Suppression of crystal nucleation in polydisperse colloids due to increase of the surface free energy

The formation of small crystallites is governed by two competing factors: the free energy gained upon transferring constituent atoms, molecules or colloidal particles from the metastable liquid to the more stable solid, and the free energy needed to create the surface area of the crystallite. Because the ratio of surface area to bulk is large for small particles, small crystallites dissolve spontaneously under conditions where larger crystallites are stable and macroscopic crystal growth occurs only if spontaneously formed crystallites exceed a critical minimum size. On theoretical grounds, the probability of forming such critical crystal nuclei is expected to increase rapidly with supersaturation. However, experiments show that the rate of crystal nucleation in many systems goes through a maximum as the supersaturation is increased. It is commonly assumed that the nucleation rate peaks because, even though the probability of forming critical nuclei increases with increasing concentration, the rate of growth of such nuclei decreases. Here we report simulations of crystal nucleation in suspensions of colloidal spheres with varying size distributions that show that the probability that critical nuclei will form itself goes through a maximum as the supersaturation is increased. We find that this effect, which is strongest for systems with the broadest particle size distribution, results from an increase with supersaturation of the solid-liquid interfacial free energy. The magnitude of this effect suggests that vitrification at high supersaturations should yield colloidal glasses that are truly amorphous, rather than nano-crystalline.