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

Abstract

A mean-field crossover generated by the Maxwell construction is defined as the dividing interface for the vapor–liquid interface area. A new density-profile equation thus derived turns out to be highly accurate not only in reproducing the density-profile simulation data but also in predicting the pressure differences. By using the density gradient theory incorporated with the mean-field equations of state, we explore the interface area with the intrinsic free energy and the isobaric heat capacity. It is found that the mean-field interface divides the interface area into vapor-dominated and liquid-dominated regions and hence is the natural extension of the Widom line in the supercritical region, defined with the maximum isobaric heat capacity in a constant pressure process. Namely, both the zeroth and the first derivatives of the state variables (temperature, pressure, density) are equal at the critical point in all three phase planes. As a result, the entire phase space is coherently divided into liquid-like and gas-like regions. This finding suggests that the two-fluid feature of the supercritical fluid is inherited from the coexistence region.