  The celebrated work of Onsager on hard particle systems, based on the
truncated second order virial expansion, is valid at relatively low volume
fractions for large aspect ratio particles. While it predicts the
isotropic-nematic phase transition, it fails to provide a realistic equation of
state in that the pressure remains finite for arbitrarily high densities. In
this work, we derive a mean field density functional form of the Helmholtz free
energy for nematics with hard core repulsion. In addition to predicting the
isotropic-nematic transition, the model provides a more realistic equation of
state. The energy landscape is much richer, and the orientational probability
distribution function in the nematic phase possesses a unique feature: it
vanishes on a nonzero measure set in orientational space.
