Diffusive growth of polydisperse hard-sphere crystals

Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e., mixtures of infinitely many components with sizes drawn from a continuous distribution. We model the crystallization of hard-sphere colloids (with/without attractions) from an initially amorphous phase. Although the polydisperse hard-sphere phase diagram has been widely studied, it is not straightforwardly applicable to real colloidal crystals, since they are inevitably out of equilibrium. The process by which colloidal crystals form determines the size distribution of the particles that comprise them. Once frozen into the crystal lattice, the particles are caged so that the composition cannot subsequently relax to the equilibrium optimum. We predict that the mean size of colloidal particles incorporated into a crystal is smaller than anticipated by equilibrium calculations. This is because small particles diffuse fastest and therefore arrive at the crystal in disproportionate abundance.