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Liquid crystal distortions revealed by an octupolar tensor
Andrea Pedrini1, Epifanio G Virga1
1Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, 27100 Pavia, Italy.
Physical Review. E
|February 20, 2020
Summary
This study introduces a new algebraic method to describe liquid crystal distortions using an octupolar tensor. This tensor helps identify directions of concentrated distortion, offering new insights into soft material elasticity.
Area of Science:
- Soft Matter Physics
- Materials Science
- Liquid Crystal Science
Background:
- The Oseen-Frank theory describes liquid crystal elasticity using a director field (n).
- Distortions occur when the director field gradient (∇n) is non-uniform.
- Understanding these distortions is crucial for applications of liquid crystals.
Purpose of the Study:
- To propose a novel algebraic and geometric framework for characterizing local liquid crystal distortions.
- To introduce the octupolar tensor (A) derived from the director field and its gradient.
- To identify and visualize directions of distortion concentration within liquid crystals.
Main Methods:
- Construction of a third-rank, symmetric, and traceless tensor (A) from n and ∇n.
- Analysis of the tensor's cubic form (Φ) and its octupolar potential on the unit sphere.
- Geometric illustration and symmetry charting of the octupolar potential in distortion characteristic space.
Main Results:
- The octupolar tensor (A) effectively quantifies local liquid crystal distortions.
- Eigenvectors of A indicate directions of concentrated distortion.
- Geometric analysis reveals symmetries and dominating elastic modes.
Conclusions:
- The proposed octupolar tensor provides a new, insightful method for analyzing liquid crystal elasticity.
- This framework aids in understanding and predicting distortion behaviors in soft materials.
- The study offers tools to visualize and capture dominant elastic modes in complex liquid crystal states.
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