Defects In Liquid Crystals Research Articles

A theoretical model of anaphase

This paper develops a theory for anaphase in cells. After a brief description of microtubules, the mitotic spindle and the centrosome, a mathematical model for anaphase is introduced and developed in the context of the cell cytoplasm and liquid crystalline structures. Prophase, prometaphase and metaphase are then briefly described in order to focus on anaphase, which is the main study of this paper. The entities involved are modelled in terms of liquid crystal defects and microtubules are represented as defect flux lines. The mathematical techniques employed make extensive use of energy considerations based on the work that was developed by Dafermos (1970) from the classical Frank–Oseen nematic liquid crystal energy (Frank, 1958; Oseen, 1933). With regard to liquid crystal theory we introduce the concept of regions of influence for defects which it is believed have important implications beyond the subject of this paper. The results of this paper align with observed biochemical phenomena and are explored in application to HeLa cells and Caenorhabditis elegans. This unified approach offers the possibility of gaining insight into various consequences of mitotic abnormalities which may result in Down syndrome, Hodgkin lymphoma, breast, prostate and various other types of cancer.

Dynamical theory of topological defects II: universal aspects of defect motion

We study the dynamics of topological defects in continuum theories governed by a free energy minimization principle, building on our recently developed framework (Romano et al 2023 J. Stat. Mech. 083211). We show how the equation of motion of point defects, domain walls, disclination lines and any other singularity can be understood with one unifying mathematical framework. For disclination lines, this also allows us to study the interplay between the internal line tension and the interaction with other lines. This interplay is non-trivial, allowing defect loops to expand, instead of contracting, due to external interaction. We also use this framework to obtain an analytical description of two long-lasting problems in point defect motion, namely the scale dependence of the defect mobility and the role of elastic anisotropy in the motion of defects in liquid crystals. For the former, we show that the effective defect mobility is strongly problem-dependent, but it can be computed with high accuracy for a pair of annihilating defects. For the latter, we show that at the first order in perturbation theory, anisotropy causes a non-radial force, making the trajectory of annihilating defects deviate from a straight line. At higher orders, it also induces a correction in the mobility, which becomes non-isotropic for the +1/2 defect. We argue that, due to its generality, our method can help to shed light on the motion of singularities in many different systems, including driven and active non-equilibrium theories.

Programmable Liquid Crystal Defects and Dynamically Manipulation with Mechanical Stress

AbstractManual intervention in the self‐assembly of soft matter to obtain a desired defect structure is a complex but significant project. Specifically, the flow and optical properties of liquid crystal (LC) materials have become the most important platform for studying topological structures in ordered physical systems. The regulation of liquid crystals (LCs) is largely limited to established means such as temperature, electric field, magnetic field, etc., however, a new effective strategy by mechanical stress is desirable but elusive. Here, using disclination controlled by stress, topologically continuous superstructure is generated to apply to touch display and wideband vector beam generator. This work demonstrates a new approach for direct controllable manipulation of disclination, unlocking the long‐sought full potential of topological defect, thus paving the way for optical and dynamic applications.

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.

Morphology and line tension of twist disclinations in a nematic liquid crystal.

We deploy optical microscopy with and without an applied magnetic field to characterize the three-dimensional morphology and measure the line tension of twist disclinations in twisted nematic liquid crystal (LC) sample cells. Twist disclinations are generated by quenching the LC, 5CB (4-cyano-4'-pentylbiphenyl), into the nematic phase; 5CB is confined between substrates with in-plane anchoring directions perpendicular to one another. The disclinations form loops separating domains of opposite twist handedness. Many segments of these loops are pinned to the substrates, and the ends of some pinned segments connect to free disclination segments that penetrate into the bulk nematic. We use confocal microscopy to measure the profiles of these free disclinations and test theoretical predictions about their shape, yielding a lower bound of ∼32 nm for the disclination core radius. We then use an applied magnetic field to deform the free disclinations into circular arcs whose curvature increases with magnetic field strength and depends on the field-induced energy difference between opposite twist domains. The line tension of the disclinations is derived from an energy-balance equation that relates disclination curvature to magnetic field. The measured line tension increases logarithmically with sample cell thickness; it ranges from 75 to 200 pN in samples with thickness spanning from 6 to 27 μm. In total, the investigation introduces new non-invasive methodologies for studies of defects in LCs, and it provides new information about the line tension and character of isolated twist disclinations, thereby testing theory and laying experimental foundation for the study of ensembles of disclinations.

