Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T16:46:42.572Z Has data issue: false hasContentIssue false
  • English
  • Français

Defects Around a Spherical Particle in Cholesteric Liquid Crystals

Part of: Foundations, constitutive equations, rheology Partial 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)
Get access

Abstract

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 methods 76A15: Liquid crystals
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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ball, J. M. and Zarnescu, A., Orientability and energy minimization in liquid crystal models, Arch. Ration. Mech. Anal., 202 (2011), pp. 493–535.CrossRefGoogle Scholar
[2] Bedford, S., Global minimisers of cholesteric liquid crystal systems, arXiv preprint arXiv: 1411.3599, (2014).Google Scholar
[3] Callan-Jones, A., Pelcovits, R. A., Slavin, V., Zhang, S., Laidlaw, D. and Loriot, G., Simulation and visualization of topological defects in nematic liquid crystals, Phys. Rev. E, 74 (2006), pp. 061701.CrossRefGoogle ScholarPubMed
[4] De Gennes, P. G. and Prost, J., The Physics of Liquid Crystals, Oxford University Press, 1993.CrossRefGoogle Scholar
[5] Ericksen, J. L., Liquid crystals with variable degree of orientation, Arch. Ration. Mech. Anal., 113 (1991), pp. 97–120.Google Scholar
[6] Foffano, G., Lintuvuori, J., Tiribocchi, A., and Marenduzzo, D., The dynamics of colloidal intrusions in liquid crystals: a simulation perspective, Liq. Cryst. Rev., 2 (2014), pp. 1–27.Google Scholar
[7] Fournier, J.-B. and Galatola, P., Modeling planar degenerate wetting and anchoring in nematic liquid crystals, Europhys. Lett., 72 (2005), pp. 403.Google Scholar
[8] Fukuda, J. and Žumer, S., Cholesteric blue phases: effect of strong confinement, Liq. Cryst., 37 (2010), pp. 875–882.CrossRefGoogle Scholar
[9] Fukuda, J.-I., Liquid crystal colloids: a novel composite material based on liquid crystals, J. Phys. Soc. Japan, 78 (2009), pp. 041003.CrossRefGoogle Scholar
[10] Fukuda, J.-I., Yoneya, M. and Yokoyama, H., Nematic liquid crystal around a spherical particle: Investigation of the defect structure and its stability using adaptive mesh refinement, Euro. Phys. J. E, 13 (2004), pp. 87–98.CrossRefGoogle ScholarPubMed
[11] Grebel, H., Hornreich, R. and Shtrikman, S., Landau theory of cholesteric blue phases, Phys. Rev. A, 28 (1983), pp. 1114.CrossRefGoogle Scholar
[12] Han, J., Luo, Y., Wang, W., Zhang, P. and Zhang, Z., From microscopic theory to macroscopic theory: a systematic study on modeling for liquid crystals, Arch. Ration. Mech. Anal., 215 (2015), pp. 741–809.Google Scholar
[13] Hornreich, R. and Shtrikman, S., Landau theory of twist-induced biaxiality in cholesteric liquid crystals, Phys. Rev. A, 29 (1984), pp. 3444.Google Scholar
[14] Hu, Y., Qu, Y. and Zhang, P., On the disclination lines of nematic liquid crystals, Commun. Comput. Phys., 19 (2016), pp. 354–379.CrossRefGoogle Scholar
[15] Kato, T., Perturbation Theory for Linear Operators, Vol. 132, Springer Science & Business Media, 2013.Google Scholar
[16] Lintuvuori, J., Marenduzzo, D., Stratford, K. and Cates, M., Colloids in liquid crystals: a lattice boltzmann study, J. Mater. Chem., 20 (2010), pp. 10547–10552.Google Scholar
[17] Lintuvuori, J., Stratford, K., Cates, M. and Marenduzzo, D., Colloids in cholesterics: size-dependent defects and non-stokesian microrheology, Phys. Rev. Lett., 105 (2010), pp. 178302.CrossRefGoogle ScholarPubMed
[18] Longa, L., Monselesan, D. and Trebin, H.-R., Phase diagrams of cholesteric liquid crystals obtained with a generalized landau-de gennes theory, Liq. Cryst., 5 (1989), pp. 889–898.Google Scholar
[19] Lubensky, T., Pettey, D., Currier, N. and Stark, H., Topological defects and interactions in nematic emulsions, Phys. Rev. E, 57 (1998), pp. 610.CrossRefGoogle Scholar
[20] Majumdar, A., Equilibrium order parameters of nematic liquid crystals in the landau-de gennes theory, Euro. J. Appl. Math., 21 (2010), pp. 181–203.Google Scholar
[21] Majumdar, A. and Zarnescu, A., Landau–de gennes theory of nematic liquid crystals: the oseen–frank limit and beyond, Arch. Ration. Mech. Anal., 196 (2010), pp. 227–280.Google Scholar
[22] Melle, M., Schlotthauer, S., Hall, C. K., Diaz-Herrera, E., and Schoen, M., Disclination lines at homogeneous and heterogeneous colloids immersed in a chiral liquid crystal, Soft Matter, 10 (2014), pp. 5489–5502.Google Scholar
[23] Mkaddem, S. and Gartland, E. C., Fine structure of defects in radial nematic droplets, Phys. Rev. E, 62 (2000), pp. 6694–6705.CrossRefGoogle ScholarPubMed
[24] Muševič, I., Škarabot, M., Tkalec, U., Ravnik, M. and Žumer, S., Two-dimensional nematic colloidal crystals self-assembled by topological defects, Science, 313 (2006), pp. 954–958.Google Scholar
[25] Onsager, L., The effects of shape on the interaction of colloidal particles, Ann. N. Y. Acad. Sci., 51 (1949), pp. 627–659.CrossRefGoogle Scholar
[26] Oseen, C., The theory of liquid crystals, Trans. Faraday Soc., 29 (1933), pp. 883–899.CrossRefGoogle Scholar
[27] Pandey, M., Ackerman, P., Burkart, A., Porenta, T., Žumer, S. and Smalyukh, I. I., Topology and self-assembly of defect-colloidal superstructure in confined chiral nematic liquid crystals, Phys. Rev. E, 91 (2015), pp. 012501.Google Scholar
[28] Poulin, P., Stark, H., Lubensky, T., and Weitz, D., Novel colloidal interactions in anisotropic fluids, Science, 275 (1997), pp. 1770–1773.CrossRefGoogle ScholarPubMed
[29] Poulin, P. and Weitz, D., Inverted and multiple nematic emulsions, Phys. Rev. E, 57 (1998), pp. 626.Google Scholar
[30] Ravnik, M. and Žumer, S., Landau–de gennes modelling of nematic liquid crystal colloids, Liq. Cryst., 36 (2009), pp. 1201–1214.Google Scholar
[31] Shen, J., Tang, T., and Wang, L.-L., Spectral Methods: Algorithms, Analysis and Applications, Vol. 41, Springer Science & Business Media, 2011.CrossRefGoogle Scholar
[32] Tasinkevych, M., Silvestre, N. and Da Gama, M. T., Liquid crystal boojum-colloids, New J. Phys., 14 (2012), pp. 073030.Google Scholar