The square-well fluid: a thermodynamic geometric view

TL;DR

This paper applies Thermodynamic Geometry to analyze the square-well fluid, providing geometric insights into phase coexistence, spinodal, and Widom lines across different potential ranges, and revealing a Clausius-Clapeyron-like relation near criticality.

Contribution

It offers a geometric approach to precisely determine spinodal curves and characterize the Widom line for square-well fluids across various potential ranges, including a new relation near the critical point.

Findings

Exact geometric results for spinodal curves across all potential ranges.

Calculation of the $R$-Widom line as a function of potential range.

Identification of a Clausius-Clapeyron-like relation near the critical point.

Abstract

The square-well fluid with hard-sphere diameters is studied within the framework of Thermodynamic Geometry (TG). Coexistence and spinodal curves, as well as the Widom line for ranges $\lambda^{*} = 1.25, 1.5, 2.0, 3.0$ for this fluid are carefully studied using geometric methods. We are able to show that, unlike coexistence curves, an exact result can be given along all the thermodynamic space and for all potential ranges for spinodal curves. Additionally, $R$-Widom line which is defined as the locus of extrema of the curvature scalar is calculated as a function of the potential range, satisfying near the critical point a kind of Clausius-Clapeyron equation. It is argued that this relation could be a signature of certain type of characteristic phase transition when crossing the boundary of the Widom line.