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

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.

References in corpus (8)

• Elastic theory of unconstrained non-Euclidean plates
• Perspective: Geometrically-Frustrated Assemblies
• Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals
• Shape Selection in Chiral Self-Assembly
• Chiral structures and defects of lyotropic chromonic liquid crystals induced by saddle-splay elasticity
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• Intrinsic Geometry and Director Reconstruction for Three-Dimensional Liquid Crystals
• Moving frames and compatibility conditions for three-dimensional director fields

Cited by in corpus (10)

• Antiferroelectric Smectic Ordering as a Prelude to the Ferroelectric Nematic:Introducing the Smectic $Z_A$ Phase
• Building blocks of non-Euclidean ribbons: Size-controlled self-assembly via discrete, frustrated particles
• Violation of Ericksen inequalities in lyotropic chromonic liquid crystals
• Explicit Demonstration of Geometric Frustration in Chiral Liquid Crystals
• Cumulative geometric frustration and superextensive energy scaling in a nonlinear classical XY-spin model
• Stress accumulation versus shape flattening in frustrated, warped-jigsaw particle assemblies
• Modulated phases of nematic liquid crystals induced by tetrahedral order
• Relieving nematic geometric frustration in the plane
• Compatible director fields in ${\mathbb{R}}^3$
• Coarse-grained theory for motion of solitons and skyrmions in liquid crystals