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Defects Around a Spherical Particle in Cholesteric Liquid Crystals

Part of:Foundations, constitutive equations, rheologyPartial differential equations, boundary value problems

Published online by Cambridge University Press:  09 May 2017

Yu Tong,
Yiwei Wang and
Pingwen Zhang
Yu Tong*
Affiliation:
Laboratory of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China
Yiwei Wang*
Affiliation:
Laboratory of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China
Pingwen Zhang*
Affiliation:
Laboratory of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China
*
*Corresponding author. Email addresses:tong_yu@pku.edu.cn (Y. Tong), yiweiwang@pku.edu.cn (Y. W. Wang), pzhang@pku.edu.cn (P. W. Zhang)
*Corresponding author. Email addresses:tong_yu@pku.edu.cn (Y. Tong), yiweiwang@pku.edu.cn (Y. W. Wang), pzhang@pku.edu.cn (P. W. Zhang)
*Corresponding author. Email addresses:tong_yu@pku.edu.cn (Y. Tong), yiweiwang@pku.edu.cn (Y. W. Wang), pzhang@pku.edu.cn (P. W. Zhang)

Abstract

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We investigate the defect structures around a spherical colloidal particle in a cholesteric liquid crystal using spectral method, which is specially devised to cope with the inhomogeneity of the cholesteric at infinity. We pay particular attention to the cholesteric counterparts of nematic metastable configurations. When the spherical colloidal particle imposes strong homeotropic anchoring on its surface, besides the well-known twisted Saturn ring, we find another metastable defect configuration, which corresponds to the dipole in a nematic, without outside confinement. This configuration is energetically preferable to the twisted Saturn ring when the particle size is large compared to the nematic coherence length and small compared to the cholesteric pitch. When the colloidal particle imposes strong planar anchoring, we find the cholesteric twist can result in a split of the defect core on the particle surface similar to that found in a nematic liquid crystal by lowering temperature or increasing particle size.

Keywords

Cholesteric liquid crystaldefectsLandau-de Gennes theoryspectral method

MSC classification

Secondary:65N35: Spectral, collocation and related methods76A15: Liquid crystals

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 2 , May 2017, pp. 205 - 221
Copyright
Copyright © Global-Science Press 2017 

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