Insights into molecular interactions gleaned from a lattice-based Helmholtz equation of state

Abstract

A bulk phase thermodynamic potential is used to account for molecular interaction energy. It is derived from the partition function and is equal to the internal energy minus the product of temperature multiplied by thermal entropy. Bulk interaction energy is a function of volume, temperature, and quantity. Thermal entropy is the negative derivative of bulk interaction energy with respect to temperature at constant volume. A Helmholtz equation of state for pure fluids, with models of bulk interaction energy and configurational entropy, is proposed and used to correlate PρT data generated by REFPROP equations for hydrogen, parahydrogen, deuterium, helium, neon, argon, krypton, xenon, and nitrogen. The difference between the proposed equation of state and REFPROP density values are on average within the reported uncertainty in REFPROP over the REFPROP range of applicability. The equation of state satisfies the ideal curves assessment indicating reasonable extrapolation behavior beyond the range of applicability. Plots of implied interaction energy isotherms versus molecular separation distance (cube root of molar volume divided by Avogadro's number) all have the same characteristic features. The strongest attraction between molecules occurs at the triple point temperature for a liquid with a density approximately 5% larger than the triple point liquid density. The separation distance at the minimum potential energy is on average within 0.1 Ả of the average value derived from empirical Lennard-Jones potential. At separations closer than this attraction drop off sharply changing rapidly to repulsion. At a given separation along the coexistence line attraction is stronger than at any other temperature with the same separation. Interactions become strictly repulsive beyond some temperature in the critical region.