# Density functional theory for dense nematics with steric interactions

## TL;DR

This paper develops a mean field density functional theory for dense nematic liquid crystals with hard core interactions, improving upon Onsager's model by providing a realistic equation of state and novel features in the orientational distribution.

## Contribution

It introduces a new density functional approach for dense nematics that captures high-density behavior and predicts a unique orientational distribution feature.

## Key findings

- Provides a realistic equation of state at high densities.
- Predicts a vanishing orientational distribution on a nonzero measure set.
- Extends the theoretical understanding of dense nematic phases.

## Abstract

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.