Liquid Crystal Configurations Research Articles

Responsive Soft Interface Liquid Crystal Microfluidics

AbstractThe multifunctional responsive interfaces of liquid crystal (LC) and water are employed in fundamental research (colloidal assembly) and promising applications (sensing, release, and material synthesis). The stagnant LC systems, however, limit their use in continuous, automated applications. A microfluidic platform is reported where stable LC flow is maintained between aqueous interfaces. The LC‐water soft interface is defined by the preferential wetting of the two phases at the chemically heterogeneous microchannel interfaces. It is shown that the LC‐water interfaces are stable up to significant pressure differences across the interfaces and maintain responsive characteristics. The stability is in a range to cover the perpendicular and flow‐aligned regimes at low and high flow velocities, respectively, in co‐current or counter‐current flow configurations. The LC configuration at the vicinity of the aqueous interfaces is influenced by the shear induced by the bulk LC flow and by the contacting aqueous phases allowing modulation of the LC strain at the responsive interfaces. The simplicity of the construction and operation of the soft‐interface LC flow platform shows promise and meets the fundamental requirements for their integration into next‐generation autonomous platforms.

Electrically tunable metasurface in twisted-nematic liquid crystal configuration with enhanced quality factor and nanofeature assisted alignment

Electrically tunable metasurface in twisted-nematic liquid crystal configuration with enhanced quality factor and nanofeature assisted alignment

Dynamic Microparticle Assembly at the Interface of Chemoresponsive Liquid Crystal Droplets.

The confinement of liquid crystals (LCs) in spherical microdroplets results in exotic internal configurations and topological defects in response to physical and chemical stimuli. Recent exploration into the placement of colloids on the surface of LC microdroplets has led to the design of a new class of functional materials with patterned surface properties. It is established that the placement of a colloid on a LC droplet surface can pin the topological defect at the interface, thereby restricting changes in the LC configuration. Herein, we build upon the handful of reports published to provide a fundamental understanding of the colloid positioning in response to external stimuli. Using polystyrene (PS) colloids, we explored the dynamics of particle self-assembly in response to an interfacial enzymatic breakdown of poly-l-lysine by trypsin. We found that for a significant population of droplets, the positioning of the colloid is unaffected by the changes in the internal ordering of LC. Inspired by the new observations, we delved deeper to understand the role of interfacial stabilizers in modulating the preferential alignment of LC and the placement of colloidal microparticles. We also demonstrated that for a certain population of droplets, the positioning of the colloids remains unperturbed in response to multistep reversible adsorption of interfacial amphiphiles. Our findings reveal interesting possibilities of correlating the stimuli-responsive switching of internal configurations of LC with colloid placement on the particle-decorated LC droplets.

Influence of Ionic Conductivity in Polymer Dispersed Antiferroelectric Liquid Crystals (PDAFLC): A Comparison of Critical Fields

Theoretically critical unwinding field was studied using Landau free energy model of three different geometrical configuration of antiferroelectric liquid crystals. In this study, we considered the influence of ionic conductivity both in pure antiferroelectric liquid crystals and polymer dispersed antiferroelectric liquid crystals. We observed that the modified elastic constant which accounted for the interaction of ionic conductivity and polymer cross-linked chains is very much responsible for the variation of critical field.

Color-selective optical edge detection enabled by thermally stimulated cholesteric liquid crystals

Optical edge detection can significantly compress the data volume and is highly pursued in imaging processing. The commonly used methods extract the optical edge information but lose the capability to distinguish colors, which is another key information for imaging. Here, a design for color-selective optical edge detection is proposed and demonstrated with a cholesteric liquid crystal q-plate. The corresponding optical edge detection exhibits a narrow reflection band characteristic due to the one-dimensional photonic crystal configuration of the cholesteric liquid crystal. The monochromatic band is thermally and reversibly tuned ∼300 nm within 5.3 °C. Color-selective optical edge detection is verified by a series of chromatic images. This work introduces a thermally responsive liquid crystal device to release the color dimension of optical edge detection, which may upgrade existing imaging processing techniques.

