Director Deformations, Geometric Frustration, and Modulated Phases in Liquid Crystals

TL;DR

This paper provides a unified framework to understand the diverse modulated phases in liquid crystals by analyzing director deformations and geometric frustration, linking molecular order to complex global structures.

Contribution

It introduces a comprehensive approach using four fundamental deformation modes to explain the formation of various modulated liquid crystal phases and their geometric frustrations.

Findings

Identifies four fundamental director deformation modes and their coupling to molecular order.

Shows how geometric frustration leads to complex global phases with defects.

Unifies understanding of diverse liquid crystal phases through local structure analysis.

Abstract

This article analyzes modulated phases in liquid crystals, from the long-established cholesteric and blue phases to the recently discovered twist-bend, splay-bend, and splay nematic phases, as well as the twist-grain-boundary (TGB) and helical nanofilament variations on smectic phases. The analysis uses the concept of four fundamental modes of director deformation: twist, bend, splay, and a fourth mode related to saddle-splay. Each mode is coupled to a specific type of molecular order: chirality, polarization perpendicular and parallel to the director, and octupolar order. When the liquid crystal develops one type of spontaneous order, the ideal local structure becomes nonuniform, with the corresponding director deformation. In general, the ideal local structure is frustrated; it cannot fill space. As a result, the liquid crystal must form a complex global phase, which may have a combination of deformation modes, and may have a periodic array of defects. Thus, the concept of an ideal local structure under geometric frustration provides a unified framework to understand the wide variety of modulated phases.