Virial coefficients and equation of state of hard ellipsoids

Abstract

The first five virial coefficients of hard ellipsoids have been evaluated numerically. Hard ellipsoids with length to breadth ratio in the range 3 to 10 were considered. Differences in the virial coefficients between prolate, oblate and biaxial ellipsoids with the same length to breadth ratio have been analysed. We were able to fit the virial coefficient data of hard ellipsoids to an empirical expression which contains only two non-sphericity parameters. This expression describes also correctly the virial coefficient of other convex bodies such as hard spherocylinders. Furthermore, computer simulations were performed for hard ellipsoids. It is found that for a given volume fraction and length to breadth ratio, the compressibility factor of the biaxial ellipsoid is smaller than that of the prolate spheroid, while the compressibility factor of the prolate spheroid is smaller than that of the oblate spheroid. However, differences in the compressibility factor for these three hard models were found to be small. This is surprising since their virial coefficients are quite different. An explanation for this is proposed. The accuracy of several analytical equations of state for hard convex bodies was analysed. Although these equations provide reasonable results they predict the same equation of state for prolate and oblate spheroids. Moreover these equations do not provide good predictions of virial coefficients for very elongated molecules. A new equation of state which uses the computed values of the first five virial coefficients of hard ellipsoids is proposed. This new equation of state is basically a truncated virial expansion, which uses Parsons-like scaling to estimate virial coefficients higher than the fifth. It is shown that this new equation of state performs better than those previously proposed for hard ellipsoids. Moreover it distinguishes between prolate, oblate and biaxial ellipsoids. The new equation of state describes satisfactorily the computer simulation data of hard spherocylinders.