Generalized Coupling Parameter Expansion: Application to Square-Well and Lennard Jones Fluids

TL;DR

This paper extends the coupling parameter expansion in thermodynamic perturbation theory to include bridge function derivatives, applying it to square-well and Lennard-Jones fluids, achieving accurate predictions of structural and thermodynamic properties even in challenging regions.

Contribution

The authors develop a generalized coupling parameter expansion incorporating bridge function derivatives and demonstrate its effectiveness for square-well and Lennard-Jones fluids.

Findings

Accurately reproduces radial distribution functions from IET and simulations.

Improves liquid-vapor phase diagram predictions for square-well fluids.

Matches equation of state for Lennard-Jones fluids with negligible deviation.

Abstract

The coupling parameter expansion in thermodynamic perturbation theory of simple fluids is generalized to include the derivatives of bridge function. We applied seventh order version of the theory to Square-Well (SW) and Lennard-Jones (LJ) fluids using Sarkisov Bridge function. In both cases, the theory reproduced the radial distribution functions obtained from integral equation theory (IET) and simulations with good accuracy. Also, the method worked inside the liquid-vapor coexistence region where the IETs are known to fail. In the case of SW fluids, the use of Carnahan-Starling expression for free energy density of Hard-Sphere reference system has improved the liquid-vapor phase diagram (LVPD) over that obtained from IET. We also obtained the surface tension of SW fluids of various ranges. Results of present theory and simulations are in good agreement. In the case of LJ fluids, the equation of state obtained from the present method matched with that obtained from IET with negligible deviation. We also obtained LVPD of LJ fluid from virial and energy routes and found that there is slight inconsistency between the two routes. The applications lead to the following conclusions. In cases where reference system properties are known accurately, the present method gives results which are very much improved over those obtained from the IET with the same bridge function. In cases where reference system data is not available, the method serves as an alternative way of solving the Ornstein-Zernike equation with a given closure relation with the advantage that solution can be obtained throughout the phase diagram with a proper choice of the reference system.