Effect of polydispersity on the phase behavior of non-additive hard spheres in solution, part II

TL;DR

This paper provides a theoretical analysis of how polydispersity and non-additivity influence the phase behavior of asymmetric binary hard sphere mixtures, revealing conditions for multi-phase separation and demixing.

Contribution

It introduces a set of equations for phase diagrams of multi-component mixtures with polydispersity and non-additivity, and compares phase behavior with monodisperse systems.

Findings

Increased incompatibility leads to three-phase separation.

Phase boundary shape depends on non-additivity and size distribution.

Polydisperse component demixes into an additional phase with increased incompatibility.

Abstract

We study the theoretical phase behavior of an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modeled in terms of the second virial coefficient and can be additive hard sphere (HS) or non-additive hard sphere (NAHS) interactions. The polydisperse component is subdivided into two sub-components and has an average size ten or three times the size of the monodisperse component. We give the set of equations that defines the phase diagram for mixtures with more than two components in a solvent. We calculate the theoretical liquid-liquid phase separation boundary for two phase separation (the binodal) and three phase separation, the plait point, and the spinodal. We vary the distribution of the polydisperse component in skewness and polydispersity, next to that we vary the non-additivity between the sub-components as well as between the main components. We compare the phase behavior of the polydisperse mixtures with binary monodisperse mixtures for the same average size and binary monodisperse mixtures for the same effective interaction. We find that when the compatibility between the polydisperse sub-components decreases, three-phase separation becomes possible. The shape and position of the phase boundary is dependent on the non-additivity between the subcomponents as well as their size distribution. We conclude that it is the phase enriched in the polydisperse component that demixes into an additional phase when the incompatibility between the sub-components increases.