Nematic Liquid Crystal Director Research Articles

On the Existence and Partial Stability of Standing Waves for a Nematic Liquid Crystal Director Field Equations

AbstractIn this paper, following the studies in Amorim et al. (Partial Differ Equ Appl 4, 36, 2023), we consider some new aspects of the motion of the director field of a nematic liquid crystal submitted to a magnetic field and to a laser beam. In particular, we study the existence and partial orbital stability of special standing waves, in the spirit of Cazenave and Lions (Commun Math Phys 85:549–561, 1982) and Hadj Selem et al. (Milan J Math 82:273–295, 2014) and we present some numerical simulations.

Control over polarization of vertically emitting random lasers based on dye doped nematic liquid crystals by applying a transverse electric field locally

Flexible control over random lasers (RLs) is highly desired. In this manuscript, a control over the polarization of random lasing emitted vertically from dye doped nematic liquid crystal (NLC) cell by the transverse component of a local ac electric field was demonstrated. The polarizing direction of the RL could be tuned continuously and monotonously with the increase of the field strength, from the direction along the NLC director without an applied electric field. The maximum rotation angle of the polarizing direction reached nearly 90° at the applied voltage of 200 V (root-mean-square value) across the 230 μm wide slit. The degree of polarization declined from 1 at zero voltage, and after reaching the minimum rose with the field strength. The lasing spectrum consists of sharp spikes corresponding to the resonant modes for all the applied voltages. The mechanisms responsible for electrically tuning the polarization of the RL were discussed. Optimizing the voltage characteristic of the polarization tunability was suggested by the preliminary experimental results.

Equilibrium locations of defects in two-dimensional configurations of the NLC director field

ABSTRACT We revisit the problem of finding the equilibrium location of the defect in two-dimensional configurations of the nematic liquid crystal (NLC) director field within the framework of the Frank-Ozeen formalism. Our analytical approach can be used for a wide class of nematic-filled regions, on the boundary surfaces of which there is a strong anchoring for the director with a piecewise constant pretilt. First, we use complex analysis to find a nematic director profile as a superposition of contributions from a set of virtual defects with appropriate topological charges acting on the defect in question. Then, we use the net zero force principle to find the equilibrium location of the defect. Our method generates the set of virtual defects automatically without using ad hoc symmetry considerations as it is in the standard method of images. We reproduce some known results using very simple calculations. We also consider several simple yet original problems. Namely, we find the equilibrium location of a disclination line near a long cylindrical particle with strong combined homeotropic-circular anchoring on its lateral surface and the equilibrium location of the disclination line in the NLC bounded by a parabolic cylinder with strong circular anchoring.

Probing shapes of microbes using liquid crystal textures

We propose a novel technique to probe shape of a single microbe embedded in a nematic liquid crystal (NLC) sample by observing geometry of dark brushes with optical microscope using a cross-polarizer set up. Assuming certain anchoring conditions for the NLC director at the surface of the microbe, we determine the resulting shapes of brushes using numerical simulations. Our results suggest that for asymmetrical microbes (such as cylindrical shaped bacteria/viruses), resulting brushes may carry the imprints of this asymmetry (e.g. the aspect ratio of cylindrical shape) at relatively large distances to be able to be seen using simple optical microscopy even for microbe sizes in few tens to few hundred nanometer range.

Thickness Dependent Electro-Optical Behaviour of Homeotropically Aligned Nematic Liquid Crystal

The homeotropically aligned liquid crystal (LC) display devices are of great interest in recent time. Thus, in the present work, the thickness dependent electro-optical behaviour of nematic liquid crystal (NLC) in homeotropic alignment (HA) has been studied. To achieve the HA of NLC, polyimide (PI) coated ITO glass substrates were used. Consequently, cleaned ITO glass substrates (with thickness of 0.7 mm) were used for the fabrication of the LC cells. The pure NLC material (LC-BYVA) was filled into PI coated cells by the capillary injection method. Subsequently, the filled cells were examined with the help of polarized optical microscope (POM), which show the good dark and bright orthoscopic textures of NLC in field ON and OFF states, respectively under cross-polarizers. The conoscopic study of the images also confirmed the perfect HA of NLC molecules. The dark states change to good bright state with the change in orientation of NLC director from homeotropic to planar at operating voltages as seen under cross-polarizers. The electro-optical (E-O) study also shows the good contrast ratio (CR) of display cells.

