A new strong principle of corresponding states for nonpolar fluids

Abstract

We present a new strong principle of corresponding states that reduces the entire pressure–volume–temperature (p–v–T) surface of a nonpolar fluid to a single curve; this curve corresponds to an effective pair distribution function at contact as a function of reduced density. This reduction of a surface to a curve is based on statistical-mechanical theory, which also furnishes the algorithms for calculating, from the intermolecular pair potential, the three temperature-dependent parameters needed for the reduction. If the pair potential is not known, data on the second virial coefficient as a function of temperature can be used instead. The principle is tested on a computer-simulated Lennard-Jones (12,6) fluid, on the noble-gas fluids (except He), on N2, CO2, CF4, SF6, and on the first four alkanes. A suitable reciprocal plot yields virtual straight lines for all the real fluids, which differ in shape from the expected Carnahan–Starling curve that describes the (12,6) fluid; we suggest that these shape differences are caused by many-body forces in the real fluids. By curve fitting straight lines to the empirical data for the real fluids, we obtain a simple analytic equation of state, cubic in the density, that can be characterized by three constants: the Boyle temperature, the Boyle volume, and a slope constant. This equation is not accurate in the nonanalytic critical and two-phase regions, but otherwise describes the volumetric behavior of nonpolar fluids very accurately over the entire range from the dilute gas to the dense liquid. It has considerable predictive power, since it permits the construction of the entire p–v–T surface from just the second virial coefficient plus a few liquid densities.