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

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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.