Defects In Nematic Liquid Crystals Research Articles

Moiré effect enables versatile design of topological defects in nematic liquid crystals

Recent advances in surface-patterning techniques of liquid crystals have enabled the precise creation of topological defects, which promise a variety of emergent applications. However, the manipulation and application of these defects remain limited. Here, we harness the moiré effect to engineer topological defects in patterned nematic liquid crystal cells. Specifically, we combine simulation and experiment to examine a nematic cell confined between two substrates of periodic surface anchoring patterns; by rotating one surface against the other, we observe a rich variety of highly tunable, novel topological defects. These defects are shown to guide the three-dimensional self-assembly of colloids, which can conversely impact defects by preventing the self-annihilation of loop-defects through jamming. Finally, we demonstrate that certain nematic moiré cells can engender arbitrary shapes represented by defect regions. As such, the proposed simple twist method enables the design and tuning of mesoscopic structures in liquid crystals, facilitating applications including defect-directed self-assembly, material transport, micro-reactors, photonic devices, and anti-counterfeiting materials.

Formation and annihilation of electrically driven defects in nematic liquid crystals with negative dielectric anisotropy

Orientationally ordered liquid crystals (LCs) exhibit remarkable physical anisotropy and responsiveness to external fields, which give rise to distinguished physical effects and have led to the emergence of a new generation of electric-optical applications. The LCs are also renowned for their abundance of phases and topological defects, which are of significance in studying both fundamental science and practical technology. One simple approach to generating umbilic defects involves applying an electric field to a homeotropically aligned nematic LC with negative dielectric anisotropy <inline-formula><tex-math id="M8">\begin{document}$\Delta \varepsilon $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M8.png"/></alternatives></inline-formula>. However, the influence of material properties and external conditions on the dynamic process of nematic LC defects remains unclear. Here, we select seven kinds of nematic LCs with negative dielectrically anisotropy, ranging from –1.1 to –11.5, to explore the dynamics of electric-field-induced umbilics. By using a linearly increasing electric field parallel to the molecular orientation of LC, we systematically investigate the effects of material property (dielectric anisotropy) and external conditions (temperature and electric field parameters) on the formation and annihilation of umbilic defects. The experimental results show that the dynamic process of forming the umbilic defects in nematic LCs is independent of dielectric anisotropy, temperature, and electric field frequency, but follows the Kibble-Zurek mechanism, in which the density of generated umbilic defects exhibits a power-law scaling with the change of the electric field ramp rate, with a scaling exponent of approximately <inline-formula><tex-math id="M9">\begin{document}$1/2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M9.png"/></alternatives></inline-formula>. Interestingly, a stronger dielectric anisotropy leads to a higher density of umbilic defects. Additionally, a change in temperature has a significant influence on the density of umbilic defects , in which higher temperature leads to greater defect density under the same external electric field conditions. Furthermore, the annihilation rate of umbilic defects is closely related to the material properties and the ramp of the applied electric field. Specifically, the annihilation rate of umbilic defects becomes faster when dielectric anisotropy is stronger or the electric field ramp is larger. This study provides valuable insights into the relationship between the formation and annihilation of defects, material properties, and external conditions in nematic LCs with dielectrically negative anisotropy, contributing to our comprehensive understanding of the dynamic process of topological defects in soft matter.

Vector Field Models for Nematic Disclinations

In this paper, a model for defects in nematic liquid crystals that was introduced in Zhang et al. (Physica D Nonlinear Phenom 417:132828, 2021) is studied. In the literature, the setting of many models for defects is the function space SBV (special functions of bounded variation). However, the model considered herein regularizes the director field to be in a Sobolev space by introducing a second vector field tracking the defect. A relaxation result in the case of fixed parameters is proved along with some partial compactness results as the defect width vanishes.

