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

The formation of small crystallites is governed by two competing factors: t he free energy gained upon transferring constituent atoms, molecules or col loidal particles from the metastable liquid to the more stable solid, and t he free energy needed to create the surface area of the crystallite(1). Bec ause the ratio of surface area to bulk is large for small particles, small crystallites dissolve spontaneously under conditions where larger crystalli tes are stable and macroscopic crystal growth occurs only if spontaneously formed crystallites exceed a critical minimum size. On theoretical grounds( 1), the probability of forming such critical crystal nuclei is expected to increase rapidly with supersaturation. However, experiments show(1,2) that the rate of crystal nucleation in many systems goes through a maximum as th e 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 pro bability that critical nuclei will form itself goes through a maximum as th e supersaturation is increased. We rnd 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 supersatur ations should yield colloidal glasses that are truly amorphous, rather than nano-crystalline.