(491o) Coupling Bulk Phase Thermodynamic Constraints and Molecular Simulations

Most cubic equations of state use bulk phase pure component parameters that are either calculated from expressions that are functions of critical properties or by fitting these parameters to vapor pressure and liquid density data.

This work takes a multi-scale approach to parameter estimation. An expression for the temperature dependent attractive parameter, a(T), for pure components is derived by using the Gibbs-Helmholtz equation to constrain the fugacity coefficient. Theoretical analysis leads to a first-order inhomogeneous differential equation in a(T), which is easily solved using one-sided Green's functions and a boundary condition at the critical point. The resulting expression for a(T) contains, among other things, the excess internal energy. Thus molecular level interactions can be captured in a(T) by computing the excess internal energy using Monte Carlo or molecular dynamics simulations as a function of current bulk phase conditions. Theoretical results for pure components are extended to mixtures and used to derive a rigorous thermodynamic mixing rule for a(T) from first principles by exploiting the Gibbs-Duhem equation.

Numerical results for a many pure components and mixtures have been determined. Results for carbon dioxide, water, carbon-dioxide-water, sodium chloride-water, and carbon dioxide-NaCl-water at high pressure are presented. Many geometric illustrations are used to elucidate key points.