Critical packing fraction at the phase separation transition in hard-core mixtures

TL;DR

This paper links the phase separation transition in binary hard-core mixtures to bond percolation, enabling estimation of critical packing fractions based on size ratio and composition, with predictions validated by simulations.

Contribution

It introduces a theoretical approach connecting phase separation to percolation, providing accurate predictions for various object shapes and mixture compositions.

Findings

Theoretical predictions match numerical simulations closely.

Critical packing fraction depends on size ratio and composition.

Method applies to different object shapes.

Abstract

In this paper, I relate the phase separation transition in binary hard-core mixtures in the limit of small size ratio to a bond percolation transition. It allows to estimate the critical packing fraction at the transition as a function of the size ratio and the composition of the mixture for different shapes of objects. The theoretical predictions are in excellent quantitative agreement with numerical simulations of binary parallel hard squares mixtures.