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Liquid crystal helical ribbons as isometric textures
M-F Achard1, M Kleman, Yu A Nastishin
1Centre de Recherche Paul Pascal, CNRS, Université Bordeaux 1, Avenue Schweitzer, 33600, Pessac, France.
The European Physical Journal. E, Soft Matter
|February 3, 2005
Summary
Isometric deformations in helical liquid crystals create frustrated textures with double-twisted ribbons. These helical ribbons, resembling screw dislocations, are proposed as explanations for observed textures in specific liquid crystal phases.
Area of Science:
- Soft Matter Physics
- Liquid Crystal Science
- Materials Science
Background:
- Isometric deformations preserving layer/columnar parallelism and distances are common in liquid crystals, leading to specific geometric features and macroscopic singularities.
- The presence of helical structures superimposed on periodicities modifies this behavior, but isometry can still be maintained.
Purpose of the Study:
- To investigate the geometric and energetic consequences of isometric deformations in a lamello-columnar liquid crystal phase with helical modulations.
- To analyze the resulting frustrated textures and their associated singularity structures.
Main Methods:
- Geometric analysis of 1D modulated layers with helical modulations.
- Modeling frustrated textures as parallel helicoids analogous to screw dislocations.
- Crude energy calculation for helical ribbons.
Main Results:
- Isometric textures in this helical system are necessarily frustrated, forming layers folded into parallel helicoids with double-twisted modulations along the helices.
- The singularity set consists of two helical disclination lines.
- A helical ribbon model is proposed and its energy crudely calculated.
Conclusions:
- The described helical ribbons are suggested as a model for textures observed in the B7 phase of banana-like molecules.
- The study proposes that describing double-twist structures using nested helicoids can be more advantageous than the traditional nested cylinder approach.