Influence of the flexoelectric effect on director alignment of nematic liquid crystals confined to the planar anchoring cylinder

ABSTRACT The influence of the flexoelectric effect on the director distribution of nematic liquid crystals confined to a cylinder with planar anchoring under an applied electric field is investigated by the continuum theory and the difference iterative method. Numerical analyses of the influence of the dielectric effect, flexoelectric effect and the coupling of these two effects on director alignment of nematic liquid crystal in a cylinder are obtained on the basis of the equilibrium equations using continuum theory. The analyses revealed that the change of director of nematic liquid crystals was caused by flexoelectric effect and dielectric effect in different directions. It provides a good theoretical basis for controlling the orientation of liquid crystal director in a cylinder and measuring of flexoelectric coefficient of liquid crystal materials.

Reentrant prewavy instability in competition between rising and twist modes in ac field-driven electroconvection.

We report on the prewavy (PW) instability in ac field-driven electrohydrodynamics that is induced in a nematic liquid crystal (NLC) sandwiched between parallel electrodes. The instability is characterized by a twist mode of the NLC director along the vertical orientation to the electrodes (i.e., the z axis), generating a periodic pattern having a large wavelength (λ_{PW}) in the xy plane. The PW periodic to the preferred director n_{0} of the NLC should be distinguished from well-known electroconvection (EC) such as normal rolls (NRs) and abnormal rolls (ARs) with similar wave vectors. A reentrant PW (PW2) was discovered by employing well-adjusted optical conditions and a dynamic image-process method. The wavelength λ_{PW2} of the PW2 accompanying turbulent EC was measured as functions of the applied ac voltage and frequency, which was distinguished from λ_{PW1} of the primary PW (PW1) separated from the NR. Moreover, the appearance, disappearance, and reappearance of the PW were investigated for five frequency regions classified in the ac field-driven EC; it was found that the high frequency and high voltage causes competition between the rising mode (θ, tilting angle to the xy plane) and twist mode (ϕ, in-plane angle to the x axis) of the director through electrohydrodynamic coupling between the director field and flows. We discuss how the PW2 can arise by considering another twist mode known as AR instability.

Controllable random lasers based on two-dimensional random gain systems with nematic liquid crystals

Controllable random lasers based on two-dimensional (2D) random gain systems with nematic liquid crystals are investigated by using the finite-difference time-domain (FDTD) methods. The dependence of random lasers on the scattering strength of nematic liquid crystals is studied. The results show that the random laser characteristics including the pump threshold, the emission intensity and the number of laser modes can be controlled by varying the pump rates, the filling fraction of nematic liquid crystals, and the included angle between the polarization direction of pump beam and the director of nematic liquid crystals. To achieve the optimal random lasers, the polarization direction of pump beam should be parallel to the director of nematic liquid crystals.

Liquid Crystal Polarisation Converter Arrays Based on Microholes Patterned Hydrophobic Layers

ABSTRACT In this study, a facile method was developed for the fabrication of liquid crystal (LC) polarisation converter arrays. To this end, arrays of LC droplets were first formed self-assembly by scribing LC onto microholes patterned hydrophobic layers, in which LC director was radially aligned in each microhole. This is because the special function of hydrophobic layer-amorphous fluoropolymer poly(butenyl vinyl) ether (also known as CYTOP), which aligns the nematic LC director perpendicular to the substrate surface. The twist-radially LC cells were assembled by combining these microholes-patterned layer with homogeneous polyimide (PI∥) substrate, which could change linearly polarised light to radially or azimuthally polarised light depending on the polarisation direction of the incident light. The obtained LC polarisation converter arrays were easy to fabricate with simple processing and patterned arrays over large areas. Furthermore, the CYTOP layers exhibited high transmittance in the visible light region combined with superior temperature resistant. In sum, the proposed LC polarisation converter arrays look promising for future applications in biological tissue analysis, particle trapping and accelerating, optical data storage, laser cutting and material processing.

