Structural properties of fluids interacting via piece-wise constant potentials with a hard core

TL;DR

This paper investigates the structural properties of fluids with molecules interacting through hard core plus piece-wise constant potentials, using a semi-analytic rational-function approximation, and compares its accuracy with integral equation theories and simulations.

Contribution

It extends a previous semi-analytic approximation method to more complex potentials and evaluates its accuracy against simulations and integral equations.

Findings

Rational-function approximation generally predicts more accurate radial distribution functions than Percus-Yevick.

The approximation is comparable or superior to hypernetted-chain theory at low to moderate densities.

Its accuracy diminishes at high densities with wider wells and barriers.

Abstract

The structural properties of fluids whose molecules interact via potentials with a hard core plus two piece-wise constant sections of different widths and heights are presented. These follow from the more general development previously introduced for potentials with a hard core plus $n$ piece-wise constant sections [Condens. Matter Phys. {\bf 15}, 23602 (2012)] in which use was made of a semi-analytic rational-function approximation method. The results of illustrative cases comprising eight different combinations of wells and shoulders are compared both with simulation data and with those that follow from the numerical solution of the Percus-Yevick and hypernetted-chain integral equations. It is found that the rational-function approximation generally predicts a more accurate radial distribution function than the Percus-Yevick theory and is comparable or even superior to the hypernetted-chain theory. This superiority over both integral equation theories is lost, however, at high densities, especially as the widths of the wells and/or the barriers increase.