Low-temperature and high-temperature approximations for penetrable-sphere fluids. Comparison with Monte Carlo simulations and integral equation theories

TL;DR

This paper develops and compares low-temperature and high-temperature analytical theories for penetrable-sphere fluids, validating them against Monte Carlo simulations and integral equation solutions to understand their accuracy across different conditions.

Contribution

It introduces two simple analytical approximations for penetrable-sphere fluids, extending known solutions and providing a practical tool validated by simulations and integral equation comparisons.

Findings

High-temperature approximation aligns well with simulations at high temperatures.

Low-temperature approximation is effective at low temperatures and densities.

Hypernetted-chain approximation performs very well except inside the core at low temperatures.

Abstract

The two-body interaction in dilute solutions of polymer chains in good solvents can be modeled by means of effective bounded potentials, the simplest of which being that of penetrable spheres (PSs). In this paper we construct two simple analytical theories for the structural properties of PS fluids: a low-temperature (LT) approximation, that can be seen as an extension to PSs of the well-known solution of the Percus-Yevick (PY) equation for hard spheres, and a high-temperature (HT) approximation based on the exact asymptotic behavior in the limit of infinite temperature. Monte Carlo simulations for a wide range of temperatures and densities are performed to assess the validity of both theories. It is found that, despite their simplicity, the HT and LT approximations exhibit a fair agreement with the simulation data within their respective domains of applicability, so that they complement each other. A comparison with numerical solutions of the PY and the hypernetted-chain approximations is also carried out, the latter showing a very good performance, except inside the core at low temperatures.