Freezing of polydisperse hard spheres

Abstract

Modern density functional theory is used to study the freezing of a polydisperse liquid of hard spheres into both face centered cubic (fcc) and hexagonally close packed (hcp) crystals. Two physically relevant, continuous distributions of particle size are studied: the gamma (or Schulz) distribution and the Gaussian distribution. The structure of a liquid of polydisperse hard spheres can be calculated analytically—and quite accurately—from the approximate Percus–Yevick integral equation. For both distributions we find that when the standard deviation of the particle size distribution exceeds approximately 5% of the mean size, the liquid no longer freezes into a crystalline array. Despite the approximations involved in the interactions between the particles in our model, this result is in agreement with experiments on real colloidal suspensions.