Note on the Perturbation Equation of State of Barker and Henderson

Abstract

Perturbation theory of equation of state due to Barker and Henderson is reformulated. This new formulation makes it possible to calculate the Helmholtz free energy of a fluid system analytically by perturbation relations of Barker and Henderson, without use of any approximation or need of any numerical table for the hard-sphere reference system other than the original Percus–Yevick approximations. The results are compared with the calculation of Barker and Henderson, and it is shown that the two agree with each other at all the temperatures which are compared, while the present method produces compressibilities slightly closer to the experimental and machine-calculated data. The results of the present method, based on average Percus–Yevick hard-sphere compressibilities, are also compared with the result of other theories of equation of state of simple fluids, molecular dynamics, and Monte Carlo calculations.

Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids

“…Therefore, it is natural to determine σ 0 so as to provide the least upper bound. This is precisely the variational scheme of Mansoori and Canfield [117,118] and Rasaiah and Stell [119], usually referred to as MC/RS, and originally implemented with the PY theory for G(s), Eq. (108).…”

Attractive energy contribution to nanoconfined fluids behavior: the normal pressure tensor

“…Such separation in configuration potential energy also separates these contributions in the pair-potential energy. For macroscopic systems there exist a variety of methods to perform perturbation or variational calculations to choose the reference potential energy function and its parameters (Mansoori et al 1969;Lan and Mansoori 1975;Barker and Henderson 1976;Kang et al 1985;Zhou 2006). However, the validity of such methods needs to be proven for nanosystems before we can use them.…”

“…In perturbation theory with analogy to potential energy the other thermodynamic properties may be separated into two parts. For example (Mansoori et al 1969) for pressure of the system we have:…”

“…Based on the statistical mechanical perturbation and variational theories, the pair-intermolecular potential energy may be separated in two parts (Mansoori et al 1969;Lan and Mansoori 1975;Barker and Henderson 1976;Kang et al 1985;Zhou 2006):…”

“…LennardJones model is shown to be a realistic model for simple molecular fluids in macroscopic systems and we assume to be equally valid for confined fluids in nanoslit pores. The theoretical basis of our approach is the statistical mechanical perturbation theory of fluids already developed and shown to be quite successful in predicting the behavior of macroscopic fluid systems (Mansoori et al 1969;Lan and Mansoori 1975;Barker and Henderson 1976;Kang et al 1985;Zhou 2006).…”