The defect structures of s = ±1/2 twist disclinations in twisted nematic and twisted chiral liquid crystals have been investigated within the Landau-de Gennes theory numerically. Our results show that there exists eigenvalue exchange across the defect core of both the two models. The defect core is essentially biaxial and never isotropic. The defect centre is uniaxial and is surrounded by a strong biaxial region.
KeywordsDisclinationsEigenvalue ExchangeDefect CoreLandau-de Gennes Theory
N. D. Mermin, “Topological Theory of Defects,” Review Modern Physics, Vol. 51, No. 3, 1979, pp. 591-648. doi:10.1103/RevModPhys.51.591
H.-R. Trebin, “The Topology of Non-Uniform Media in Condensed Matter Physics,” Advances in Physics, Vol. 31, No. 3, 1982, pp. 195-254.
P. Chaikin and T. Lubensky, “Principles of Condensed Matter Physics,” Cambridge University Press, Cambridge, 1995.
M. Kléman, “Points, Lines and Walls in: Liquid Crystals, Magnetic Systems and Various Disordered Media,” Wiley, New York, 1983.
M. V. Kurik and O. D. Lavrentovich, “Defects in Liquid Crystals: Homotopy Theory and Experimental Studies,” Soviet Physics Uspekhi, Vol. 31, No. 3, 1988, pp. 196-224.
S. Kralj and E. G. Virga, “Universal Fine Structure of Nematic Hedgehogs,” Journal of Physics A, Vol. 34, No. 4, 2001, pp. 829-838.
N. Schopohl and T. J. Sluckin, “Defect Core Structure in Nematic Liquid Crystals,” Physical Review Letters, Vol. 59, No. 22, 1987, pp. 2582-2584.
R. Rosso and E. G. Virga, “Metastable Nematic Hedgehogs,” Journal of Physics A, Vol. 29, No. 14, 1996, pp. 4247-4264.
S. Kralj, E. G. Virga and S. ?umer, “Biaxial Torus around Nematic Point Defects,” Physical Review E, Vol. 60, No. 2, 1999, pp. 1858-1866.
M. Ambrozic, S. Kralj and E. G. Virga, “Defect-Enhanced Nematic Surface Order Reconstruction,” Physical Review E, Vol. 75, No. 3, 2007, pp. 1-9.
R. Barberi, F. Ciuchi, G. E. Durand, M. Iovane, D. Sikharulidze, A. M. Sonnet and E. G. Virga, “Electric Field Induced Order Reconstruction in a Nematic Cell,” European Physical Journal E, Vol. 13, No. 1, 2004, pp. 61-71.
S. Kralj, R. Rosso and E. G. Virga, “Finite-Size Effects on Order Reconstruction around Nematic Defects,” Physical Review E, Vol. 81, No. 2, 2010, pp. 1-15.
D. Pires and Y. Galerne, “Recording of Virtual Disclination Lines by Means of Surface Polymerization in a Nematic Liquid Crystal,” Molecular Crystal and Liquid Crystals, Vol. 438, No. 1, 2005, pp. 1681-1686.
P. G. De Gennes and J. Prost, “The Physics of Liquid Crystals,” Oxford University Press, Oxford, London, 1993.
A. D. Kiselev and T. J. Sluckin, “Twist of Cholesteric Liquid Crystal Cells: Stability of Helical Structures and Anchoring Energy Effects,” Physical Review E, Vol. 71, No. 3, 2005, pp. 1-11.
P. G. De Gennes, “Long Range Order and Thermal Fluctuations in Liquid Crystals,” Molecular Crystal and Liquid Crystals, Vol. 7, No. 1, 1969, pp. 325-345.
T. J. Scheffer, “Structures and Energies of Grandjean-Cano Liquid-Crystal Disclinations,” Physical Review A, Vol. 5, No. 3, 1972, pp. 1327-1336.
I. I. Smalyukh and O. D. Lavrentovich, “Three-Dimensional Director Structures of Defects in Grandjean-Cano Wedges of Cholesteric Liquid Crystals Studied by Fluorescence Confocal Polarizing Microscopy,” Physical Review E, Vol. 66, No. 5, 2002, pp. 1-16.