Dynamic Motions of Topological Defects in Nematic Liquid Crystals under Spatial Confinement

AbstractTopological defects (TDs) have become a sensational topic due to their significant influence on the unusual optical and physiochemical characteristics of the material. To facilitate their application across a wide range of disciplines it is desirable to analyze and gain fundamental understanding of TDs in both equilibrium and nonequilibrium systems. Liquid crystals (LCs) are considered an ideal system for study given the direct visualization of TDs and a straightforward analyzation process. In addition to the equilibrium morphology of LC TDs, it is also of great interest to track and control the formation and annihilation of defects during thermodynamic processes. However, controlling the dynamic behavior of formed defects remains a challenge. Here, nematic LCs confined in a cell exhibiting surfaces with periodic anchoring conditions containing surface topography are relied on. The effects of patterned surface characteristics such as width, periodicity, and degree of curvature on defects dynamic motion, stabilization, and annihilation are explored. The computational experiments recapitulate the TDs transition path and provide free energy‐based predictions of critical distances for defect annihilation. Taken together, this simple approach offers a promising opportunity to control the dynamics of TDs in LCs through chemical patterned surfaces with topography.

Disclination lines in nematic liquid crystal between a structured photoalignment layer and a homeotropic alignment layer

Topological defects in nematic liquid crystals (NLCs) are an interesting material system to study both from a theoretical point of view and for applications in photonics, soft-robotics and colloidal assembly. By using a photo-aligned template at one or both confining substrates, different disclination interconnections in the bulk can be readily stabilized. We imposed a periodic defect grid of 1/2 and −1/2 defects at the surface with the help of photoalignment and combined this with a uniform homeotropic counter substrate. This alignment configuration was used to study the optical properties and the relative stability of different types of disclinations in detail. The arrays of disclination lines are investigated by polarizing optical microscopy for different orientations of the polarizers and for different applied voltages. A theoretical analysis is performed to understand the relative frequency of occurrence for distinct types of disclinations and numerical simulations are used to verify the difference in optical appearance. The unequal elastic constants for splay, twist and bend strongly influence both properties and make it possible to identify different types of disclination lines form their optical appearance.

Hydrodynamics of fringing-field induced defects in nematic liquid crystals

Consumer demand for high resolution and high refresh-rate displays has naturally led to the fabrication of liquid crystal displays with ever smaller pixels. As a consequence, fringing fields between adjacent pixels grow in magnitude, leading to abrupt changes in orientation. Electric field strengths above some threshold can lead to order melting and, in turn, disclinations. This paper presents accurate modeling of disclinations induced by fringing fields due to interdigitated electrodes in a nematic liquid crystal calculated by means of the Landau–de Gennes theory. Disclination paths are determined while taking into account the flow of the liquid crystal. Making use of interdigitated electrodes, precise electrical control over the creation and positioning of defects is demonstrated for homeotropic, planar, hybrid, and in-plane surface alignments.

Fabrication of optical vortex array by fixing standing wave mediated periodic defects in nematic liquid crystals via photopolymerization

ABSTRACT Optical vortex beams have attracted significant research interest owing to their potential for application in optical communication and imaging. In this study, we demonstrated devices with electrically switchable topological defects as well as those with permanent topological defects using reactive mesogen (RM) and vertically aligned LC cells. A defect array was created via standing wave-mediated periodic LC orientation control by applying pulse train waves. At a low RM concentration (0.6 wt%), polymerisation induced a pretilt angle, and the periodic LC alignment was memorised with a topological defect array. Thus, the memorised defect structure reappeared upon applying a direct current field or standard square electric fields. In contrast, at a high RM concentration (3 wt.%), a permanent defect array device was realised. Thus, depending on the RM concentration, various types of defect arrays were selectively created. The devices developed in this study can be used for various potential applications, such as in digital data transfer and imaging systems.

