(153d) Modeling of Near-Critical and Supercritical Properties Via the Virial Equation of State

The virial equation of state is a foundational method in the statistical mechanics of fluids. It is unique in its ability to provide a thermodynamic equation of state with parameters that are rigorously given in terms of a detailed molecular model. As such, it has capability as a modeling method of real predictive capability, in some cases rivaling experiment in its accuracy. It also provides a valuable tool for assessing strengths and weaknesses in molecular models.

We consider application of the virial equation of state to the description of supercritical and near-critical fluid systems, considering both pure substances and mixtures. We report coefficients up to seventh order, computed using Mayer sampling Monte Carlo and Wheatleyâ??s recursive method for cluster summation, for a variety of realistic molecular model potentials. These results are used to generate expressions for volumetric (e.g., pressure) and thermal (e.g., heat capacity) properties, and others derived from them (e.g., speed of sound), as a function of density and temperature. We also examine prediction of the critical point and (for mixtures) critical lines. The ability to describe properties accurately from the virial coefficients is enhanced through the application of an approximant that is formulated to have correct scaling in the critical region. The property calculations are tested against available data from molecular simulation for the same model potentials, and from experiment.