D. Engstrom, R. P. Trivedi, M. Persson, M. Goksor, K. A. Bertness and I. I. Smalyukh, “Three-Dimensional Imaging of Liquid Crystal Structures and Defects by Means of Holographic Manipulation of Colloidal Nanowires with Faceted Sidewalls,” Soft Matter, Vol. 7, No. 13, 2011, pp. 6304-6312.
I. I. Smalyukh, S. V. Shiyanovskii and O. D. Lavrentovich, “Three-Dimensional Imaging of Orientational Order by Fluorescence Confocal Polarizing Microscopy,” Chemical Physics Letters, Vol. 336, No. 1-2, 2001, pp. 88-96.
I. I. Smalyukh and O. D. Lavrentovich, “Anchoring-Mediated Interaction of Edge Dislocations with Bounding Surfaces in Confined Cholesteric Liquid Crystals,” Physical Review Letters, Vol. 90, No. 8, 2003, pp. 1-4.
E. G. Virga, “Variational Theories for Liquid Crystals,” Chapman Hall, London, 1994.
P. Kaiser, W. Wiese and S. Hess, “Stability and Instability of a Uniaxial Alignment against Biaxial Distortions in the Isotropic and Nematic Phases of Liquid Crystals,” Journal of Non-Equilibrium Thermodynamics, Vol. 17, No. 2, 1992, pp. 153-169.
D. C. Wright and N. D. Mermin, “Mermin, Crystalline Liquids: The Blue Phases,” Reviews of Modern Physics, Vol. 61, No. 2, 1989, pp. 385-432.
X. Zhou, Z. D. Zhang and L. Xuan, “Surface-Groove-Induced Boundary-Roughness Effects in Nematics: A Comparison between Models Allowing or Not,” Molecular Crystal and Liquid Crystals, Vol. 562, No. 1, 2012, pp. 66-75.
J. Fukuda, “Stabilization of a Blue Phase by a Guest Component: An Approach Based on a Landau-de Gennes Theory,” Physical Review E, Vol. 82, No. 6, 2010, pp. 1-5.
J. Fukuda and S. Zumer, “Ring Defects in a Strongly Confined Chiral Liquid Crystal,” Physical Review Letters, Vol. 106, No. 9, 2011, pp. 1-4.
Z. Bradac, S. Kralj and S. Zumer, “Molecular Dynamics Study of the Isotropic-Nematic Quench,” Physical Review E, Vol. 65, No. 2, 2002, pp. 1-10.
H. Mori and H. Nakanishi, “On the Stability of Topologically Non-Trivial Point Defects,” Journal of the Physical Society of Japan, Vol. 57, No. 4, 1988, pp. 1281-1286.
N. V. Priezjev and R. A. Pelcovits, “Disclination Loop Behavior near the Nematic-Isotropic Transition,” Physical Review E, Vol. 64, No. 3, 2001, pp. 1-7.
Z. L. Xie and H. S. Kwok, “New Bistable Twisted Nematic Liquid Crystal Displays,” Journal of Applied Physics, Vol. 84, No. 1, 1998, pp. 77-82.
Z. Zhuang, Y. J. Kim and J. S. Patel, “Bistable Twisted Nematic Liquid-Crystal Optical Switch,” Applied Physics Letters, Vol. 75, No. 19, 1999, pp. 3008-3010.
Z. L. Xie, Y. M. Dong, S. Y. Xu, H. J. Gao and H. S. Kwok, “π/2 and 5π/2 Twisted Bistable Nematic Liquid Crystal Display,” Journal of Applied Physics, Vol. 87, No. 6, 2000, pp. 2673-2676.
F. S. Y. Yeung and H. S. Kwok, “Truly Bistable Twisted Nematic Liquid Crystal Display Using Photoalignment Technology,” Applied Physics Letters, Vol. 83, No. 21, 2003, pp. 4291-4293.