The equation of state of the two-dimensional Lennard–Jones fluid

Abstract

By combining pressure and energy data from the virial equation of state, through fifth virial coefficients, with the second and third virial coefficients themselves and the results of computer-simulation calculations, we have constructed an equation of state for the two-dimensional Lennard–Jones fluid for 0.45 ≤ T* ≤ 5 and 0.01 ≤ ρ* ≤ 0.8. The fitted data include some in the metastable region, and, therefore, the equation of state also describes "van der Waals loops" including unstable regions. The form used is a modified Benedict–Webb–Rubin equation having 33 parameters including one nonlinear one. The fitting was done using a nonlinear least squares algorithm based on a Levenberg–Marquardt method. A total of 211 simulation points, 97 reported here for the first time, were used in the fitting, and the overall standard deviation is less than 2% for both energy and pressure. Second and third virial coefficients derived from the fit in the supercritical region are in excellent agreement with exact values. The critical constants derived from the fit are in reasonable agreement with published estimates.