A reduced Landau-de Gennes study for nematic equilibria in three-dimensional prisms

Abstract We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal cross-section and Dirichlet boundary conditions on all prism surfaces. We work in a reduced Landau-de Gennes framework, and the Dirichlet conditions on the top and bottom surfaces are special in the sense that they are critical points of the reduced Landau-de Gennes energy on the polygonal cross-section. The choice of the boundary conditions allows us to make a direct correspondence between the three-dimensional Landau-de Gennes critical points and pathways on the two-dimensional Landau-de Gennes solution landscape on the polygonal cross-section. We explore this concept by means of asymptotic analysis and numerical examples, with emphasis on a cuboid and a hexagonal prism, focusing on three-dimensional multistability tailored by two-dimensional solution landscapes.

Gradient polarization volume grating with wide angular bandwidth for augmented reality.

Angular bandwidth, which is critical to field-of-view, plays important role in diffractive optical waveguide augmented reality display. However, design and fabrication of large angular bandwidth is still a challenge. Herein, we demonstrate a liquid crystal reflective gradient polarization volume grating with three-dimensional gradient periodic structure for waveguide near-eye display. Two-beam polarization interference with special designed periodic gradient photomask are applied to chiral-dopant reactive mesogens doped with ultraviolet dye for generating gradient three-dimensional configuration of liquid crystals, resulting in gradient polarization volume grating with extended angle bandwidth of 61° while keeping 80% diffraction efficiency, with peak efficiency near 100%. The proposed gradient polarization volume grating provides an effective method to broaden the angular bandwidth in waveguide for wide field-of-view augmented reality display.

Effect of rubbing symmetry on polarization distribution in ferroelectric nematic liquid crystal cells

It is a significant issue in controlling the polarization distribution in ferroelectric nematic liquid crystal cells. We investigated the polarization configuration of ferroelectric nematic liquid crystals on the surface and in the bulk of parallel/anti-parallel cells with rubbed substrates and proposed the polarization models in each cell. It is found that on the surface of rubbed polyimide films, the polarization direction is fixed and opposite to the rubbing direction. Splay and twist distribution of the polarization are formed in parallel and anti-parallel cells, respectively.

TIC Reorientation under Electric and Magnetic Fields in Homeotropic Samples of Cholesteric LC with Negative Dielectric Anisotropy

In this paper, we numerically and experimentally show that the director field orientation degeneracy within the Translationally Invariant Configuration (TIC) of a cholesteric liquid crystal under an electric field can be lifted by imposing a magnetic field B→ parallel to the electrodes. The configuration can be either parallel or perpendicular to the magnetic field depending on the values of the sample thickness, pitch, and applied voltage, with two equiprobable orientations in each case. The transition between the parallel and perpendicular orientations has hysteresis, suggesting that it is first order. When B→ is slightly tilted with respect to the electrode plane, the indeterminacy on the TIC orientation is removed when the TIC is directed along B→.

Polarization-insensitive liquid crystal Fresnel lens based on self-assembly polymer gravels and chiral dopant.

A polarization-insensitive liquid crystal (LC) Fresnel lens is developed with binary LC configurations of 90°-twisted nematic (TN) and vertically-aligned (VA) domains in the adjacent zones. A LC mixture comprised of nematic host, photopolymer and chiral material is initially filled into the VA cell with orthogonal rubbing treatment. After the ultraviolet irradiation on the filled LC cell through a photomask with Fresnel zone plate pattern, the interactions among orthogonal rubbing treatment, self-assembly polymer gravels, and chiral material induce the 90°-TN structure in the odd zones, whereas the initial VA structures are maintained in the even zones. The fabricated LC Fresnel lens with binary configuration emerges a maximum diffraction efficiency of around 35% at a voltage of 2.3 V, close to the theoretical diffraction limit of around 41%. The diffractive focus of the LC Fresnel lens is polarization-insensitive at the voltage above 2 V. When the voltage reaches 10 V, the diffractive focus vanishes. The numerical calculation confirms that the polarization-insensitive property appears in the primary focus of the LC Fresnel lens. This work reports a simple method to develop a highly efficient, polarization-insensitive, and electrically tunable LC Fresnel lens which is favorable for imaging system.

