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Singular values, nematic disclinations, and emergent biaxiality
Simon Čopar1, Mark R Dennis, Randall D Kamien
1Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA.
Summary
This study introduces a novel method to define a biaxial frame for nematic liquid crystals, extending beyond the standard uniaxial description. This approach reveals new insights into the orientational ordering and quasidefects within these materials.
Area of Science:
- Materials Science
- Condensed Matter Physics
Background:
- Nematic liquid crystals exhibit orientational ordering of molecular building blocks.
- Uniaxial nematics orient along one axis, while biaxial nematics orient along three.
Purpose of the Study:
- To extend the description of nematic order beyond the uniaxial phase.
- To analyze the similarities and differences between uniaxial and biaxial nematic phases.
Main Methods:
- Singular value decomposition of the director field gradient to establish a biaxial frame.
- Application of quaternion group algebra to the uniaxial phase.
Main Results:
- A method to extract a full biaxial frame from the director field gradient was developed.
- Quasidefects were identified as degrees of freedom in the extended biaxial frame.
- Algebraic rules of the quaternion group were applied to analyze the uniaxial phase.
Conclusions:
- The extended biaxial frame provides a more comprehensive understanding of nematic liquid crystal ordering.
- The framework allows for detailed comparison between uniaxial and biaxial nematic phases.
- This research offers new perspectives on the topological defects and orientational dynamics in liquid crystals.
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