Vapor-liquid equilibrium and equation of state of two-dimensional fluids from a discrete perturbation theory

TL;DR

This paper develops an analytical equation of state for two-dimensional fluids using a discrete perturbation theory, validated against simulations for Lennard-Jones and Yukawa potentials, advancing understanding of low-dimensional fluid properties.

Contribution

It introduces a new analytical Helmholtz free energy expression for 2D fluids within the Barker-Henderson framework and implements it in a discrete perturbation theory for general potentials.

Findings

The equation of state shows semi-quantitative agreement with simulation data.

Validated against existing and new simulation results for 2D Lennard-Jones and Yukawa fluids.

Provides a theoretical tool for studying 2D fluid thermodynamics.

Abstract

The interest in the description of the properties of fluids of restricted dimensionality is growing for theoretical and practical reasons. In this work, we have firstly developed an analytical expression for the Helmholtz free energy of the two-dimensional square-well fluid in the Barker--Henderson framework. This equation of state is based on an approximate analytical radial distribution function for $d$-dimensional hard-sphere fluids ($1\leq d\leq 3$) and is validated against existing and new simulation results. The so-obtained equation of state is implemented in a discrete perturbation theory able to account for general potential shapes. The prototypical Lennard-Jones and Yukawa fluids are tested in its two-dimensional version against available and new simulation data with semi-quantitative agreement.