Exact equations of state for nematics

TL;DR

This paper introduces a novel wave equation approach to derive exact equations of state for nematic liquid crystals, revealing phase transition mechanisms and complex phase diagram structures analytically.

Contribution

It presents the first analytical derivation of nematic phase diagrams using nonlinear wave equations, linking phase transitions to shock wave phenomena.

Findings

Exact equations of state for biaxial nematics derived

Classical isotropic-uniaxial transition explained as shock wave

Rich phase diagram structures characterized analytically

Abstract

We propose a novel approach to the solution of nematic Liquid Crystal models based on the derivation of a system of nonlinear wave equations for order parameters such that the occurrence of uniaxial and biaxial phase transitions can be interpreted as the propagation of a two-dimensional shock wave in the space of thermodynamic parameters. We obtain the exact equations of state for an integrable model of biaxial nematic liquid crystals and show that the classical transition from isotropic to uniaxial phase in absence of external fields is the result of a van der Waals type phase transition, where the jump in the order parameters is a classical shock generated from a gradient catastrophe at a non-zero isotropic field. The study of the equations of state provides the first analytical description of the rich structure of nematics phase diagrams in presence of external fields.