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High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal
Published on: October 31, 2019
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Global defect topology in nematic liquid crystals.
Thomas Machon1, Gareth P Alexander1
1Department of Physics and Centre for Complexity Science , University of Warwick , Coventry CV4 7AL, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|August 6, 2016
Summary
This study classifies nematic textures using twisted cohomology, linking homotopy classes to homology groups of branched double covers for knotted defects. Planar textures and meron obstructions are identified, relating to experiments and cholesteric τ lines.
Area of Science:
- Soft Matter Physics
- Topological Matter Physics
- Liquid Crystal Science
Background:
- Nematic textures exhibit complex topological structures.
- Understanding defect behavior in liquid crystals is crucial for applications.
- Weak anchoring conditions present unique classification challenges.
Purpose of the Study:
- To provide a global homotopy classification of nematic textures.
- To analyze textures with arbitrary defect sets and weak anchoring.
- To establish a framework for relating topological properties to experimental observations.
Main Methods:
- Utilizing twisted cohomology for classification.
- Explicit computation for knotted and linked defects.
- Employing branched double covers and homology groups.
Main Results:
- A one-to-one correspondence between homotopy classes and the first homology group of the branched double cover.
- Identification of planar textures for defect classes of order 2.
- Characterization of obstructions for other classes using merons.
Conclusions:
- Global defect topology, not local features, defines planar textures.
- The classification relates to nematic droplet experiments.
- Order 4 elements correlate with τ lines in cholesterics.
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