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Journal of Shanghai University >

2022 , Vol. 28 >Issue 6: 1094 - 1105

DOI: https://doi.org/10.12066/j.issn.1007-2861.2340

Research Articles

Topological structure of free energy density of nematic liquid crystals

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  • 1. College of Sciences, Shanghai University, Shanghai 200444, China
    2. Shanghai Key Lab for Astrophysics, Shanghai 200234, China

Received date: 2021-06-29

  Online published: 2021-10-08

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Abstract

Through the investigation to the classical expressions of free energy density of nematic liquid crystal, a surface term was added to represent the free energy of defects in liquid crystals. By means of $\phi $-mapping method and topological current theory, the new expression of free energy density which was concentrated on the defects was studied. It is shown that the free energy density concentrated on the defects is topologically quantized in the unit of $\frac{1}{2}k\pi $, and the topological quantum numbers are determined by Hopf index and Brouwer degree. The configurations of molecules of liquid crystal around the different disclination strengths of defects are also given in this paper.

Key words： liquid crystal; director; free energy; defect; topological current

Cite this article

ZHANG Canyu, YANG Guohong . Topological structure of free energy density of nematic liquid crystals[J]. Journal of Shanghai University, 2022 , 28(6) : 1094 -1105 . DOI: 10.12066/j.issn.1007-2861.2340

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