Rational-function approximation for fluids interacting via piece-wise constant potentials

Santos Santos,Yuste Yuste,Lopez De Haro Lopez De Haro

doi:10.5488/cmp.15.23602

Abstract

The structural properties of fluids whose molecules interact via potentials with a hard-core plus n piece-wise constant sections of different widths and heights are derived using a (semi-analytical) rational-function approximation method. The results are illustrated for the cases of a square-shoulder plus square-well potential and a shifted square-well potential and compared both with simulation data and with those that follow from the (numerical) solutions of the Percus-Yevick integral equation.

Highlights

Simple models of intermolecular interaction have proven to be useful tools in understanding diverse phenomena in real fluids
In this paper we have proposed a method of deriving the structural properties of a particular kind of discrete-potential fluids, namely the ones in which molecules interact via a potential consisting of a hard-core plus n-step constant sections of different heights and widths
Two approximations were considered: one in which some unknown constants are fixed at their zero density value (RFA1) and one which enforces the continuity of the derivative of the cavity function (RFA2)

Summary

Introduction

Simple models of intermolecular interaction have proven to be useful tools in understanding diverse phenomena in real fluids. In previous papers [22, 40], following a methodology that, approximate, has proven successful for many other systems [41], the structural properties of the square-well and the square-shoulder fluids were derived. The main aim of this paper is to use a similar methodology, referred to as the method of rational-function approximation (RFA), to generalize the previous results and derive the structural properties of fluids whose molecules interact via potentials with a hard-core plus piece-wise constant sections of different widths and heights. The consistency of the present approach with the results for both the square-well and square-shoulder results is proven in an appendix

Fundamental relations

The general n-step case

Particularization to two-step potentials

Illustration of the approximation for two-step potentials

Conclusions