ЭКВИВАЛЕНТНОСТЬ УРАВНЕНИЯ ХАНТЕРА-САКСОНА И ОБОБЩЕННОГО УРАВНЕНИЯ ФЕРРОМАГНЕТИКА ГЕЙЗЕНБЕРГА

Integrable systems play an important role in modern mathematics, theoretical and mathematical physics. The display of integrable equations with exact solutions and some special solutions can provide important guarantees for the analysis of its various properties. The Hunter-Saxton equation belongs to the family of integrable systems. The extensive and interesting mathematical theory, underlying the Hunter-Saxton equation, creates active mathematical and physical research. The Hunter-Saxton equation (HSE) is a high-frequency limit of the famous Camassa-Holm equation. The physical interpretation of HSE is the propagation of weakly nonlinear orientation waves in a massive nematic liquid crystal director field. In this paper, we propose a matrix form of the Lax representation for HSE in 𝑠𝑢ሺ𝑛 ൅ 1ሻ/𝑠ሺ𝑢ሺ1ሻ ⊕ 𝑢ሺ𝑛ሻሻ - symmetric space for the case 𝑛 ൌ 2. Lax pairs, introduced in 1968 by Peter Lax, are a tool for finding conserved quantities of integrable evolutionary differential equations. The Lax representation expands the possibilities of the equation we are considering. For example, in this paper, we will use the matrix Lax representation for the HSE to establish the gauge equivalence of this equation with the generalized Heisenberg ferromagnet equation (GHFE). The famous Heisenberg Ferromagnet Equation (HFE) is one of the classical equations integrable through the inverse scattering transform. In this paper, we will consider its generalization. Andalso the connection between the decisions of the HSE and the GHFE will be presented.

Lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation

Abstract The aim of this article was to address the lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation with the aid of Hirota bilinear technique. This model concerns in a massive nematic liquid crystal director field. By choosing the function f in Hirota bilinear form, as the general quadratic function, trigonometric function and exponential function along with appropriate set of parameters, we find the lump, lump-one stripe, multiwave and breather solutions successfully. We also interpreted some three-dimensional and contour profiles to anticipate the wave dynamics. These newly obtained solutions have some arbitrary constants and so can be applicable to explain diversity in qualitative features of wave phenomena.

Electrically tunable polarization of random lasing from dye-doped nematic liquid crystals.

Tunable polarizing direction of random lasing emission by an applied electric field which radiated from the lateral end face of homogeneously aligned, dye-doped nematic liquid crystal (NLC) cell was demonstrated for the first time, to the best of our knowledge. The lasing emission was partially polarized in the direction along the director of the NLC without the applied electric field. By tuning the applied electric field, the NLC director could be rotated to arbitrary direction from homogeneous to homeotropic alignment, resulting in the polarizing direction of lasing emission to any direction from parallel to perpendicular to the substrate surface in the end face.

Effect of iron oxide (γ-Fe2O3) nanoparticles on the morphological, electro-optical and dielectric properties of a nematic liquid crystalline material

The effect of Iron Oxide Nanoparticles (γ-Fe2O3 NPs) on a room temperature nematic liquid crystalline material namely 4-(4′-hexylcyclohexyl) isothiocyanatobenzene (6CHBT) has been studied. The ferronematic composites have been characterized using differential scanning calorimetry, polarizing optical microscopy, dielectric spectroscopy and electro-optical measurements. It is found that the ferronematic with the low concentration of γ-Fe2O3 NPs enhanced the orientational ordering of nematic matrix due to the strong orientational coupling between magnetic dipole moments associated to nanoparticles and nematic liquid crystal director, which is the essential feature of these systems. It resulted the improvement of various parameters of liquid crystals important for the application. In the ferronematics, the nematic to isotropic transition temperature increased as compared to that of the pure material. Dielectric spectroscopy has shown an increase of dielectric anisotropy in the composite systems. Electro-optical results reveal a decrement in both the splay elastic constant and the electric threshold voltage, in line with a noteworthy improvement of the steepness of transmission- voltage curves.

ABERRATIONAL PATTERN DURING THE SELF-ACTION OF THE ТЕМ01 MODE OF LIGHT RADIATION IN NEMATIC LIQUID CRYSTALS

Abstract—The properties of the aberrational pattern resulting from the self-action of the light radiation mode TEM01 in liquid-crystal systems are studied. It is found that the interference of light rays corresponding to two peaks of intensity and nonlinear phase shift leads to the formation of a system of fringes in the Fraunhofer region; their angular period is controlled by the distance between peaks. These fringes fill the entire aberrational pattern (concentric ring pattern) or only its part, depending on the type of the profile of the light-induced phase shift. The possibilities of using the properties of the aberrational pattern in the TEM01 mode for studying the light-induced reorientation of the nematic liquid crystal director are shown.

