Reentrant Melting in Polydispersed Hard Spheres

The effect of polydispersity on the freezing transition of hard spheres is examined within a moment description. At low polydispersities a single fluid-to-crystal transition is recovered. With increasing polydispersity we find a density above which the crystal melts back into an amorphous phase. The range of densities over which the crystalline phase is stable shrinks with increasing polydispersity until, at a certain level of polydispersity, the crystal disappears completely from the equilibrium phase diagram. The two transitions converge to a single point which we identify as the polydisperse analog of a point of equal concentration. At this point, the freezing transition is continuous in a thermodynamic sense.