The Widom Line and the Lennard-Jones Potential

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Computational Physics

Background:

• The Widom line describes a key feature of fluid behavior near the vapor-liquid critical point.
• Understanding its behavior is crucial for characterizing supercritical fluids.
• Previous studies have primarily focused on theoretical models.

Purpose of the Study:

• To investigate the phenomenological behavior of the Widom line above the vapor-liquid critical point for the Lennard-Jones potential.
• To compare predictions from accurate equations of state (EoS) with molecular dynamics (MD) simulation data.
• To analyze the role of thermodynamic properties in defining the Widom line.

Main Methods:

• Utilized four accurate equations of state (EoS) for the Lennard-Jones (LJ) potential.
• Calculated supercritical maximum values for isochoric heat capacity (C_v), isobaric heat capacity (C_p), isothermal compressibility (β_T), and thermal expansion coefficient (α_p).
• Compared EoS predictions with existing molecular dynamics (MD) simulation data.

Main Results:

• All investigated LJ EoS successfully predict the pressure-temperature (p-T) Widom line behavior.
• However, no LJ EoS accurately predicts the temperature-density (T-ρ) Widom line behavior observed in MD simulations.
• The isothermal compressibility (β_T) plays a significant role in determining the pressure and temperature range of Widom line phenomena.

Conclusions:

• The study highlights discrepancies between theoretical EoS and MD simulations for the T-ρ Widom line.
• Analysis of MD data suggests a Clausius-Clapeyron-type relationship extends to the supercritical region.
• The Widom line can be described as a critical portion of a larger curve where thermodynamic functions exhibit maxima.