Critical point for de-mixing of binary hard spheres

TL;DR

This paper introduces a two-level simulation approach to accurately locate the critical demixing point in binary hard sphere mixtures, revealing unexpected size ratio effects linked to three-body interactions.

Contribution

The study develops a coarse-grained model with two-body and three-body interactions and applies it within a two-level simulation to determine the critical point of demixing.

Findings

Critical point depends strongly on size ratio

Three-body interactions influence demixing behavior

Universal form matching confirms critical point location

Abstract

We use a two-level simulation method to analyse the critical point associated with demixing of binary hard sphere mixtures. The method exploits an accurate coarse-grained model with two-body and three-body effective interactions. Using this model within the two-level methodology allows computation of properties of the full (fine-grained) mixture. The critical point is located by computing the probability distribution for the number of large particles in the grand canonical ensemble, and matching to the universal form for the $3d$ Ising universality class. The results have a strong and unexpected dependence on the size ratio between large and small particles, which is related to three-body effective interactions, and the geometry of the underlying hard sphere packings.