Hydrodynamics of polar liquid crystals

TL;DR

This paper derives the hydrodynamic equations for polar liquid crystals, revealing a splay instability caused by symmetry-violating terms, and analyzes the system's linear modes.

Contribution

It introduces a hydrodynamic framework for polar liquid crystals with local $C_{ abla v}$-symmetry, highlighting the impact of symmetry-breaking terms on stability.

Findings

Identification of a splay instability in polarized states

Derivation of hydrodynamic equations using Poisson-bracket formalism

Confirmation of instability through mode analysis

Abstract

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local $C_{\infty v}$-symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals ($D_{\infty h}$) in that it contains terms violating the ${\bf{n}}\to -{\bf{n}}$ symmetry. First we show that these $\mathcal{Z}_2$-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.