Conic sections in ferroelectric nematics: experiments and mathematical modeling

TL;DR

This paper explores the unique domain structures in ferroelectric nematic liquid crystals, demonstrating that conic-shaped domain walls form to minimize electrostatic energy, modeled through a simplified elastic approach.

Contribution

It introduces a mathematical model explaining conic domain walls in ferroelectric nematics, highlighting the role of elastic constants and polarization alignment in domain formation.

Findings

Conic domain walls are observed in ferroelectric nematic films with colloidal inclusions.

A simplified elastic model effectively predicts the polydomain textures seen experimentally.

The divergence of polarization is heavily penalized, leading to conic-shaped domain walls.

Abstract

Domain structure of a fluid ferroelectric nematic is dramatically different from the domain structure of solid ferroelectrics since it is not restricted by rectilinear crystallographic axes and planar surface facets. We demonstrate that thin films of a ferroelectric nematic seeded by colloidal inclusions produce domain walls in the shape of conics such as a parabola. These conics reduce the bound charge within the domains and at the domain walls. An adequate description of the domain structures requires one to analyze the electrostatic energy, which is a challenging task. Instead, we demonstrate that a good approximation to the experimentally observed polydomain textures is obtained when the divergence of spontaneous polarization - which causes the bound charge is heavily penalized by assuming that the elastic constant of splay in the Oseen-Frank energy is much larger than those for twist and bend. The model takes advantage of the fact that the polarization vector is essentially parallel to the nematic director throughout the sample.