Relaxation kinetics of stretched disclination lines in a nematic liquid crystal

Energy dissipation mechanism of annihilating reverse tilt domains for various applied voltages

When a voltage is applied to a uniformly aligned nematic liquid crystal, a characteristic texture designated as reverse tilt domain (RTD) appears. The RTD, surrounded by a domain wall, gradually shrinks and finally disappears. The domain wall splits into a pair of disclination lines by increase of the voltage. This work examines the energy dissipation mechanism of annihilation dynamics by ascertaining the phenomenological viscosity Γ based on experimentation. To evaluate Γ, the time dependence of curvature radius R is analyzed using an equation R=Asqrt[t_{0}-t], where A is a fitting parameter. Parameter A decreased linearly with increasing applied voltage and suddenly became constant. Also, Γ was evaluated from A as a function of voltage. When the voltage reaches a critical value, Γ increased sharply to be one order of magnitude greater than that under low voltages. The critical voltage is consistent with the theoretically expected value at which the splitting of domain wall occurs. The transition of Γ is described clearly by localized deformation of the director field.

Nematic bits and universal logic gates

Liquid crystals (LCs) can host robust topological defect structures that essentially determine their optical and elastic properties. Although recent experimental progress enables precise control over nematic LC defects, their practical potential for information storage and processing has yet to be explored. Here, we introduce the concept of nematic bits (nbits) by exploiting a quaternionic mapping from LC defects to the Poincaré-Bloch sphere. Through theory and simulations, we demonstrate how single-nbit operations can be implemented using electric fields, to construct LC analogs of Pauli, Hadamard, and other elementary logic gates. Using nematoelastic interactions, we show how four-nbit configurations can realize universal classical NOR and NAND gates. Last, we demonstrate the implementation of generalized logical functions that take values on the Poincaré-Bloch sphere. These results open a route toward the implementation of classical digital and nonclassical continuous computation strategies in topological soft matter systems.

Deck the Walls with Anisotropic Colloids in Nematic Liquid Crystals

Nematic liquid crystals (NLCs) offer remarkable opportunities to direct colloids to form complex structures. The elastic energy field that dictates colloid interactions is determined by the NLC director field, which is sensitive to and can be controlled by boundaries including vessel walls and colloid surfaces. By molding the director field via liquid-crystal alignment on these surfaces, elastic energy landscapes can be defined to drive structure formation. We focus on colloids in otherwise defect-free director fields formed near undulating walls. Colloids can be driven along prescribed paths and directed to well-defined docking sites on such wavy boundaries. Colloids that impose strong alignment generate topologically required companion defects. Configurations for homeotropic colloids include a dipolar structure formed by the colloid and its companion hedgehog defect or a quadrupolar structure formed by the colloid and its companion Saturn ring. Adjacent to wavy walls with wavelengths larger than the colloid diameter, spherical particles are attracted to locations along the wall with distortions in the nematic director field that complement those from the colloid. This is the basis of lock-and-key interactions. Here, we study ellipsoidal colloids with homeotropic anchoring near complex undulating walls. The walls impose distortions that decay with distance from the wall to a uniform director in the far field. Ellipsoids form dipolar defect configurations with the colloid's major axis aligned with the far field director. Two distinct quadrupolar defect structures also form, stabilized by confinement; these include the Saturn I configuration with the ellipsoid's major axis aligned with the far field director and the Saturn II configuration with the major axis perpendicular to the far field director. The ellipsoid orientation varies only weakly in bulk and near undulating walls. All configurations are attracted to walls with long, shallow waves. However, for walls with wavelengths that are small compared to the colloid length, Saturn II is repelled, allowing selective docking of aligned objects. Deep, narrow wells prompt the insertion of a vertical ellipsoid. By introducing an opening at the bottom of such a deep well, we study colloids within pores that connect two domains. Ellipsoids with different aspect ratios find different equilibrium positions. An ellipsoid of the right dimension and aspect ratio can plug the pore, creating a class of 2D selective membranes.

