Pseudo-steady rates of crystal nucleation in suspensions of charged colloidal particles

Abstract

We develop an analytical model to describe crystal nucleation in suspensions of charged colloidal particles. The particles are assumed to interact with a repulsive hard-core Yukawa potential. The thermodynamic properties of the suspensions are determined by mapping onto an effective hard-sphere system using perturbation theory. Hydrodynamic effects are calculated by approximating particle interactions with the excluded shell potential. The rates of particle aggregation and dissociation from cluster surfaces in supersaturated suspensions are determined by solving the diffusion and Smoluchowski equations, respectively, which allow the calculation of pseudo-steady rates of crystal nucleation. By decoupling thermodynamic and hydrodynamic effects, we find intriguing non-monotonic dependencies of the nucleation rate on the strength and the range of particle repulsions. In particular, we find that the rate at any effective hard-sphere volume fraction can be lower than that of the hard-sphere system at that volume fraction. Model calculations are in qualitative agreement with recent experiments and semi-quantitative agreement with simulations.