Isotropic and nematic phases of the hard spheroid fluid: a virial approach.

We use a high level virial expansion to investigate the properties of the isotropic and nematic phases of the hard spheroid fluid. We use the Monte Carlo techniques described previously to calculate the virial coefficients up to seventh order and we represent the dependence of these coefficients on particle orientations via a spherical harmonic expansion. The expansion coefficients are determined using Lebedev quadrature which carries out the angular integration required exactly. For fairly spherical spheroids (1/3<a/b<3, where a and b are the semiaxes of the spheroid) the virial expansion appears to be convergent in both the isotropic and nematic phases up to high density. For more aspherical particles, the predictions varied in a more erratic fashion upon increasing the number of virials. The use of a finite angular basis set to represent the orientationally dependent virial coefficients could be a contributory cause to this.