(A) perturbation theory of classical equilibrium fluids and solids

Abstract

A new perturbation theory is presented which is reliable over wide region of temperature and density for both fluid and solid. Characteristic features of this new theory are its ability to deal both fluid and solid on a same theoretical footing. The new theory reduces to the theory of Weeks, Chandler, and Andersen at fluid density near or below the triple point density and at solid density near melting transition below the triple point temperature. For fluid-state calculation, the present theory is not only successful at low density but also it can accurately predict thermodynamic properties at higher densities near the freezing line of the fluid. For solid-state calculation, the agreement of this theory extends from an anharmonic region near the melting line to a harmonic region, where the hard-sphere system achieves 92\% of close-packed density. Beyond this region errors in the analytical fits to the radial distribution functions of hard-sphere solid make an accurate test of the new theory difficult. The success of the present theory is achieved by employing an optimized reference potential whose repulsive range decreases with increase in density. Thermodynamic properties for the Lennard-Jones, exponential-6, and inverse nth-power (n=12,9,6, and 4) have been calculated from the new theory. Comparison of the calculated data with available Monte Carlo simulations and additional simulations carried out in this work shows that the theory gives excellent thermodynamic results for these systems, except the softest (n=4) repulsive systems of solid. The present theory also gives a physically reasonable hard-sphere diameter over the entire fluid and solid region. Since the present formulation is the same for both solid and fluid phases, we used the theory to compute the melting and freezing data of the aforementioned model systems. Comparison with other theoretical models of solid and fluid is also discussed.