Tuneable optical diffractive structures from liquid crystalline materials incorporated into periodic polymeric scaffolds

ABSTRACTDiffractive optical elements (DOEs) are micro-structured components used in various photonic devices to manipulate propagation direction and often also polarisation state of optical beams. The simplest type of DOEs are one-dimensional diffraction gratings. We perform theoretical investigation of electrical and magnetic tunability of such gratings composed as a periodic assembly of polymer and ferromagnetic nematic liquid crystal (LC) layers. We analyse how various grating parameters and boundary conditions influence the LC configuration in the assembly. For static response to external electric and/or magnetic fields, the distortion profile of the director field is determined numerically and analytically by minimisation of the Landau-de Gennes free energy, while for the dynamic response only numerical solutions are provided. The resulting optical diffraction properties are determined numerically via solving the Maxwell’s equations by using the rigorous coupled-wave analysis. We demonstrate that the described methodology provides an efficient tool for designing various new types of polarisation-sensitive LC-based DOEs, such as three-state polarisation switches for application in spectroscopic, optical communication, and remote sensing systems.

Fast Reconfigurable Phase Shifter Based on a Chiral Liquid Crystal Configuration

Fast Reconfigurable Phase Shifter Based on a Chiral Liquid Crystal Configuration

Defect absorption and emission for p-atic liquid crystals on cones.

We investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on fixed curved surfaces. We focus on the intrinsic geometry and show that isothermal coordinates are particularly convenient as they explicitly encode a geometric contribution to the elastic potential. In the special case of a cone with half-angle β, the apex develops an effective topological charge of -χ, where 2πχ=2π(1-sinβ) is the deficit angle of the cone, and a topological defect of charge σ behaves as if it had an effective topological charge Q_{eff}=(σ-σ^{2}/2) when interacting with the apex. The effective charge of the apex leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. For total topological defect charge 1, e.g., imposed by tangential boundary conditions at the edge, we find that for a disk the ground-state configuration consists of p defects each of charge +1/p lying equally spaced on a concentric ring of radius d=(p-1/3p-1)^{1/2p}R, where R is the radius of the disk. In the case of a cone with tangential boundary conditions at the base, we find three types of ground-state configurations as a function of cone angle: (i) for sharp cones, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones, all of the +1/p defects lie equally spaced along a concentric ring on the flank. Here the defect positions and the absorption transitions depend intricately on p and the deficit angle, which we analytically compute. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement.

On the flow of liquid crystals through 90° bends

During the processing of nematic soft solids through process flow elements (pipe bends, elbows, etc.), the constitutive behavior makes its presence felt via processing (with rheology driven effects increasing pressure drop) and the final product microstructure. This paper explores the flow and microstructure configurations of nematic liquid crystals in a pressure driven flow through 90° pipe bends with different types of wall anchoring. The governing equations of the Leslie–Ericksen theory are solved numerically in a newly developed OpenFOAM solver. We show that the bend curvature deforms the nematic axis distribution; the distortion can be driven either by elastic or hydrodynamic effects. The interaction between the nematic microstructure and flow field generates non-zero normal stresses (in the radial, azimuthal, and streamwise directions), which produce a secondary flow and increase pressure losses. The strength of the secondary flow depends on the type of wall anchoring and Ericksen number; in configurations with homeotropic anchoring, decreasing the Ericksen number increases the relative strength of the secondary flow (with respect to the mean flow velocity). Conversely, homogeneous (planar) anchoring reduces normal stresses, thus weakening the secondary flow strength. We show that as the fluid enters/leaves the bend, there is a perturbation in the transverse velocity caused by streamwise stress gradients. The perturbation magnitude depends on material properties and can be of different values at the bend exit and entrance. Finally, we show that the spatial development of the nematic field downstream of the bend exit is controlled by both material properties and the Ericksen number.

Stability of a split-core configuration induced by saddle-splay elasticity in a submicron nematic liquid crystal spherical droplet

ABSTRACT We use Landau–de Gennes theory to investigate the configurations of liquid crystals confined to a submicron spherical droplet subject to weak homeotropic anchoring. The results show that in a one-constant approximation, there are three equilibrium configurations: radial hedgehog, ring disclination and uniform, where the radial hedgehog configuration is a stable state. With increasing elastic anisotropy, which is essentially an increase in the splay elastic constant, the radial hedgehog configuration transforms into a split-core configuration, which is metastable. The split-core configuration becomes the lowest-energy state induced by saddle-splay elasticity within appropriate ranges of the radius and elastic anisotropy.

Photoaligned Liquid Crystal Devices with Switchable Hexagonal Diffraction Patterns.

