Computing Chemical Potential using the Phase Space Multi-histogram Method

TL;DR

This paper introduces a novel simulation method that uses a parameter-dependent potential to calculate free energy and chemical potential in hard particle systems, enabling detailed study of phase transitions.

Contribution

The method combines phase space multi-histogram techniques with a parametrized potential to accurately compute thermodynamic properties of hard particles.

Findings

Successfully applied to square platelet systems

Determined coexistence pressure for phase transition

Provides an intuitive approach for hard particle phase studies

Abstract

We present a new simulation method to calculate the free energy and the chemical potential of hard particle systems. The method relies on the introduction of a parameter dependent potential to smoothly transform between the hard particle system and the corresponding ideal gas. We applied the method to study the phase transition behavior of monodispersed infinitely thin square platelets. First, we equilibrated the square platelet system for different reduced pressures with a usual isobaric Monte Carlo (MC) simulation and obtained a reduced pressure-chemical potential plot. Then we introduce the parametrized potential to interpolate the system between the ideal gas and the hard particles. After selecting the potential, we performed isochoric MC runs, ranging from the ideal gas to the hard particle limit. Through an iterative procedure, we compute the free energy and the chemical potential of the square platelet system by evaluating the volume of the phase space attributed to the hard particles, and then we find the coexistence pressure of the system. Our method provides an intuitive approach to investigate the phase transitions of hard particle systems.