Stability of Disclinations in Nematic Liquid Crystals |
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Authors: | WANG Yu-Sheng YANG Guo-Hong TIAN Li-Jun DUAN Yi-Shi |
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Institution: | 1. Department of Physics, Shanghai University, Shanghai 200444, China
;2. Department of Mathematics and Information Sciences, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450008, China
;3. Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China |
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Abstract: | In the light of φ-mapping method and topological current theory, the stability of disclinations
around a spherical particle in nematic liquid crystals is studied.
We consider two different defect structures around a spherical
particle: disclination ring and point defect at the north or south
pole of the particle. We calculate the free energy of these different defects in the elastic theory. It is pointed out that the total Frank free energy density can be divided into two parts.
One is the distorted energy density of director field around the
disclinations. The other is the free energy density of disclinations themselves, which is shown to be concentrated at the defect and to be topologically quantized in the unit of
(k-k24)π/2. It is shown that in the presence of
saddle-splay elasticity a dipole (radial and hyperbolic hedgehog)
configuration that accompanies a particle with strong homeotropic
anchoring takes the structure of a small disclination ring, not a point defect. |
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Keywords: | director field topological defect free energy bifurcation |
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