Topological Defects in Nematic Liquid Crystals: Laboratory of Fundamental Physics

Topological Defects The curvature of a closed manifold exhibiting orientational order has a strong impact on positions and the number of topological defects (TDs). The surface integrated Gaussian curvature determines the total winding number of TDs within the manifold. If a region possessing a large enough negative Gaussian curvature is introduced it can trigger pairs {defect, antidefect}, possessing opposite signs of the winding number. More details can be found in article number 2000752 by Mitja Kralj, Marko Kralj, and Samo Kralj.

Micropatterning in Nematic Liquid Crystals: A General Control Strategy to Micropattern Topological Defects in Nematic Liquid Crystals Using Ionically Charged Dielectric Surface (Adv. Mater. Interfaces 11/2021)

In article number 2100379, Yuji Sasaki and co-workers introduce a general method for fabricating functional surfaces enabling a micropattern formation of topological defects in nematic liquid crystals irrespective of the chemical structure of compounds. Area-selective modification of surfaces using ultraviolet-ozone treatment allows to obtain highly self-organized microstructures with tunability, which dramatically improves the fabrication efficiency.

A General Control Strategy to Micropattern Topological Defects in Nematic Liquid Crystals Using Ionically Charged Dielectric Surface

AbstractTailoring 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.

Topological Defects in Nematic Liquid Crystals: Laboratory of Fundamental Physics

Topological defects (TDs) appear in all branches of physics due to the simplicity of generic mechanisms: The necessary condition for their existence is spontaneous symmetry breaking in a relevant physical field. Nematic liquid crystals (NLCs) represent an ideal testbed for their study and they can display point, line, textures, and in favorable conditions also wall defects. TDs in NLCs can be relatively easily created, controlled, and experimentally observed. This enables a detailed and controlled analysis of their physical properties, leading to the cross‐fertilization of knowledge among different areas of physics, including condensed matter, particle physics, and cosmology. Furthermore, TDs in NLCs could be exploited in diverse applications. Herein, some salient features of most common TDs in NLCs, their generic mechanisms, their importance for fundamental science, and possible applications based on them are illustrated.

Phase-field simulation of two-dimensional topological charges in nematic liquid crystals

The concept of topological quantum number, or topological charge, has been used extensively to describe topological defects or solitons. Nematic liquid crystals contain both integer and half-integer topological defects, making them useful models for testing the rules that govern topological defects. Here, we investigated topological defects in nematic liquid crystals using the phase-field method. If there are no defects along a loop path, the total charge number is described by an encircled loop integral. We found that the total charge number is conserved, and the conservation of defects number is determined by a boundary during the generation and annihilation of positive–negative topological defects when the loop integral is confined. These rules can be extended to other two-dimensional systems with topological defects.

A moving mesh method for modelling defects in nematic liquid crystals

The properties of liquid crystals can be modelled using an order parameter which describes the variability of the local orientation of rod-like molecules. Defects in the director field can arise due to external factors such as applied electric or magnetic fields, or the constraining geometry of the cell containing the liquid crystal material. Understanding the formation and dynamics of defects is important in the design and control of liquid crystal devices, and poses significant challenges for numerical modelling. In this paper we consider the numerical solution of a Q-tensor model of a nematic liquid crystal, where defects arise through rapid changes in the Q-tensor over a very small physical region in relation to the dimensions of the liquid crystal device. The efficient solution of the resulting six coupled partial differential equations is achieved using a finite element based adaptive moving mesh approach, where an unstructured triangular mesh is adapted towards high activity regions, including those around defects. Spatial convergence studies are presented using a stationary defect as a model test case, and the adaptive method is shown to be optimally convergent using quadratic triangular finite elements. The full effectiveness of the method is then demonstrated using a challenging two-dimensional dynamic Pi-cell problem involving the creation, movement, and annihilation of defects.

