Microscopic description of the liquid-gas coexistence curve for Morse fluids in the immediate vicinity of the critical point

TL;DR

This paper develops an analytical model for the liquid-gas coexistence curve near the critical point of Morse fluids, incorporating non-Gaussian fluctuations, and compares results with Monte Carlo simulations for sodium.

Contribution

It introduces a new analytical procedure that accounts for non-Gaussian fluctuations to accurately describe the coexistence curve near the critical point.

Findings

Including the temperature-dependent analytical term improves agreement with simulation data.

Better fit is achieved when the term is included in the liquid branch but omitted in the gas branch.

The approach offers insights into critical phenomena in complex fluid systems.

Abstract

The present work is aimed at investigating the behavior of Morse fluids in the immediate vicinity of the critical point within the framework of a cell model. This region is of both fundamental and practical importance, yet presents analytical challenges due to the significant influence of order parameter fluctuations. An analytical procedure is developed to construct the upper part of the liquid-gas coexistence curve and calculate its diameter, incorporating the non-Gaussian (quartic) distribution of fluctuations. An explicit expression is derived for the temperature-dependent analytical term appearing in the expression for the rectilinear diameter. The numerical evaluation of the relevant quantities is carried out using Morse potential parameters representative of sodium. The coexistence curve is constructed both with and without the inclusion of the analytical temperature-dependent term in the calculation. A specific condition is identified under which the agreement between the presented binodal branches and Monte Carlo simulation data from other study, extrapolated to the immediate vicinity of the critical point, is improved. It is shown that better agreement is achieved when the analytical term is included in the calculation of the liquid branch and omitted in the gas branch. The proposed analytical approach may provide useful insight for the theoretical study of critical phenomena in more complex fluid systems.