The Widom Line and the Lennard-Jones Potential.

Abstract

The phenomenological behavior of the Widom line above the vapor-liquid critical point for the Lennard-Jones (LJ) potential is investigated using four accurate equations of state (EoS) and a comparison with molecular dynamics (MD) simulation data. This involved calculating the supercritical maximum values of the isochoric heat capacity (CV), isobaric heat capacity (Cp), isothermal compressibility (βT), and thermal expansion coefficient (αp). All LJ EoS predict the pressure (p)-temperature (T) Widom line behavior. In contrast, the T-density (ρ) Widom line behavior, observed in MD simulations, is not predicted by any LJ EoS. The calculations highlight the important role of βT in determining the range of p and T for which Widom line behavior is observed. Analysis of MD data for the supercritical maximum/minimum of CV and Cp suggests the extension of a Clausius-Clapeyron-type relationship from the triple point to the supercritical region. This provides a new description of the Widom line as the near critical part of this larger curve for which other thermodynamic functions also have maximum values.