Virial coefficients and demixing of athermal nonadditive mixtures

TL;DR

This study calculates the fourth virial coefficient for binary nonadditive hard-sphere mixtures and uses it to analyze fluid-fluid coexistence, revealing instability towards crystallization in certain regimes relevant to colloidal systems.

Contribution

It introduces a new approach to predict fluid-fluid coexistence in nonadditive mixtures using the fourth virial coefficient and a $y$ expansion, validated against simulation data.

Findings

Fluid-fluid critical point is unstable in certain nonadditivity regimes.

The $y$ expansion effectively traces coexistence lines.

Results are relevant for colloidal mixture modeling.

Abstract

We compute the fourth virial coefficient of a binary nonadditive hard-sphere mixture over a wide range of deviations from diameter additivity and size ratios. Hinging on this knowledge, we build up a $y$ expansion [B. Barboy and W. N. Gelbart, J. Chem. Phys. {\bf 71}, 3053 (1979)] in order to trace the fluid-fluid coexistence lines which we then compare with the available Gibbs-ensemble Monte Carlo data and with the estimates obtained through two refined integral-equation theories of the fluid state. We find that in a regime of moderately negative nonadditivity and largely asymmetric diameters, relevant to the modelling of sterically and electrostatically stabilized colloidal mixtures, the fluid-fluid critical point is unstable with respect to crystallization.