Direct control of disclinations via hybrid planar solitons in nematic liquid crystals

Tailoring self‐organized nano/microstructures in soft materials is crucial for exploiting intrinsic functional properties toward emerging applications. Engineered topological defects in liquid crystals are interesting for electro‐optical devices as well as for soft actuators morphing surface. Despite the promising potential, there are currently few bottom‐up methods for positioning a large number of defects periodically over a large area. It is highly challenging to develop essential techniques for achieving high‐throughput fabrication with simple procedure. Using ultraviolet/ozone treatment, herein we present a general and robust strategy to produce the surface that can be a platform for a self‐organized micropattern of topological defects in nematic liquid crystals, irrespective of the chemical structure of compounds including polymerizable monomers. The micropattern formation is controllable by applying area‐selective surface modification, which dramatically improves the fabrication efficiency. By low frequency impedance spectroscopy, the distinctive frequency dependence of the apparent threshold voltage at the micropattern formation is experimentally assigned to a unique reorientational response which occurs when a dielectric surface is charged by ionic additives. This characterization provides crucial guidance in further engineering self‐organized topological defects in liquid crystals.

Preface. 1. Classification of defects in liquid crystals H.-R. Trebin. 2. Alignment tensor versus director description in nematic liquid crystals A.M. Sonnet, S. Hess. 3. Liquid crystal colloidal dispersions H. Stark, et al. 4. Computer simulations and defects in confined liquid crystal lattice models C. Chiccoli, et al. 5. Molecular simulations and theory of planar interfaces and defects in nematic liquid crystals M.P. Allen. 6. Topological defect behavior in a quenched nematic liquid crystal R.A. Pelcovits, et al. 7. Restoring forces on nematic disclinations R. Rosso, E.G. Virga. 8. Challenges in the dynamics of point defects A.M. Sonnet, E.G. Virga. 9. Numerical simulation of elastic anisotropy in nematic liquid crystalline polymers H. Tu, et al. 10. Computer Simulations and Fluorescence Confocal Polarizing Microscopy of Structures in Cholesteric Liquid Crystals S.V. Shiyanovskii, et al. 11. Defects and Undulation in Layered Liquid Crystals T. Ishikawa, O.D. Lavrentovich. 12. Liquid crystals under shear: role of defects M. Kleman, C. Meyer. 13. Numerical simulation of defects in quasicrystals H.-R. Trebin. Index.

Researchers in computational condensed matter physics deal with complex data sets consisting of time varying 3D tensor, vector, and scalar quantities. Particularly, in the research of topological defects in nematic liquid crystals (LC) displaying the results of the computer simulation of molecular dynamics presents a challenge. Combining existing immersive and interactive visualization methods we developed new methods that attempt to provide a clear, efficient, and intuitive way to visualize and explore LC data. In addition, the visualization of the data has presented us with a novel method of obtaining the locations of the topological defects present in a liquid crystal system.

The nonsingular soliton-like defects in plane nematic liquid crystal (NLC) layers and spherical NLC drops are experimentally detected and studied when the interaction of NLC molecules with a bounding surface is varied. The dynamics and the annihilation of nonsingular defects of opposite signs on a plane surface are investigated. Periodic transformations of the soliton-like defects in NLC drops in an electric field are detected. The theory of elasticity is used to show that the surface energy taken into account in the total free energy of NLC in the case of weak anchoring leads to the possibility of nonsingular solutions of a director equilibrium equation. The calculated pictures of director distribution in a plane NLC layer and in a spherical NLC drop characterized by weak surface anchoring agree well with the results of polarized light optical observations.