Highly efficient optical diffraction can be realized with the help of micrometer-thin liquid crystal (LC) layers with a periodic modulation of the director orientation. Electrical tunability is easily accessible due to the strong stimuli-responsiveness in the LC phase. By using well-designed photoalignment patterns at the surfaces, we experimentally stabilize two dimensional periodic LC configurations with switchable hexagonal diffraction patterns. The alignment direction follows a one-dimensional periodic rotation at both substrates, but with a 60° or 120° rotation between both grating vectors. The resulting LC configuration is studied with the help of polarizing optical microscopy images and the diffraction properties are measured as a function of the voltage. The intricate bulk director configuration is revealed with the help of finite element Q-tensor simulations. Twist conflicts induced by the surface anchoring are resolved by introducing regions with an out-of-plane tilt in the bulk. This avoids the need for singular disclinations in the structures and gives rise to voltage induced tuning without hysteretic behavior.

Skyrmion tubes in achiral nematic liquid crystals.

We analyze the interaction with uniform external fields of nematic liquid crystals within a recent generalized free energy posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i.e., uniform heliconical structures, which correspond to the so-called twist-bend nematic phase and we also study the transition between this phase and the standard uniform nematic one. The twist-bend phase is further reproduced by three-dimensional simulations. Moreover, we find liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Skyrmion tubes. Skyrmion tubes are characterized by a localized cylindrically symmetric pattern surrounded by either twist-bend or uniform nematic phase. We study the equilibrium differential equations and find numerical solutions and analytical approximations.

Director configuration of liquid crystals in a cylindrical cavity with homeotropic anchoring conditions

We study numerically the equilibrium configurations of nematic liquid crystals confined in cylindrical cavities with strong and weak homeotropic anchoring conditions, respectively, on the basis of the elastic continuum theory and the difference iterative method. The lyotropic chromonic liquid crystal disodium cromoglycate exhibits a completely different spontaneous chiral configuration from 5CB due to the large ratio of the saddle-splay elastic constant to the twist elastic constant. We show that how the elastic constants affect the director alignment in chiral structure with strong homeotropic anchoring conditions. For the weak homeotropic anchoring conditions, the theoretically predicted transition from a twisted and escaped radial to an escaped twisted configuration of DSCG and the transition from an escaped radial to a UA configuration of 5CB, on reduction of the anchoring coefficient below a certain threshold, are confirmed to occur at A∼10−8J/m2. Remarkably, it provides a more accurate theoretical analysis for the prediction of director configurations in cylindrical cavities under different conditions in experiments.

Reflective optical components based on chiral liquid crystal for head-up displays

ABSTRACT The emerging near-eye displays for see-through augmented reality (AR) and virtual reality (VR) have inspired new applications of optical gratings, for example, as waveguide-coupling components. For such applications, reflective diffraction gratings and reflective lenses based on self-organised chiral liquid crystal (CLC) are strong contenders because of their high diffraction efficiency and unique polarisation selectivity. However, in order to design optical systems that use such components, the optical properties of CLC diffraction gratings need to be thoroughly investigated and understood. In order to better understand the structure and diffraction properties of such components we simulated the behaviour of two cholesteric liquid crystal configurations (planar and slanted) and compared them with experimental results. This paper covers advancements in CLC diffraction grating research, comparison between different theories for the director configuration in the bulk and further investigation of the optical properties of the devices. The evolution of reflective CLC lenses is discussed and lenses with a small f – number are described. In this review paper we show that progress made in the field of CLC-based flat optics has a high potential for AR/VR display systems.

Chromonic liquid crystals and packing configurations of bacteriophage viruses.

We study equilibrium configurations of hexagonal columnar liquid crystals in the context of characterizing packing structures of bacteriophage viruses in a protein capsid. These are viruses that infect bacteria and are currently the focus of intense research efforts, with the goal of finding new therapies for bacteria-resistant antibiotics. The energy that we propose consists of the Oseen-Frank free energy of nematic liquid crystals that penalizes bending of the columnar directions, in addition to the cross-sectional elastic energy accounting for distortions of the transverse hexagonal structure; we also consider the isotropic contribution of the core and the energy of the unknown interface between the outer ordered region of the capsid and the inner disordered core. The problem becomes of free boundary type, with constraints. We show that the concentric, azimuthal, spool-like configuration is the absolute minimizer. Moreover, we present examples of toroidal structures formed by DNA in free solution and compare them with the analogous ones occurring in experiments with other types of lyotropic liquid crystals, such as food dyes and additives. This article is part of the theme issue 'Topics in mathematical design of complex materials'.