Phase diagram of the hard-sphere potential model in three and four dimensions using a pseudo-hard-sphere potential

TL;DR

This study evaluates the effectiveness of a continuous pseudo-hard-sphere potential in replicating the phase behavior and equation of state of true hard-sphere systems in three and four dimensions, using simulations and theoretical models.

Contribution

It extends the validation of the pseudo-hard-sphere potential to higher dimensions and across fluid-solid coexistence, comparing simulation results with theoretical predictions.

Findings

The pseudo-hard-sphere potential accurately reproduces the hard-sphere equation of state in three and four dimensions.

Simulation results align well with theoretical models across the phase diagram.

The approach facilitates simulation of hard-sphere systems without discontinuous forces.

Abstract

The hard-sphere potential has become a cornerstone in the study of both molecular and complex fluids. Despite its mathematical simplicity, its implementation in fixed time-step molecular simulations remains a formidable challenge due to the discontinuity at contact. To circumvent the issues associated with the ill-defined force at contact, a continuous potential--referred to here as the pseudo-hard-sphere (pHS) potential--has recently been proposed [J. Chem, Phys. 149, 164907 (2018)]. This potential is constructed to match the second virial coefficient of the hard-sphere potential and is expected to mimic its thermodynamic properties. However, this hypothesis has only been partially validated within the fluid region of the phase diagram for hard-sphere dispersions in two and three dimensions. In this contribution, we examine the ability of the continuous pHS potential to reproduce the equation of state of a hard-sphere fluid, not only in the fluid phase but also across the fluid-solid coexistence region. Our focus is primarily on hard-sphere systems in three and four dimensions. We compare the results obtained from Brownian dynamics simulations of the pHS potential with those derived from refined event-driven simulations of the corresponding hard-sphere potential. Furthermore, we provide a comparative analysis with theoretical equations of state based on both mean-field and integral equation approximations.