By lunching the beam into the chiral nematic liquid crystals it is possible to achieve a non-diffractive beam similar to a soliton. This effect is caused by the molecular reorientation i.e. nonlinear response of the material forming the areas of higher refractive index. Diffraction is suppressed by the focusing effect. For appropriate launching conditions it is also possible to achieve a beam which splits into two or more separate beams. Such phenomenon is discussed in this article and analyzed theoretical. To model this effect Fully Vectorial Beam Propagation Method coupled with the Frank-Oseen elastic theory is used. Simulations are performed for various input beam powers, widths, polarization angles and launching positions. Full Text: PDF ReferencesG. Assanto and M. A. Karpierz, "Nematicons: self-localised beams in nematic liquid crystals", Liq. Cryst. 36, 1161–1172 (2009) CrossRef G. Assanto, Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals, John Wiley & Sons Inc. Hoboken, New Jersey (2013) DirectLink A. Piccardi, A. Alberucci, U. Bortolozzo, S. Residori, and G. Assanto, "Soliton gating and switching in liquid crystal light valve", Appl. Phys. Lett. 96, 071104 (2010). CrossRef D. Melo, I. Fernandes, F. Moraes, S. Fumeron, and E. Pereira, "Thermal diode made by nematic liquid crystal", Phys. Lett. A 380, 3121 – 3127 (2016). CrossRef U. Laudyn, M. Kwaśny, F. A. Sala, M. A. Karpierz, N. F. Smyth, G. Assanto, "Curved optical solitons subject to transverse acceleration in reorientational soft matter", Sci. Rep. 7, 12385 (2017) CrossRef M. Kwaśny, U. A. Laudyn, F. A. Sala, A. Alberucci, M. A. Karpierz, G. Assanto, "Self-guided beams in low-birefringence nematic liquid crystals", Phys. Rev. A 86, 013824 (2012) CrossRef F. A. Sala, M. M. Sala-Tefelska, "Optical steering of mutual capacitance in a nematic liquid crystal cell", J. Opt. Soc. Am. B. 35, 133-139 (2018) CrossRef U. A. Laudyn, A. Piccardi, M. Kwasny, M. A. Karpierz, G. Assanto, "Thermo-optic soliton routing in nematic liquid crystals", Opt. Lett. 43, 2296-2299 (2018) CrossRef F. A. Sala, M. M. Sala-Tefelska, M. J. Bujok, J. "Influence of temperature diffusion on molecular reorientation in nematic liquid crystals", Nonlinear Opt. Phys. Mater. 27, 1850011 (2018) CrossRef I-C Khoo Liquid crystals John Wiley & Sons, Inc (2007) DirectLink P. G. de Gennes, J. Prost, The Physics of Liquid Crystals, Clarendon Press (1995) DirectLink U. A. Laudyn, P. S. Jung, M. A. Karpierz, G. Assanto, "Quasi two-dimensional astigmatic solitons in soft chiral metastructures", Sci. Rep. 6, 22923 (2016) CrossRef J. Beeckman, A. Madani, P. J. M. Vanbrabant, P. Henneaux, S-P. Gorza, M. Haelterman, "Switching and intrinsic position bistability of soliton beams in chiral nematic liquid crystals", Phys. Rev. A 83, 033832 (2011) CrossRef A. Madani, J. Beeckman, K. Neyts, "An experimental observation of a spatial optical soliton beam and self splitting of beam into two soliton beams in chiral nematic liquid crystal", Opt. Commun. 298–299, 222-226, (2013) CrossRef G. D. Ziogos, E. E. Kriezis, "Modeling light propagation in liquid crystal devices with a 3-D full-vector finite-element beam propagation method", Opt. Quant. Electron 40, 10 (2008) CrossRef F. A. Sala, M. A. Karpierz, "Chiral and nonchiral nematic liquid-crystal reorientation induced by inhomogeneous electric fields", J. Opt. Soc. Am. B 29, 1465-1472 (2012) CrossRef F. A. Sala, M. A. Karpierz, "Modeling of molecular reorientation and beam propagation in chiral and non-chiral nematic liquid crystals", Opt. Express 20, 13923-13938 (2012) CrossRef F. A. Sala, "Design of false color palettes for grayscale reproduction", Displays, 46, 9-15 (2017) CrossRef

The presence of topological defects in liquid crystals is know since the very discovery of this interesting state of matter. However, the number of studies considering the dynamics of defects started to increase only recently [Ericksen (1996), Guidone Peroli (1998)]. One of the most interesting features of liquid crystal dynamics is the coupling between the director reorientation and the mass flow (“back flow“ effect). It results from the anisotropy of the liquid crystal molecules and leads to complicated viscous phenomena. Even in the case of the simplest liquid crystal phase (uniaxial nematic), there are five independent viscosities, entering the set of nematodynamic equations, described in detail by Ericksen (1960), Leslie (1966), and Parodi (1970). Recently, dynamics of defects in a cylindrical tube filled with a nematic liquid crystal was studied experimentally for the case of homeotropic anchoring (director prefers perpendicular alignment at the cavity wall) [Hillig (1997)]. Unsolved problems in the theory of defect dynamics and new experiments encouraged us to theoretically examine the annihilation of two point defects with opposite topological charge.

