Modulated phases of nematic liquid crystals induced by tetrahedral order

TL;DR

This paper develops a theoretical framework linking tetrahedral order to a fourth director deformation mode in nematic liquid crystals, predicting new modulated phases such as spontaneous cholesteric and splay nematic phases due to geometric frustration.

Contribution

It introduces a novel theory connecting tetrahedral order with the $ riangle$ deformation mode, predicting new modulated phases in nematic liquid crystals.

Findings

Tetrahedral order couples to the $ riangle$ mode of director deformation.

Geometric frustration leads to spontaneous cholesteric or splay nematic phases.

The theory predicts new modulated phases induced by tetrahedral order.

Abstract

Recent theoretical research has developed a general framework to understand director deformations and modulated phases in nematic liquid crystals. In this framework, there are four fundamental director deformation modes: twist, bend, splay, and a fourth mode $\Delta$ related to saddle-splay. The first three of these modes are known to induce modulated phases. Here, we consider modulated phases induced by the fourth mode. We develop a theory for tetrahedral order in liquid crystals, and show that it couples to the $\Delta$ mode of director deformation. Because of geometric frustration, the $\Delta$ mode cannot fill space by itself, but rather must be accompanied by twist or splay. Hence, it may induce a spontaneous cholesteric phase, with either handedness, or a splay nematic phase.