Comments on the repulsive term of Van der Waals equation of state

TL;DR

This paper refines the repulsive term of the Van der Waals equation using probabilistic configurational entropy, assessing its applicability to dense fluids and proposing a new entropy mixing model for phase continuity.

Contribution

It offers an improved probabilistic derivation of the Van der Waals repulsive term and introduces a new configurational entropy mixing model to explore phase continuity.

Findings

Accurately describes systems of independent Hard Spheres at low packing fractions

Inclusion of holes improves the model below certain densities

Model cannot describe clustering or high-density fluids

Abstract

The repulsive term of Van der Waals equation of state has been deduced and improved in this work using a probabilistic description of the configurational entropy. The aim is to find out whether its physical basis is suitable for the study of dense fluids like liquids and glasses. The extended Van der Waals model accurately describes a system composed of independent Hard Spheres below packing fraction {\eta} < 0.3, giving a pole at {\eta} ~ 0.51 in close agreement with Molecular Dynamic simulation results. The inclusion of holes in the configurational entropy description improves the model but only below {\eta} < 0.2, precluding its application to high density fluids and glasses. In addition, neither local nor global clustering of Hard Spheres can be described using this approach. A physical model other than Van der Waals equation of state is required to accurately describe the continuity of gaseous and liquid states with the same expression. In this work, a model for the configurational entropy of mixing is proposed which could reveal whether such continuity really exists.