Hard ellipsoids of revolution

Abstract

Virial coefficients have been calculated for hard ellipsoids of revolution covering a wide range of shapes, from highly oblate, (length/breadth = 1/10) to highly prolate, (L/B = 10). It is found that prolate and oblate molecules which have the same value for their Isihara shape factor do not have equal values for their higher virial coefficients, and that the differences can be quite substantial for molecules of significantly non-spherical shape. For prolate molecules with L/B > 8 the fourth virial coefficient is found to be negative, while the fourth virials of the oblate molecules remain positive. Conversely, for oblate molecules with L/B < 1/6 the fifth virial coefficients have negative values, while the fifth virial coefficients of the prolate molecules remain positive. A number of approaches to analytical representations of the equation of state are considered for the case of moderately anisotropic molecules.