Ferroelectric nematic liquids with conics

TL;DR

This paper reveals that domain walls in ferroelectric nematic liquid crystals naturally form conic sections, which help minimize electric charges and could aid in designing polarization patterns.

Contribution

It demonstrates that in ferroelectric nematic liquids, domain walls are shaped as conic sections, a novel finding linking classical geometry with liquid crystal physics.

Findings

Domain walls are conic sections in ferroelectric nematic liquids.

Conic-shaped domain walls minimize electric charge accumulation.

Findings may inform design of polarization and charge patterns.

Abstract

Spontaneous electric polarization of solid ferroelectrics follows aligning directions of crystallographic axes. Domains of differently oriented polarization are separated by domain walls (DWs), which are predominantly flat and run along directions dictated by the bulk translational order and the sample surfaces. Here we explore DWs in a ferroelectric nematic (NF) liquid crystal, which is a fluid with polar long-range orientational order but no crystallographic axes nor facets. We demonstrate that DWs in the absence of bulk and surface aligning axes are shaped as conic sections. The conics bisect the angle between two neighboring polarization fields to avoid electric charges. The remarkable bisecting properties of conic sections, known for millennia, play a central role as intrinsic features of liquid ferroelectrics. The findings could be helpful in designing patterns of electric polarization and space charge.