Shape control of surface-stabilized disclination loops in nematic liquid crystals

Recent studies on topological defects in conventional and active nematic liquid crystals have revealed their potential as sources of advanced functionality whereby the collective behavior of the constituent molecules or cells is controlled. On the other hand, the fact that they have high energies and are metastable makes their shape control a nontrivial issue. Here, we demonstrate stabilization of arbitrary-shaped closed disclination loops with 1/2 strength floating in the bulk by designing the twist angle distribution in a liquid crystal cell. Continuous variation of the twist angle from below to above |π/2| allows us to unambiguously position reverse twist disclinations at will. We also analyze the elastic free energy and uncover the relationship between the twist angle pattern and shrink rate of the surface-stabilized disclination loop.

Disclination elastica model of loop collision and growth in confined nematic liquid crystals

Theory and modeling are used to characterize disclination loop-loop interactions in nematic liquid crystals under capillary confinement with strong homeotropic anchoring. This defect process arises when a mesogen in the isotropic phase is quenched into the stable nematic state. The texture evolution starts with +1/2 disclination loops that merge into a single loop through a process that involves collision, pinching and relaxation. The process is characterized with a combined Rouse-Frank model that incorporates the tension and bending elasticity of disclinations and the rotational viscosity of nematics. The Frank model of disclinations follows the Euler elastica model, whose non-periodic solution, known as Poleni's curve, is shown to locally describe the loop-loop collision and to shed light on why loop-loop merging results in a disclination intersection angle of approximately 60°. Additional Poleni invariants demonstrate how tension and bending pinch the two loops into a single +1/2 disclination ring. The Rouse model of disclination relaxation yields a Cahn-Hilliard equation whose time constant combines the confinement, tension/bending stiffness ratio and disclination diffusivity. Based on predictions made using this three stage process, a practical procedure is proposed to find viscoelastic parameters from defect geometry and defect dynamics. These findings contribute to the evolving understanding of textural transformations in nematic liquid crystals under confinement using the disclination elastica methodology.

Colloidal nanoparticles trapped by liquid-crystal defect lines: a lattice Monte Carlo simulation

Lattice-based Monte Carlo simulations are performed to study a confined liquid crystal system with a topological disclination line entangling a colloidal nanoparticle. In our microscopic study the disclination line is stretched by moving the colloid, as in laser tweezing experiments, which results in a restoring force attempting to minimize the disclination length. From constant-force simulations we extract the corresponding disclination line tension, estimated as ∼50 pN, and observe its decrease with increasing temperature.

Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities

Topological defect lines are ubiquitous and important in a wide variety of fascinating phenomena and theories in many fields ranging from materials science to early-universe cosmology, and to engineering of laser beams. However, they are typically hard to control in a reliable manner. Here we describe facile erasable “optical drawing” of self-assembled defect clusters in liquid crystals. These quadrupolar defect clusters, stabilized by the medium's chirality and the tendency to form twisted configurations, are shaped into arbitrary two-dimensional patterns, including reconfigurable phase gratings capable of generating and controlling optical phase singularities in laser beams. Our findings bridge the studies of defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators.

Reconfigurable interactions and three-dimensional patterning of colloidal particles and defects in lamellar soft media

Colloidal systems find important applications ranging from fabrication of photonic crystals to direct probing of phenomena typically encountered in atomic crystals and glasses. New applications--such as nanoantennas, plasmonic sensors, and nanocircuits--pose a challenge of achieving sparse colloidal assemblies with tunable interparticle separations that can be controlled at will. We demonstrate reconfigurable multiscale interactions and assembly of colloids mediated by defects in cholesteric liquid crystals that are probed by means of laser manipulation and three-dimensional imaging. We find that colloids attract via distance-independent elastic interactions when pinned to the ends of cholesteric oily streaks, line defects at which one or more layers are interrupted. However, dislocations and oily streaks can also be optically manipulated to induce kinks, allowing one to lock them into the desired configurations that are stabilized by elastic energy barriers for structural transformation of the particle-connecting defects. Under the influence of elastic energy landscape due to these defects, sublamellar-sized colloids self-assemble into structures mimicking the cores of dislocations and oily streaks. Interactions between these defect-embedded colloids can be varied from attractive to repulsive by optically introducing dislocation kinks. The reconfigurable nature of defect-particle interactions allows for patterning of defects by manipulation of colloids and, in turn, patterning of particles by these defects, thus achieving desired colloidal configurations on scales ranging from the size of defect core to the sample size. This defect-colloidal sculpturing may be extended to other lamellar media, providing the means for optically guided self-assembly of mesoscopic composites with predesigned properties.