A revisit of the vapor-liquid interface of the Lennard-Jones fluid

In this work a mean-field crossover generated by the Maxwell construction is defined as the dividing interface for the vapor-liquid interface area. An accurate and physically preferable density-profile equation is used correlate the local density and to predict various interfacial properties. By using the density gradient theory and mean-field equation of state for the Lennard-Jones fluid, we are able to extensively explore the interface system in terms of the Gibbs free energy, the Helmholtz free energy and heat capacity. The peak of the intrinsic free energy at the interface reveals the most unstable state and suggests that the interface area is thus divided into vapor-enriched and liquid-enriched sub-regions. The local maxima of the intrinsic isobaric heat capacity echo such a dividing, which is in accordance with the Widom line in the supercritical region. Consequently the mean field dividing interface is the natural extension of the Widom line into the coexistence region. Hence the entire phase space is coherently divided into liquid-like and gas-like regions in all three (temperature-pressure-volume) planes. Finally, the modeling of adsorption on the interface is briefly discussed.