Freezing in polydisperse colloidal suspensions

The phase behaviour of a polydisperse mixture of hard spheres is examined within a moment-density approximation. The role of size fractionation and the difference between quenched and annealed phase behaviour is outlined. The quenched phase diagram shows a terminal level of polydispersity above which no fluid-crystal transition occurs. It is demonstrated that this singularity arises from the re-entrant nature of the freezing transition at high polydispersities. In the annealed situation by contrast, the polydisperse crystal is spinodally unstable with respect to fluctuations in polydispersity. The direction of the instability suggests that the equilibrium annealed state is a fractionated crystal.