Equations of state and excess entropy of repulsive inverse power particle potential fluids with variable stiffness

Analytic expressions for the equation of state in terms of the compressibility factor, Z, and excess entropy, sex, of inverse power (IP) potential fluids are derived and parameterized using molecular dynamics simulation data. The IP pair potential is ϕ(r) ∼ r-n, where r is the pair separation and n is an exponent that governs the steepness of the potential. A number of parameterizations of the dependence of Z on number density and n are proposed and compared. These include multiparameter global series expansion fits and more simple formulas based on the very soft (small n) and hard sphere particle representation limits. The excess entropy can be represented over the whole fluid and n > 3+ range well by a single analytic expression with n-dependent parameters. It is shown that sex is a concave function of density for n greater than about 6 and convex for smaller values of the exponent. The excess entropy varies with n for a constant value of the density normalized by its freezing point value.