Analytical Virial Coefficients and New Equations of State of Hard Ellipsoid Fluids

Abstract

The complexity of calculations for high order virial coefficients of ellipsoids makes it difficult to obtain accurate analytical high order coefficients and equation of state for such systems. Using analytical method, the virial coefficients up to third order are calculated. For higher ones, the numerical values were taken from publications of other researchers, based on Monte Carlo integration method. By fitting the available numerical virial coefficients, sixth to eighth order, the two shape parameter analytical expressions of the hard convex molecules are obtained. Using these available data, up to eighth order, we have obtained the approximate one shape parameter analytical expressions of the hard prolate and oblate ellipsoid molecules. The fitted virial coefficients are in agreement with the simulation results. Moreover, the approximate analytical expressions for the equation of state of isotropic hard ellipsoid fluids are proposed. The proposed equations of state are in good agreement with the simulations up to medium elongations. In addition, our equations show a better agreement comparing to other works. Also, the newest equation is used for both prolate and oblate ellipsoid fluids and is convenient for elongations, k<10.0.