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.

Directing and reconfiguring colloidal assembly by disclination networks in nematic liquid crystal as templates

Exotic structures with interesting physical and chemical properties can be achieved by self-organizing engineered building blocks. The central aim for self-assembly is to precisely control the position and orientation of individual building blocks. In this work, we use topological defects (disclinations) in nematic liquid crystals as templates to direct the self-assembly of colloidal particles into designable 3D structures. By photopatterning preprogrammed molecular orientations at two confining surfaces, we created pre-designable disclination networks and characterized their interactions with spherical colloidal particles. We find that colloidal particles are attracted to different disclinations depending on the orientation of the point defect (elastic dipole) around the colloids. We demonstrate that the positions, network structures, and orientation of the elastic dipoles of the colloidal chains can be pre-designed and reconfigured with remote illumination of polarized light.

Parameters Affecting Interfacial Assembly and Alignment of Nanotubes.

Tangential flow interfacial self-assembly (TaFISA) is a promising scalable technique enabling uniformly aligned carbon nanotubes for high-performance semiconductor electronics. In this process, flow is utilized to induce global alignment in two-dimensional nematic carbon nanotube assemblies trapped at a liquid/liquid interface, and these assemblies are subsequently deposited on target substrates. Here, we present an observational study of experimental parameters that affect the interfacial assembly and subsequent aligned nanotube deposition. We specifically study the water contact angle (WCA) of the substrate, nanotube ink composition, and water subphase and examine their effects on liquid crystal defects, overall and local alignment, and nanotube bunching or crowding. By varying the substrate chemical functionalization, we determine that highly aligned, densely packed, individualized nanotubes deposit only at relatively small WCA between 35 and 65°. At WCA (< 10°), high nanotube bunching or crowding occurs, and the film is nonuniform, while aligned deposition ceases to occur at higher WCA (>65°). We find that the best alignment, with minimal liquid crystal defects, occurs when the polymer-wrapped nanotubes are dispersed in chloroform at a low (0.6:1) wrapper polymer to nanotube ratio. We also demonstrate that modifying the water subphase through the addition of glycerol not only improves overall alignment and reduces liquid crystal defects but also increases local nanotube bunching. These observations provide important guidance for the implementation of TaFISA and its use toward creating technologies based on aligned semiconducting carbon nanotubes.

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.

Deposition of tungsten in methane atmosphere using a low energy plasma focus device

Deposition of tungsten in methane atmosphere was performed using a low energy plasma focus device. The resulting compounds were synthesized and investigated during the deposition process. Carbon-rich contamination was identified as an organic viscous liquid crystal defect. Tungsten carbide (W2C) and dark-black oxygen-deficient tungsten trioxide (WO3-x) thin films were synthesized by plasma focus device using different number of focused shots. The synthesis of each thin film, which was dependent upon operation of plasma focus device was verified and discussed. Tungsten carbide W2C was synthesized during the deposition process while the dark-black WO3-x was created after the deposition process in atmosphere. All compounds were investigated by spectroscopy, crystalline, and microscopy methods. Nano indentation test disclosed higher value of hardness for the film containing tungsten carbide compound (10.01 GPa) compared to both pure tungsten (5.72 GPa) and the dark-black WO3-x thin film (6.83 GPa). The verified band gap energy of dark-black WO3-x was around 1.475 eV.

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.

External field induced defect transformation in circular confined Gay-Berne liquid crystals.

Normally, defects in two-dimensional, circular, confined liquid crystals can be classified into four types based on the position of singularities formed by liquid crystal molecules, i.e., the singularities located inside the circle, at the boundary, outside the circle, and outside the circle at infinity. However, it is considered difficult for small aspect ratio liquid crystals to generate all these four types of defects. In this study, we use molecular dynamics simulation to investigate the defect formed in Gay-Berne, ellipsoidal liquid crystals, with small aspect ratios confined in a circular cavity. As expected, we only find two types of defects (inside the circle and at the boundary) in circular, confined, Gay-Berne ellipsoids under static conditions at various densities, aspect ratios, and interactions between the wall and liquid crystals. However, when introducing an external field to the system, four types of defects can be observed. With increasing the strength of the external field, the singularities in the circular, confined system change from the inside to the boundary and the outside, and the farthest position that the singularities can reach depends on the strength of the external field. We further introduce an alternating, triangular wave, external field to the system to check if we can observe the transformation of different defects within an oscillating period. We find that the position of the singularities greatly depends on the oscillating intensity and oscillating period. By changing the oscillating intensity and oscillating period of the external field, the defect types can be adjusted, and the transformation between different defects can be easily observed. This provides a feasible way to modulate liquid crystal defects and investigate the transformation between different defects.

