Monte Carlo Equation of State of Molecules Interacting with the Lennard-Jones Potential. I. A Supercritical Isotherm at about Twice the Critical Temperature

Abstract

Values obtained by Monte Carlo calculations are reported for the compressibility factor, excess internal energy, excess constant-volume heat capacity, and the radial distribution function of Lennard-Jones (12,6) molecules at the reduced temperature kT/ε*=2.74, and at thirteen volumes between v/v*=0.75 and 7.5. (v is the molar volume; v*=2—½N0r*3; N0 is Avogadro's number; ε* is the depth, and r* the radius of the Lennard-Jones potential well.) The results are compared with the experimental observations of Michels (∼150–2000 atmos) and Bridgman (∼2000–15 000 atmos) on argon at 55°C, using Michels' second virial coefficient values for the potential parameters. Close agreement with Michels is found, but significant disagreement with Bridgman. The Monte Carlo calculations display the fluid-solid transition; the transition pressure and the volume and enthalpy increments are not precisely determined. The Lennard-Jones-Devonshire cell theory gives results which disagree throughout the fluid phase, but agree on the solid branch of the isotherm. Limited comparisons with the Kirkwood-Born-Green results indicate that the superposition approximation yields useful results at least up to v/v*=2.5.