Flexoelectricity and pattern formation in nematic liquid crystals

TL;DR

This paper analyzes the flexoelectric instability in nematic liquid crystals under alternating electric fields, revealing how frequency influences pattern formation and distinguishes between flexodomains and convection patterns.

Contribution

It provides a detailed theoretical analysis of flexoelectric pattern formation in nematics, highlighting the role of frequency as a control parameter and contrasting it with electro-hydrodynamic instabilities.

Findings

Flexodomains appear periodically in time at small finite frequencies.

Frequency $$ leads to a singular limit with stationary patterns.

Frequency can be used to control and distinguish pattern types.

Abstract

We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency $\omega$), which leads to stripe patterns (flexodomains) in the plane of the layer. This equilibrium transition is governed by the free energy of the nematic which describes the elasticity with respects to the orientational degrees of freedom supplemented by an electric part. Surprisingly the limit $\omega \to 0$ is highly singular. In distinct contrast to the dc-case, where the patterns are stationary and time-independent, they appear at finite, small $\omega$ periodically in time as sudden bursts. Flexodomains are in competition with the intensively studied electro-hydrodynamic instability in nematics, which presents a non-equilibrium dissipative transition. It will be demonstrated that $\omega$ is a very convenient control parameter to tune between flexodomains and convection patterns, which are clearly distinguished by the orientation of their stripes.