Umbilical defects were induced in a nematic liquid crystal with negative dielectric anisotropy, confined to Hele-Shaw cells with homeotropic boundary conditions, and their annihilation dynamics were investigated experimentally. Dynamic scaling laws, previously proposed for Schlieren defects, were verified also for electric field induced umbilical defects while varying external parameters, such as electric field amplitude, frequency, Hele-Shaw cell gap, and temperature. In all cases, scaling relations of rho(t) proportional to t(-1) for the defect density and D proportional to (t(0) - t)(1/2) for the defect pair separation were obtained, independent of external field parameters. The experimental results give evidence of the universality of scaling relations for the annihilation of topological defects in liquid crystals, extended to umbilical defects and their annihilation dynamics under applied external fields.

Arrays of topological defects in liquid crystals are fascinating systems, as isotropic and anisotropic phases of the same material can co-exist and be arranged in regular periodic structures. The arrays thus form spatially-varying optical pathways, in patterns that can be used for optics, as novel photonic structures, optical gratings, lenses or metamaterials, and for molecular and colloidal self-assembly. However, for practical applications, it is necessary that the arrays are tunable without direct intervention of the experimenters. Here, we demonstrate single-domain, tunable arrays of topological defects in nematic liquid crystals, using a method inspired by the recent work by Orihara and colleagues. The regularity and domain size of the defect arrays are obtained by using periodic lateral modulation of electric fields generated by incompletely etched electrodes with periodic conductivity. The period of the arrays, i.e. the characteristic spacing between defects, is controllable not only through the applied electric field strength and frequency but also by varying the size of the patterned electrodes. We believe these results open a new way to design and fabricate large-scale, single-domain, tunable and scalable device architectures that are optically functional.

In 1989 Ericksen proposed a new theory to model defects in liquid crystals. In this paper I give an account of a few problems that have been solved in the light of Ericksen’s new theory.

Nematics — mathematical and physical aspects : J.-M. Coron, J.-M., Chidaglia and F. Helein (eds.), NATO ASI Series. Kluwer, Dordrecht, 1991. 428 pp., Dfl.215, US$140, UK£74, ISBN 0-7923-1113-2.

In this work, we show that Janus washers, genus-one colloids with hybrid anchoring conditions, form topologically required defects in nematic liquid crystals. Experiments under crossed polarizers reveal the defect structure to be a rigid disclination loop confined within the colloid, with an accompanying defect in the liquid crystal. When confined to a homeotropic cell, the resulting colloid-defect ring pair tilts relative to the far field director, in contrast to the behavior of toroidal colloids with purely homeotropic anchoring. We show that this tilting behavior can be reversibly suppressed by the introduction of a spherical colloid into the center of the toroid, creating a new kind of multi-shape colloidal assemblage.

We show that backflow, the coupling between the order parameter and the velocity fields, has a significant effect on the motion of defects in nematic liquid crystals. In particular, the defect speed can depend strongly on the topological strength in two dimensions and on the sense of rotation of the director about the core in three dimensions.

After briefly describing the usually observed defects in nematic liquid crystals, we give a summary of our observations on high strength line defects and a regular network of point disclinations on the nematic-isotropic interface.

In recent years, important advances have been made in developing the first mathematically rigorous, nonlinear theory of defects in materials. It deals with the static theory of point defects in nematic liquid crystals. This is a brief exposition of important results, along with some discussion of possible formations of droplet problems. Also included are very interesting and hitherto unpublished data from Pat Cladis’s laboratory, on the motion of two point defects in a capillary, a fairly simple physical example of a kind of dynamical problem not yet treated by theorists.

Recently, Miyoshi et al . (Miyoshi et al . 2024 Proc. R. Soc. A 480 , 20240405 (doi: 10.1098/rspa.2024.0405 )) derived analytical formulas for the Frank free energy associated with multiple topological defects in nematic liquid crystals confined to an arbitrary simply connected domain. The energy formulas, derived using an analogy with the so-called Kirchhoff–Routh path function in point vortex dynamics, required the evaluation of contour integrals involving analytical formulas associated with the crystal alignment field. Equilibria for topological defects were then obtained by finding local extrema of this Frank free energy. By contrast, in vortex dynamics, it is rare to find point vortex equilibria by minimizing the Kirchhoff–Routh path function that is a regularized kinetic energy; more commonly, a local ‘non-self-induction rule’ is used that is equivalent to each point vortex being free of net force. It is shown here that an analogous equivalent set of local force conditions can also be used to find equilibria for topological defects in nematic liquid crystals in confined domains, and without any need to evaluate the Frank free energy. This observation is significant theoretically and also because, at a technical level, the new local force conditions are easier to formulate and solve.