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Transition of Defect Patterns from 2D to 3D in Liquid Crystals

Published online by Cambridge University Press:  07 February 2017

Yang Qu ,
Ying Wei  and
Pingwen Zhang
Yang Qu*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China
Ying Wei*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China
Pingwen Zhang*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China
*
*Corresponding author. Email addresses:quyang@pku.edu.cn (Y. Qu), wyheyhey@163.com (Y. Wei), pzhang@pku.edu.cn (P. Zhang)
*Corresponding author. Email addresses:quyang@pku.edu.cn (Y. Qu), wyheyhey@163.com (Y. Wei), pzhang@pku.edu.cn (P. Zhang)
*Corresponding author. Email addresses:quyang@pku.edu.cn (Y. Qu), wyheyhey@163.com (Y. Wei), pzhang@pku.edu.cn (P. Zhang)
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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.

Keywords

Transition of defectsliquid crystalLandau-de Gennes modelspectral method
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 3 , March 2017 , pp. 890 - 904
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Hu, Y. C., Qu, Y. and Zhang, P. W., On the disclination lines of nematic liquid crystals, Commun. Comput. Phys., 19 (2016), 354–379.Google Scholar
[2] Cheng, H. and Zhang, P. W., A tensor model for liquid crystals on a spherical surface, Sci. China Math., 56 (2013), 2549–2559.CrossRefGoogle Scholar
[3] Zhang, W.-Y., Jiang, Y. and Chen, J. Z. Y., Onsager model for the structure of rigid rods confined on a spherical surface, Phys. Rev. Lett., 108 (2012), 057801.CrossRefGoogle ScholarPubMed
[4] Lavrentovich, O. D., Defects in Liquid Crystals: Surface and Interfacial Anchoring Effects, in Patterns of Symmetry Breaking, Springer Netherlands, Dordrecht, 2003, 161–195.Google Scholar
[5] Kralj, S., Rosso, R. and Virga, E. G., Fingered core structure of nematic boojums, Phys. Rev. E, 78 (2008), 031701.Google Scholar
[6] Lubensky, T. C., David Pettey, Nathan Currier and Holger Stark, Topological defects and interactions in nematic emulsions, Phys. Rev. E, 57 (1998), 610.CrossRefGoogle Scholar
[7] Tasinkevych, M., Silvestre, N. and Telo da Gama, M.M., Liquid crystal boojum-colloids, New J. Phys., 14 (2012), 073030.Google Scholar
[8] Nelson, D. R., Toward a tetravalent chemistry of colloids, Nano Lett., 2 (2002), 1125–1129.CrossRefGoogle Scholar
[9] Lopez-Leon, T., Koning, V., Vitelli, V., Davaiah, K. B. S. and Fernandez-Nieves, A., Frustrated nematic order in spherical geometries, Nature Physics, 7 (2011), 391.CrossRefGoogle Scholar
[10] Vitelli, V. and Nelson, D. R., Nematic texures in spherical shells, Phys. Rev. E, 74 (2006), 021711.CrossRefGoogle Scholar
[11] Ravnik, M. and Zumer, S., Landau-de Gennes modelling of nematic liquid crystal colloids, Liq. Cryst., 36 (2009), 1201.Google Scholar
[12] Poulin, P. and Weitz, D. A., Inverted and multiple nematic emulsions, Phys. Rev. E, 57 (1998), 626.Google Scholar
[13] Kralj, S., Rosso, R. and Virga, E. G., Curvature control of valence on nematic shells, Soft Matter, 7 (2011), 670–683.Google Scholar
[14] Bates, M. A., Skačej, G. and Zannoni, C., Defects and ordering in nematic coatings on uniaxial and biaxial colloids, Soft Matter, 6 (2010), 655–663.Google Scholar
[15] Majumdar, A., Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory, Eur. J. Appl. Math, 21 (2010), 181–203.Google Scholar
[16] Mkaddem, S. and Gartland, E. Jr, Fine structure of defects in radial nematic droplets, Phys. Rev. E, 62 (2000), 6694.CrossRefGoogle ScholarPubMed
[17] Porenta, T., Ravnik, M. and Zumer, S., Effect of flexoelectricity and order electricity on defect cores in nematic droplets, Soft Matter, 7 (2011), 132.Google Scholar
[18] de Gennes, P. G. and Prost, J., The physics of liquid crystals, Oxford University Press, Oxford, second ed., 1995.Google Scholar
[19] Lin, F. H. and Liu, C., Static and dynamic theories of liquid crystals, J. Partial Differ. Equ., 14 (2001), 289–330.Google Scholar
[20] Callan-Jones, A. C., Pelcovits, R. A., Slavin, V. A., Zhang, S., Laidlaw, D. H. and Loriot, G. B., Simulation and visualization of topological defects in nematic liquid crystals, Phys. Rev. E, 74 (2006), 061701.Google Scholar
[21] Miller, D. S., Wang, X. and Abbott, N. L., Design of functional materials based on liquid crystalline droplets, Chem. Mater., 26 (2013), 496–506.CrossRefGoogle Scholar
[22] Kralj, S., Virga, E. G. and Žumer, S., Biaxial torus around nematic point defects, Phys. Rev. E, 60 (1999), 1858–1866.Google Scholar
[23] Zernike, F., Diffraction theory of the cut procedure and its improved form, the phase contrast method, Physica, 1 (1934), 689–704.Google Scholar
[24] Avriel, M., Nonlinear programming: analysis and methods, Courier Dover Publications, 2003.Google Scholar
[25] Lopez-Leon, T. and Fernandez-Nieves, A., Drops and shells of liquid crystal, Colloid Polym Sci., 289 (2011), 345–359.Google Scholar
[26] Canevari, G., Ramaswamy, M. and Majumdar, A., Radial symmetry on three-dimensional shells in the Landau-de Gennes theory, Physica D: Nonlinear Phenomena, 314 (2016), 18–34.Google Scholar
[27] Seyednejad, S. R., Mozaffari, M. R. and Ejtehadi, M. R., Confined nematic liquid crystal between two spherical boundaries with planar anchoring, Phys. Rev. E, 88 (2013), 012508.Google Scholar
[28] Lopez-Leon, T., Bates, M. A. and Fernandez-Nieves, A., Defect coalescence in spherical nematic shells, Phys. Rev. E., 86 (2012), 030702.Google Scholar
[29] Seč, David, Lopez-Leon, T., Nobili, M., Blanc, C., Fernandez-Nieves, A., Ravnik, M. and ŽZumer, S., Defect trajectories in nematic shells: Role of elastic anisotropy and thickness heterogeneity, Phys. Rev. E., 86 (2012), 020705.Google Scholar
[30] Fernández-Nieves, A., Vitelli, V., Utada, A. S., Link, D. R. and Márquez, M., Nelson, D. R. and Weitz, D. A., Novel Defect Structures in Nematic Liquid Crystal Shells, Phys. Rev. Lett., 99 (2007), 157801.Google Scholar