The Geometry of the Cholesteric Phase

Abstract

We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an orthonormal triad determined by this axis, the director, and the mutually perpendicular direction. With this tool we are able to compare defect structures in cholesterics, biaxial nematics, and smectics. Though they all have similar ground state manifolds, the defect structures are different and cannot be, in general, translated from one phase to the other.

5 pages, the full catastrophe

References in corpus (2)

• Electrooptic response of chiral nematic with oblique helicoidal director
• Smectics: Symmetry Breaking, Singularities, and Surfaces

Cited by in corpus (16)

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• Helfrich-Hurault elastic instabilities driven by geometrical frustration
• Reversal of Helicoidal Twist Handedness Near Point Defects of Confined Chiral Liquid Crystals
• The Topology of Dislocations in Smectic Liquid Crystals
• Undulation instabilities in cholesteric liquid crystals induced by anchoring transitions
• Point Defects, Chirality and Singularity Theory in Cholesteric Liquid Crystal Droplets
• Intrinsic Geometry and Director Reconstruction for Three-Dimensional Liquid Crystals
• Contact Topology and the Structure and Dynamics of Cholesterics
• Contact Topology and the Classification of Disclination Lines in Cholesteric Liquid Crystals
• Network topology of interlocked chiral particles
• A Bouquet for Apollonius: Focal Conics in Sessile Cholesteric Droplets
• Unavoidable emergent biaxiality in chiral molecular-colloidal hybrid liquid crystals
• Topological Rigidity and Non-Abelian defect junctions in chiral nematic systems with effective biaxial symmetry
• Dislocations and Fibrations: The Topological Structure of Knotted Smectic Defects