Effect of polydispersity on the phase behavior of additive hard spheres in solution, part I

TL;DR

This paper presents a theoretical analysis of how polydispersity in the larger component of a binary hard sphere mixture influences phase behavior, including phase boundaries, critical points, and fractionation effects.

Contribution

It introduces a set of equations for phase diagrams of multi-component mixtures with polydispersity and compares their phase behavior to monodisperse mixtures, highlighting the impact of the largest species.

Findings

Largest species causes significant shift in phase boundary and critical point.

Polydispersity induces fractionation, with smaller species favoring the phase enriched in smaller particles.

Polydisperse mixtures show higher volume fraction in the phase with smaller species.

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 modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten 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 (the binodal), the critical point and the spinodal. We vary the distribution of the polydisperse component in skewness, modality, polydispersity and number of sub-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 the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher volume fraction compared to the monodisperse mixture.