Generalized coupling parameter expansion: Application to square well and Lennard-Jones fluids

Abstract

The coupling parameter expansion in thermodynamic perturbation theory of simple fluids is generalized to include the derivatives of bridge function with respect to coupling parameter. 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 Helmholtz free energy density of Hard-Sphere reference system has improved the liquid-vapor phase diagram (LVPD) over that obtained from IET with the same bridge function. The derivatives of the bridge function are seen to have significant effect on the liquid part of the LVPD. For extremely narrow SW fluids, we found that the third order theory is more accurate than the higher order versions. However, considering the convergence of the perturbation series, we concluded that the accuracy of the third order version is a spurious result. We also obtained the surface tension for 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.

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“…[58] Theoretical advances in models based on statistical thermodynamics, molecular simulation, ab initio methods, etc., have allowed the unprecedented evolution from empirical EoS to those with robust theoretical bases [59]- [63]. The variety of equations of state with strong molecular bases is very wide, and they are generally based on one of two theoretical lines that were already mentioned above: (1) integral equation theory (IET), involving the solution of the Ornstein-Zernike equation [40] by means of a closure model such as Percus-Yevick [41] or hypernetted-chain equation [42], [64], or (2) thermodynamic perturbation theory [33]- [39]. Though EIT could be more accurate and rigorous in describing, for example, the molecular structure of fluids (i.e., the RDF), it is quite complex and has the main disadvantage that, for example, closure methods generally have no solution within the twophase region.…”