Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals
arXiv:1901.06306 · doi:10.1080/21680396.2019.1581103
Abstract
This article re-examines a classic question in liquid-crystal physics: What are the elastic modes of a nematic liquid crystal? The analysis uses a recent mathematical construction, which breaks the director gradient tensor into four distinct types of mathematical objects, representing splay, twist, bend, and a fourth deformation mode. With this construction, the Oseen-Frank free energy can be written as the sum of squares of the four modes, and saddle-splay can be regarded as bulk rather than surface elasticity. This interpretation leads to an alternative way to think about several previous results in liquid-crystal physics, including: (1) free energy balance between cholesteric and blue phases, (2) director deformations in hybrid-aligned-nematic cells, (3) spontaneous twist of achiral liquid crystals confined in a torus or cylinder, and (4) curvature of smectic layers.
References in corpus (2)
Cited by in corpus (28)
- Review: Topology of solitons and singular defects in chiral liquid crystals
- Director Deformations, Geometric Frustration, and Modulated Phases in Liquid Crystals
- Theory of the splay nematic phase: Single vs. double splay
- Geometry and mechanics of disclination lines in 3D nematic liquid crystals
- Patterning of morphogenetic anisotropy fields
- Intrinsic Geometry and Director Reconstruction for Three-Dimensional Liquid Crystals
- Liquid Crystal Distortions Revealed by an Octupolar Tensor
- Moving frames and compatibility conditions for three-dimensional director fields
- Kinematics and dynamics of disclination lines in three-dimensional nematics
- Geometry of Bend: Singular Lines and Defects in Twist-Bend Nematics
- Anisotropic disclination cores in nematic liquid crystals modelled by a self consistent molecular field theory
- Explicit Demonstration of Geometric Frustration in Chiral Liquid Crystals
- Violation of Ericksen inequalities in lyotropic chromonic liquid crystals
- Nematic Tactoid Population
- Modulated phases of nematic liquid crystals induced by tetrahedral order
- Double Splay Nematic Order in Confined Polar Fluids
- Computational molecular field theory for nematic liquid crystals
- Nemato-elasticity of hybrid molecular-colloidal liquid crystals
- The Thermodynamic Origins of Chiral Twist in Monolayer Assemblies of Hard Rod-like Colloids
- Shape Bistability in Squeezed Chromonic Droplets
- Ionically charged topological defects in nematic fluids
- Relieving nematic geometric frustration in the plane
- Skyrmion Tubes in achiral nematic liquid crystals
- Topological transition from a hopfion to a toron via flexoelectric self-polarization in chiral liquid crystals
- Non-uniform localised distortions in generalised elasticity for liquid crystals
- Microswimmers knead nematics into cholesterics
- Compatible director fields in
- Deformed states in paraelectric and ferroelectric nematic liquid crystals