Thermodynamic response functions of fluids with repulsive inverse power pair potentials

The repulsive inverse power (IP) pair potential, ϕ(r)∼r^{-n}, where r is the particle pair separation and the exponent n determines the steepness of the potential, is widely used as a reference model for real fluid and solid systems. Some aspects of the density ρ, temperature T, pressure P, and n dependence of IP fluid systems are derived and explored analytically and numerically using accurate IP equations of state derived from molecular-dynamics simulations. The focus of the work is on deriving analytic expressions for the derivatives or response functions of the total and excess entropies of the IP system with respect to these independent variables. The analytic expressions assist in navigating through the [ρ,T,P] and n multidimensional equation-of-state space of the IP system. Statistical mechanical expressions are derived for the derivatives of the potential energy, Helmholtz free energy, and excess entropy with respect to n, which were implemented in molecular-dynamics simulations for the excess entropy case. The relationships between the hard sphere, IP, and Lennard-Jones potential response functions as a function of temperature, density, and pressure, particularly at high temperature are investigated, in the latter case using an approximate statistical mechanical analysis.