fractal aggregates which eventually fill the entire system volume to form a gel, the sol to gel transition, is presented. Both simulation and experiment present a coherent description of the kinetics and resulting morphologies of this process. Enhanced kinetics occurs when the system is cluster dense. Surprisingly, the enhanced kinetics is governed by the mean-field Smoluchowski equation deep into the aggregation process, displays universality with cluster volume fraction (or, equivalently the ratio of cluster separation to size, or time normalized by the gel time), and is described by one parameter, the aggregation kernel homogeneity. Aggregates show canonical cluster–cluster morphology until the point where the cluster volume fraction is unity; then hybrid superaggregates with fractal dimensions of ca. 1.8 over small length scales and 2.6 over large length scales form.