Pseudo-steady rates of crystal nucleation in suspensions of charged colloidalparticles

Abstract

We develop an analytical model to describe crystal nucleation in suspensions ofcharged colloidal particles. The particles are assumed to interact with a repulsivehard-core Yukawa potential. The thermodynamic properties of the suspensions aredetermined by mapping onto an effective hard-sphere system using perturbationtheory. Hydrodynamic effects are calculated by approximating particleinteractions with the excluded shell potential. The rates of particle aggregationand dissociation from cluster surfaces in supersaturated suspensions aredetermined by solving the diffusion and Smoluchowski equations, respectively,which allow the calculation of pseudo-steady rates of crystal nucleation. Bydecoupling thermodynamic and hydrodynamic effects, we find intriguingnon-monotonic dependencies of the nucleation rate on the strength and the rangeof particle repulsions. In particular, we find that the rate at any effectivehard-sphere volume fraction can be lower than that of the hard-sphere system atthat volume fraction. Model calculations are in qualitative agreement withrecent experiments and semi-quantitative agreement with simulations.