Free-volume theory of the freezing of polydisperse hard-sphere mixtures: Initial preparation, fractionation, and terminal polydispersity

Abstract

The freezing of hard-sphere mixtures of arbitrary polydispersity is studied within a van der Waals-type free-volume approximation. The present theory is simple enough to allow for a thorough numerical investigation of all the polydispersity effects on the order–disorder transition of hard spheres. Within this context we have studied the influence on the order–disorder transition of the initial preparation, the subsequent fractionation, and the possible terminal polydispersity. It is found that the order–disorder transition occupies a finite domain of the initial density–initial polydispersity plane and the frontier of this domain is determined. Considerable variation within this domain is found with respect to the initial density, while the influence of the specific form of the initial size-distribution is found to be only marginal.