Equilibrium phase behavior of polydisperse hard spheres

TL;DR

This study accurately maps the phase behavior of polydisperse hard spheres, revealing no re-entrant melting and identifying a terminal polydispersity for solid phases, with implications for understanding complex phase coexistence.

Contribution

It provides the first complete phase diagram including fractionation effects for polydisperse hard spheres, challenging previous simplified models.

Findings

No re-entrant melting at high densities.

Fluid cloud curve extends to 14% polydispersity.

Terminal polydispersity for solids is around 7%.

Abstract

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energy expressions for the fluid and solid phases. Cloud and shadow curves, which determine the onset of phase coexistence, are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation effects. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or re-entrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus only be defined for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find in addition that coexistence of several solids with a fluid phase is also possible.