Cubic and quartic hard-sphere and Lennard-Jones chain equations of state as foundations for complex fluid modeling

Abstract

Hard-sphere compressibility factor Z and hard-dimer radial distribution function at contact gHD(σ) are fit to simple packing fraction η expressions and are used in the dimer version of Wertheim’s perturbation theory to obtain five cubic equations of state (EOS’s) for athermal hard-sphere chain fluids. The predicted Zm versus η for various chain lengths m and the reduced second-virial coefficient versus m are compared with simulation data and the original noncubic dimer perturbation theory EOS’s. A cubic analog of the Boublik–Mansoori–Carnahan–Starling (BMCS) EOS successfully represents the unlike pair correlation function g12(σ) and Z versus η for binary hard-sphere mixtures of moderate size difference in the components. The new CTPT-D models are extended to calculate Zm versus η for binary homonuclear hard-sphere chain mixtures. The choice of a suitable EOS dispersion term to simultaneously represent single phase PVT and phase equilibria is briefly explored. A similar TPT approach was used to derive a quartic EOS for Lennard-Jones chain fluids, and Zm versus η isotherms are determined and compared with simulation results for chains up to 100 segments long. The new cubic and quartic EOS’s provide a simple foundation for developing equations of state for complex fluids including multipolar and association effects.