The topology of knots and links in nematics

ABSTRACTWe review some our results concerning the topology of knotted and linked defects in nematic liquid crystals. We discuss the global topological classification of nematic textures with defects, showing how knotted and linked defect lines have a finite number of ‘internal states’, counted by the Alexander polynomial of the knot or link. We then give interpretations of these states in terms of umbilic lines, which we also introduce, as well as planar textures. We show how Milnor polynomials can be used to give explicit constructions of these textures. Finally, we discuss some open problems raised by this work.

Visualising the crossover between 3D and 2D topological defects in nematic liquid crystals

ABSTRACTThe topological properties of disclinations are quite different for liquid crystals in two dimensions (2D) or three dimensions (3D). In 2D, there are distinct types of disclinations with topological charges or winding numbers of any half-integer or integer. By contrast, in 3D, all half-integer disclinations are topologically equivalent to each other, and integer disclinations are not defects at all. In this study, we use numerical simulations to explore the crossover between 3D and 2D. We show that certain disclination lines between patterned surfaces can exist when the director field is free to rotate in 3D, but not when the director field is forced into the 2D plane (by an electric field applied to a liquid crystal with negative dielectric anisotropy). As a result, these disclinations are expelled from the liquid crystal.

Tunable large-scale regular array of topological defects in nematic liquid crystals.

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.

Temperature control of the ultra-short laser pulse compression in a one-dimensional photonic band gap structure with nematic liquid crystal as a defect layer

We investigate numerically the controllable chirped pulse compression in a one-dimensional photonic structure containing a nematic liquid crystal defect layer using the temperature dependent refractive index of the liquid crystal. We consider the structure under irradiation by near-infrared ultra-short laser pulses polarized parallel to the liquid crystal director at a normal angle of incidence. It is found that the dispersion behaviour and consequently the compression ability of the system can be changed in a controlled manner due to the variation in the defect temperature. When the temperature increased from 290 to 305 K, the transmitted pulse duration decreased from 75 to 42 fs in the middle of the structure, correspondingly. As a result, a novel low-loss tunable pulse compressor with a really compact size and high compression factor is achieved. The so-called transfer matrix method is utilized for numerical simulations of the band structure and reflection/transmission spectra of the structure under investigation.

Large-scale self-organization of reconfigurable topological defect networks in nematic liquid crystals.

Topological defects in nematic liquid crystals are ubiquitous. The defects are important in understanding the fundamental properties of the systems, as well as in practical applications, such as colloidal self-assembly, optical vortex generation and templates for molecular self-assembly. Usually, spatially and temporally stable defects require geometrical frustration imposed by surfaces; otherwise, the system relaxes because of the high cost of the elastic energy. So far, multiple defects are kept in bulk nematic liquid crystals by top-down lithographic techniques. In this work, we stabilize a large number of umbilical defects by doping with an ionic impurity. This method does not require pre-patterned surfaces. We demonstrate that molecular reorientation controlled by an AC voltage induces periodic density modulation of ions accumulated at an electrically insulating polymer interface, resulting in self-organization of a two-dimensional square array of umbilical defects that is reconfigurable and tunable.

Fluorescence microscopy reveals molecular localisation at line defects in nematic liquid crystals.

Topological defects easily form in liquid crystals (LCs) as a result of frustrations in spatially dependent anisotropic molecular ordering, and have been regarded as promising tools for facilitating manipulation of relatively large non-LC materials such as colloids. However, it remains unclear whether low-molecular-weight (LMW) impurities that do not aggregate or self-assemble in bulk LCs because of the dominance of entropy can localise at LC defects. Here, by fluorescence microscopy, we directly show the localisation of LMW molecules at the topological line defects of a nematic LC. It is theoretically explained that excess free energy density of nematic ordering at the defect core allows LMW solutes to accumulate at a non-negligible level overcoming the entropy leading to their uniform distributions. Our results demonstrate the usefulness of LC defects as a bottom-up field that enables micromanipulation of LMW molecules and realisation of transformable three-dimensional micro-architectures composed of versatile small functional molecules.

Soliton-like defects in nematic liquid crystal thin layers

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.