Penetrable Square-Well fluids: Exact results in one dimension

TL;DR

This paper introduces an exactly solvable one-dimensional penetrable square-well fluid model, providing detailed structural and thermodynamic analysis, and benchmarks approximate theories against exact low-density results.

Contribution

It develops an exact one-dimensional model of penetrable square-well fluids, deriving low-density expansions and analyzing stability, serving as a benchmark for approximate theories.

Findings

Exact low-density coefficients for radial distribution function

Benchmarking of Percus-Yevick and hypernetted chain theories

Identification of thermodynamic stability region

Abstract

We introduce a model of attractive penetrable spheres by adding a short range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point. The model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions. We derive the exact coefficients of a low density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion. These exact results are used as a benchmark to test the reliability of approximate theories (Percus-Yevick and hypernetted chain). Notwithstanding the lack of an exact solution for arbitrary densities, our results are expected to be rather precise within a wide range of temperatures and densities. A detailed analysis of some limiting cases is carried out. In particular we provide a complete solution of the sticky penetrable-sphere model in one dimension up to the same order in density. The issue of Ruelle's thermodynamics stability is analyzed and the region of a well defined thermodynamic limit is identified.