Demixing in a single-peak distributed polydisperse mixture of hard spheres

TL;DR

This paper analytically investigates the phase behavior of polydisperse mixtures of hard spheres, revealing conditions under which they demix or remain mixed, with implications for experimental systems.

Contribution

It derives the spinodal for polydisperse mixtures and shows that such mixtures can demix depending on the approximation used and the size distribution.

Findings

In Percus-Yevick approximation, the mixture never demixes.

In Boublik-Mansoori-Carnahan-Starling-Leland approximation, it demixes with wide log-normal distributions.

Log-normal distributions can cause phase separation despite being unimodal.

Abstract

An analytic derivation of the spinodal of a polydisperse mixture is presented. It holds for fluids whose excess free energy can be accurately described by a function of a few moments of the size distribution. It is shown that one such mixture of hard spheres in the Percus-Yevick approximation never demixes, despite its size distribution. In the Boublik-Mansoori-Carnahan-Starling-Leland approximation, though, it demixes for a sufficiently wide log-normal size distribution. The importance of this result is twofold: first, this distribution is unimodal, and yet it phase separates; and second, log-normal size distributions appear in many experimental contexts. The same phenomenon is shown to occur for the fluid of parallel hard cubes.