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Volume 21, Issue 3
Transition of Defect Patterns from 2D to 3D in Liquid Crystals

Yang Qu, Ying Wei & Pingwen Zhang

Commun. Comput. Phys., 21 (2017), pp. 890-904.

Published online: 2018-04

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  • Abstract

Defects arise when nematic liquid crystals are under topological constraints at the boundary. Recently the study of defects has drawn a lot of attention because of the growing theoretical and practical significance. In this paper, we investigate the relationship between two-dimensional defects and three-dimensional defects within nematic liquid crystals confined in a shell. A highly accurate spectral method is used to solve the Landau-de Gennes model to get the detailed static structures of defects. Interestingly, the solution is radial-invariant when the thickness of the shell is sufficiently small. As the shell thickness increases, the solution undergoes symmetry break to reconfigure the disclination lines. We study this three-dimensional reconfiguration of disclination lines in detail under different boundary conditions. In particular, we find that the temperature plays an important role in deciding whether the transition between two-dimensional defects and three-dimensional defects is continuous or discontinuous for the shell with planar anchoring condition on both inner and outer surfaces. We also discuss the characterization of defects in two- and three-dimensional spaces within the tensor model.

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@Article{CiCP-21-890, author = {Yang Qu, Ying Wei and Pingwen Zhang}, title = {Transition of Defect Patterns from 2D to 3D in Liquid Crystals}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {3}, pages = {890--904}, abstract = {

Defects arise when nematic liquid crystals are under topological constraints at the boundary. Recently the study of defects has drawn a lot of attention because of the growing theoretical and practical significance. In this paper, we investigate the relationship between two-dimensional defects and three-dimensional defects within nematic liquid crystals confined in a shell. A highly accurate spectral method is used to solve the Landau-de Gennes model to get the detailed static structures of defects. Interestingly, the solution is radial-invariant when the thickness of the shell is sufficiently small. As the shell thickness increases, the solution undergoes symmetry break to reconfigure the disclination lines. We study this three-dimensional reconfiguration of disclination lines in detail under different boundary conditions. In particular, we find that the temperature plays an important role in deciding whether the transition between two-dimensional defects and three-dimensional defects is continuous or discontinuous for the shell with planar anchoring condition on both inner and outer surfaces. We also discuss the characterization of defects in two- and three-dimensional spaces within the tensor model.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0034}, url = {http://global-sci.org/intro/article_detail/cicp/11264.html} }
TY - JOUR T1 - Transition of Defect Patterns from 2D to 3D in Liquid Crystals AU - Yang Qu, Ying Wei & Pingwen Zhang JO - Communications in Computational Physics VL - 3 SP - 890 EP - 904 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.OA-2016-0034 UR - https://global-sci.org/intro/article_detail/cicp/11264.html KW - AB -

Defects arise when nematic liquid crystals are under topological constraints at the boundary. Recently the study of defects has drawn a lot of attention because of the growing theoretical and practical significance. In this paper, we investigate the relationship between two-dimensional defects and three-dimensional defects within nematic liquid crystals confined in a shell. A highly accurate spectral method is used to solve the Landau-de Gennes model to get the detailed static structures of defects. Interestingly, the solution is radial-invariant when the thickness of the shell is sufficiently small. As the shell thickness increases, the solution undergoes symmetry break to reconfigure the disclination lines. We study this three-dimensional reconfiguration of disclination lines in detail under different boundary conditions. In particular, we find that the temperature plays an important role in deciding whether the transition between two-dimensional defects and three-dimensional defects is continuous or discontinuous for the shell with planar anchoring condition on both inner and outer surfaces. We also discuss the characterization of defects in two- and three-dimensional spaces within the tensor model.

Yang Qu, Ying Wei and Pingwen Zhang. (2018). Transition of Defect Patterns from 2D to 3D in Liquid Crystals. Communications in Computational Physics. 21 (3). 890-904. doi:10.4208/cicp.OA-2016-0034
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