The mean-field dividing interface is united with the Widom line

TL;DR

This paper introduces a mean-field approach that unifies the Widom line with the vapor-liquid interface, providing a comprehensive framework for phase diagram analysis and interface characterization.

Contribution

It develops a mean-field theory based on the Maxwell construction and density-profile equations to unify the Widom line with the vapor-liquid interface.

Findings

Intrinsic free energy peaks at the interface

Local maxima of isobaric heat capacity at the interface

The mean-field interface extends the Widom line into the coexistence region

Abstract

We define a mean-field crossover generated by the Maxwell construction as the dividing interface for the vapor-liquid interface area and a highly accurate density-profile equation is thus derived. By using a mean-field equation of sate for the Lennard-Jones fluid incorporated with the density gradient theory, we show that the intrinsic free energy peaks and the isobaric heat capacity exhibits local maxima at the interface. We demonstrate that the mean-field interface is the natural extension of the Widom line into the coexistence region, hence the entire space is coherently divided into liquid-like and gas-like regions in all three (temperature-pressure-volume) planes. Finally, the mean-field theory is found holding all the information for composing the phase diagrams over the entire phase space.