Nanoparticle localization within chiral liquid crystal defect lines and nanoparticle interactions.

Self-assembly of colloidal particles into predefined structures is a promising way to design inexpensive manmade materials with advanced macroscopic properties. Doping of nematic liquid crystals (LCs) with nanoparticles has a series of advantages in addressing these grand scientific and engineering challenges. It also provides a very rich soft matter platform for the discovery of unique condensed matter phases. The LC host naturally allows the realization of diverse anisotropic interparticle interactions, enriched by the spontaneous alignment of anisotropic particles due to the boundary conditions of the LC director. Here we demonstrate theoretically and experimentally that the ability of LC media to host topological defect lines can be used as a tool to probe the behavior of individual nanoparticles as well as effective interactions between them. LC defect lines irreversibly trap nanoparticles enabling controlled particle movement along the defect line with the use of a laser tweezer. Minimization of Landau-de Gennes free energy reveals a sensitivity of the ensuing effective nanoparticle interaction to the shape of the particle, surface anchoring strength, and temperature, which determine not only the strength of the interaction but also its repulsive or attractive character. Theoretical results are supported qualitatively by experimental observations. This work may pave the way toward designing controlled linear assemblies as well as one-dimensional crystals of nanoparticles such as gold nanorods or quantum dots with tunable interparticle spacing.

Hydrodynamic Enhancement of p-atic Defect Dynamics.

We investigate numerically and analytically the effects of hydrodynamics on the dynamics of topological defects in p-atic liquid crystals, i.e., two-dimensional liquid crystals with p-fold rotational symmetry. Importantly, we find that hydrodynamics fuels a generic passive self-propulsion mechanism for defects of winding number s=(p-1)/p and arbitrary p. Strikingly, we discover that hydrodynamics always accelerates the annihilation dynamics of pairs of ±1/p defects and that, contrary to expectations, this effect increases with p. Our Letter paves the way toward understanding cell intercalation and other remodeling events in epithelial layers.

Liquid crystal defect structures with Möbius strip topology

Topological solitons commonly appear as energy-minimizing field configurations, but examples of stable, spatially localized objects with coexisting solitonic structures and singular defects are rare. Here we use a nonpolar chiral liquid crystal system to show how twist domain walls can co-self-assemble with vortices to form spatially localized topological objects with spontaneous folding. These soliton–vortex assemblies, which we call ‘möbiusons’, have a topology of the molecular alignment field resembling that of the Möbius strip’s surface and package localized field excitations into folded structures within a confinement-frustrated uniform far-field background. Upon supplying energy in the form of electric pulses, möbiusons with different overall symmetries of structure exhibit folding-dependent rotational and translational motions, as well as topological cargo-carrying abilities that can be controlled by tuning the amplitude and frequency of the applied fields. We demonstrate on-demand transformations between various möbiusons and show examples of encoding information by manipulating folds in such structures. A model based on the energetics of solitons and vortices provides insights into the origins of the folding instability, whereas minimization of the Landau–de Gennes free energy closely reproduces details of their internal structure. Our findings may provide a route towards topology-enabled light-steering designs.

Structures, thermodynamics and dynamics of topological defects in Gay-Berne nematic liquid crystals.

