The weirdest martensite: Smectic liquid crystal microstructure and Weyl-Poincaré invariance

Abstract

Smectic liquid crystals are remarkable, beautiful examples of materials microstructure, with ordered patterns of geometrically perfect ellipses and hyperbolas. The solution of the complex problem of filling three-dimensional space with domains of focal conics under constraining boundary conditions yields a set of strict rules, which are similar to the compatibility conditions in a martensitic crystal. Here we present the rules giving compatible conditions for the concentric circle domains found at two-dimensional smectic interfaces with planar boundary conditions. Using configurations generated by numerical simulations, we develop a clustering algorithm to decompose the planar boundaries into domains. The interfaces between different domains agree well with the smectic compatibility conditions. We also discuss generalizations of our approach to describe the full three-dimensional smectic domains, where the variant symmetry group is the Weyl-Poincaré group of Lorentz boosts, translations, rotations, and dilatations.

5 pages, 4 figures (main paper); added supplemental text

References in corpus (4)

• Conformal Smectics and their Many Metrics
• The Power of Poincaré: Elucidating the Hidden Symmetries in Focal Conic Domains
• Focal Conic Flower Textures at Curved Interfaces
• Visualization, coarsening and flow dynamics of focal conic domains in simulated Smectic-A liquid crystals

Cited by in corpus (7)

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• Helfrich-Hurault elastic instabilities driven by geometrical frustration
• Defect dynamics in active smectics induced by confining geometry and topology
• Network topology of interlocked chiral particles
• Colloidal smectics in button-like confinements: experiment and theory
• Topology of orientational defects in confined smectic liquid crystals
• Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals