Algebraic equations of state for the liquid crystalline phase behavior of hard rods

TL;DR

This paper introduces algebraic free energy models for smectic-A and crystal phases of hard spherocylinders, enabling efficient phase behavior calculations and serving as benchmarks for studying interrod interactions.

Contribution

It presents simplified algebraic free energy expressions derived from previous numerical data, improving computational efficiency and accuracy in phase behavior predictions.

Findings

Quantitative agreement with simulation data.

Applicable to all aspect ratios.

Useful as benchmarks for interaction studies.

Abstract

Based on simplifications of previous numerical calculations [Graf and L\"{o}wen, Phys. Rev. E \textbf{59}, 1932 (1999)], we propose algebraic free energy expressions for the smectic-A liquid crystal phase and the crystal phases of hard spherocylinders. Quantitative agreement with simulations is found for the resulting equations of state. The free energy expressions can be used to straightforwardly compute the full phase behavior for all aspect ratios and to provide a suitable benchmark for exploring how attractive interrod interactions mediate the phase stability through perturbation approaches such as free-volume or van der Waals theory.