Topological defects are a ubiquitous phenomenon across different physical systems. A better understanding of defects can be helpful in elucidating the physical behaviors of many real materials systems. In nematic liquid crystals, defects exhibit unique optical signatures and can segregate impurities, showing their promise as molecular carriers and nano-reactors. Continuum theory and simulations have been successfully applied to link static and dynamical behaviors of topological defects to the material constants of the underlying nematic. However, further evidence and molecular details are still lacking. Here we perform molecular dynamics simulations of Gay-Berne particles, a model nematic, to examine the molecular structures and dynamics of +1/2 defects in a thin-film nematic. Specifically, we measure the bend-to-splay ratio K3/K1 using two independent, indirect measurements, showing good agreement. Next, we study the annihilation event of a pair of ±1/2 defects, of which the trajectories are consistent with experiments and hydrodynamic simulations. We further examine the thermodynamics of defect annihilation in an NVE ensemble, leading us to correctly estimate the elastic modulus by using the energy conservation law. Finally, we explore effects of defect annihilation in regions of nonuniform temperature within these coarse-grained molecular models which cannot be analysed by existing continuum level simulations. We find that +1/2 defects tend to move toward hotter areas and their change of speed in a temperature gradient can be quantitatively understood through a term derived from the temperature dependence of the elastic modulus. As such, our work has provided molecular insights into structures and dynamics of topological defects, presented unique and accessible methods to measure elastic constants by inspecting defects, and proposed an alternative control parameter of defects using temperature gradient.

Hybrid Tamm and quasi-BIC microcavity modes.

The microcavity in the form of a liquid crystal defect layer embedded in a one-dimensional photonic crystal is considered. The microcavity mode has a tunable radiation decay rate in the vicinity of a bound state in the continuum. It is demonstrated that coupling between the microcavity mode and a Tamm plasmon polariton results in hybrid Tamm-microcavity modes with a tunable Q factor. The measured spectral features of hybrid modes are explained in the framework of the temporal coupled mode theory.

Quasicrystalline Arrays and Moiré Patterns in Nematic Liquid Crystals for Soft Photonics

AbstractThe search for new strategies for large‐scale, self‐assembled arrays of soft objects is key for many applications in photonics and bottom‐up manufacturing. This work shows how liquid crystal topological defects can be assembled in controlled, aperiodic arrays. In particular, the focus is on two typical examples: quasicrystals and moiré patterns. Thanks to a combination of topographical cues, specifically a micropillar array and electrical switching, defects can be assembled in a quasicrystal structure, as seen from polarized optical microscopy and from diffraction patterns. In this setting, the liquid crystal defects assemble in multiple patterns that can be switched by tuning the applied electric field and retain the quasicrystalline symmetry. Using topographic cues, it is also possible to induce moiré patterns of defects, characterized by a long wavelength superimposed on the periodic structures over a short scale. Even when the defect density increases and the short‐scale periodicity is lost, the long‐scale one remains. This work shows how versatile the combination of topographic confinement and electro‐optic effect is, giving access to patterns that are otherwise difficult to realize.

Defect-Polymorphism-Controlled Electrophoretic Propulsion of Anisometric Microparticles in a Nematic Liquid Crystal

Nontrivial shape of colloidal particles create complex elastic distortions and topological defects in liquid crystals and play a key role in governing their electrophoretic propulsion through the medium. Here, we report experimental results on defects and electrophoretic transport of anisometric (snowman-shaped) dielectric particles subjected to an alternating electric field perpendicular to the director in a nematic liquid crystal. We demonstrate that the shape asymmetry gives rise to defect-polymorphism by nucleating point or ring defects at multiple locations on the particle and controls the direction as well as the magnitude of the electrophoretic propulsion. Our findings unveil a novel degree of freedom in translocating microparticles in liquid crystals for applications in microfluidics, controlled transport and assembly.

Spatial manipulation of topological defects in nematic shells.

It is well known that positions of topological defects (TDs) in liquid crystals can be manipulated experimentally by locally distorting the liquid crystalline (LC) order, as for example by melting induced by optical tweezers. In this work, we study numerically the nematic ordering profiles and the corresponding topological defect configurations in thin nematic liquid crystalline shells controlled by imposed local distortion of LC order. We demonstrate that within curved LC films such manipulations could be strongly affected by local Gaussian curvature if it exhibits strong spatial variations. We use mesoscopic approach in which the shell geometry and LC orientational order are described by curvature of the surface and nematic order parameter tensor. For illustration purposes, we consider LC shells exhibiting spherical topology. We show that on increasing prolateness of shells, which imposes spatially inhomogeneous Gaussian curvature, TDs are relatively strongly "glued" to a local Gaussian curvature.