# Equation of state of polydisperse hard-disk mixtures in the high-density regime

## TL;DR

This paper proposes a method to relate the equation of state of polydisperse hard-disk mixtures to that of monocomponent fluids, validated through molecular dynamics simulations in high-density regimes, including metastable states.

## Contribution

It introduces a novel approach linking mixture and monocomponent equations of state, validated with extensive simulations across various size distributions.

## Key findings

- Excellent collapse of data curves in stable regions.
- Good performance of the approach in metastable regimes.
- Size distribution variance > 0.01 prevents crystallization.

## Abstract

A proposal to link the equation of state of a monocomponent hard-disk fluid to the equation of state of a polydisperse hard-disk mixture is presented. Event-driven molecular dynamics simulations are performed to obtain data for the compressibility factor of the monocomponent fluid and of 26 polydisperse mixtures with different size distributions. Those data are used to assess the proposal and to infer the values of the compressibility factor of the monocomponent hard-disk fluid in the metastable region from those of mixtures in the high-density region. The collapse of the curves for the different mixtures is excellent in the stable region. In the metastable regime, except for two mixtures in which crystallization is present, the outcome of the approach exhibits a rather good performance. The simulation results indicate that a (reduced) variance of the size distribution larger than about $0.01$ is sufficient to avoid crystallization and explore the metastable fluid branch.