From the vapor-liquid coexistence region to the supercritical fluid: the van der Waals fluid

TL;DR

This paper investigates the interface properties of the van der Waals fluid across phase transitions using density gradient and mean-field theories, revealing detailed phase behavior and interface characteristics.

Contribution

It introduces a highly accurate density profile model for the van der Waals fluid interface based on mean-field theory and Maxwell construction, enhancing predictive capabilities.

Findings

The intrinsic Helmholtz free energy peaks at the interface.

Maximum pressure tensor difference aligns with intrinsic Gibbs free energy maximum.

Phase space divided into gas-like and liquid-like regions by the mean-field interface and Widom line.

Abstract

In this work the interface system of the van der Waals fluid is investigated by using the density gradient theory incorporated with the mean-field theory. Based on the mean-field dividing interface generated by the Maxwell construction, we propose a highly accurate density profile model for the density gradient theory, which facilitates reliable predictions of various properties for the interface region. It is found that the local intrinsic Helmholtz free energy peaks at the interface and that the maximum difference of the normal and tangential components of the pressure tensor corresponds to the maximum of the intrinsic Gibbs free energy. It is found that the entire phase space is divided into gas-like and liquid-like regions by the single line composed of the mean-field interface and the Widom line. The two-fluid feature of the supercritical fluid is hence inherited from the coexistence region. Phase diagrams extended into the coexistence region in all the temperature-pressure-volume planes are thus completed with the solutions to the vapor-liquid equilibrium problem by the van der Waals equation of state.