Phase behavior of weakly polydisperse sticky hard spheres: Perturbation theory for the Percus-Yevick solution

TL;DR

This paper develops a perturbation theory to analyze how slight size variations in sticky hard spheres influence their phase behavior, providing predictions for phase coexistence and fractionation that can be validated experimentally.

Contribution

It introduces a perturbation expansion approach for the Percus-Yevick solution to account for polydispersity effects on phase behavior of sticky hard spheres.

Findings

Size polydispersity shifts the cloud and shadow curves.

Polydispersity affects the extent of size fractionation.

The model applies to colloid-polymer mixtures like the Asakura-Oosawa system.

Abstract

We study the effects of size polydispersity on the gas-liquid phase behaviour of mixtures of sticky hard spheres. To achieve this, the system of coupled quadratic equations for the contact values of the partial cavity functions of the Percus-Yevick solution is solved within a perturbation expansion in the polydispersity, i.e. the normalized width of the size distribution. This allows us to make predictions for various thermodynamic quantities which can be tested against numerical simulations and experiments. In particular, we determine the leading-order effects of size polydispersity on the cloud curve delimiting the region of two-phase coexistence and on the associated shadow curve; we also study the extent of size fractionation between the coexisting phases. Different choices for the size-dependence of the adhesion strengths are examined carefully; the Asakura-Oosawa model of a mixture of polydisperse colloids and small polymers is studied as a specific example.