Thermodynamic Properties and Phase Equilibrium Study of Lennard-Jones Model and Application to Real Molecules

Both a free volume approach for Helmholtz free energy and a theoretically-based fitted formula for radial distribution function (rdf) of hard sphere solid were employed to describe the Helmholtz free energy of Lennard-Jones (LJ) solid in the framework of first order thermodynamic perturbation theory. Dividing the LJ potential follows from a modified WCA prescription, the specification of equivalent hard sphere diameter was determined by a simple iteration procedure devised originally for liquid state, but extended to solid state in the present study. Two hundred shells were used in the rdf to get an accurate perturbation term. Bulk fluid thermodynamic property of the LJ model is from a recently proposed equation of state. The present approach is very accurate for the description of excess Helmholtz free energy and equation of state of LJ solid, but shows some deviation from the simulation for excess Helmholtz free energy of uniform LJ fluid when the reduced temperature is lower than 0.75. The present approach is satisfactory for description of phase equilibrium of the LJ model. By choosing the appropriate LJ potential parameter, the present approach can describe the melting curve of real molecules accurately.