Two-dimensional director configurations in a nematic-filled cylindrical capillary with the hybrid director alignment on its surface

ABSTRACTWe analytically calculate two-dimensional equilibrium configurations of the nematic liquid crystal (NLC) director in a right cylindrical capillary with the hybrid director alignment on its inner surface. A part of this surface is treated to impose the strong homeotropic alignment, while on the remaining part the strong circular alignment, perpendicular to the capillary axis, is imposed. Owing to the system homogeneity along the capillary axis, a disclination line emerges in the bulk of the NLC, which runs parallel to the axis. It is shown that there exist either one or two equilibrium locations of the disclination line depending on the ratio of capillary surface parts with homeotropic and circular alignment. The technique that allows to obtain an analytical expression for the system free energy as a function of a disclination line location is presented. It considerably simplifies calculations and can be used while solving a variety of problems in which a defect location is sought.

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.

Electrically controlled random lasing from dye-doped nematic liquid crystals containing Ag nanoparticles within thin in-plane switching cells

Electrically controlled random lasing from dye-doped nematic liquid crystals (NLCs) containing Ag nanoparticles (NPs) within thin in-plane switching (IPS) cells is investigated. As far as we know, this study reports for the first time on random lasing using the IPS cell. Because of the Ag NPs’ presence, it is possible for the random lasers to occur in the thin IPS cells. The lasing output intensity depends on the applied electric field on the IPS cell when the pump energy is held constant. As the electric field intensity increases from 0 V µm−1 to 0.50 V µm−1, the output intensity increases gradually. However, as the electric field intensity increases from 0.5 V µm−1 to 1.00 V µm−1, the output intensity decreases gradually. At last, when the electric field intensity increases from 1.00 V µm−1 to 1.67 V µm−1, the emission intensity is basically stable. The variation in the output intensity can be partially attributed to the change in the NLC director distribution under the action of the electric field. This feature can be used to design adjustable light intensity devices.

Numerical Modeling of the Static Electric Field Effect on the Director of the Nematic Liquid Crystal Director

A two-dimensional model of the Frederiks effect is used to investigate the static electric field effect on the orientation of the nematic liquid crystal (LC) director in a side-electrode cell. The solutions are obtained by the standard finite-difference methods. The programs for the numerical solution of a two-dimensional parabolic partial differential equation are developed both in FORTRAN and C/C++. The Frederiks transition threshold for the central part of the cell and the dependences of the director’s orientation distribution on a high electric field are obtained. The results of the calculation are compared with the experimental data.

Light-induced hydrodynamic reorientation of hybrid aligned nematic liquid crystals caused by direct volume expansion

ABSTRACTThe dynamics of the direct volume expansion mechanism of light-induced hydrodynamic motions in hybrid-oriented nematic liquid crystal (NLC) have been studied experimentally. It was shown that heating caused by the absorption of a laser beam results in expansion of a NLC volume and induces hydrodynamic flow in a planar capillary. The hydrodynamic flow reorients the NLC molecules and thus the optical properties of the NLC layer are changing. A change of the tilt direction of the NLC director is demonstrated experimentally, and it is shown that hybrid-oriented NLC could be considered as ‘flexible ribbon’. Velocity gradient brings about an increase of curvature when hydrodynamic flow velocity is directed out of the ‘flexible ribbon’s’ curvature. The ‘flexible ribbon’ reverses its curvature when velocity is directed into ‘flexible ribbon’s’ curvature.

Liquid crystal metasurfaces on micropatterned polymer substrates.

Formation of photonic liquid crystal metasurfaces on rubbed polyimide substrates patterned by focused ion beam is demonstrated. Modulation of the surface anchoring conditions with periods from 1 to 6 micrometers gives rise to periodic deformation of the nematic liquid crystal director field. The exact periodicity is confirmed by the light diffraction measurements. Distinct colors originating from the specific zero-order diffraction spectra are observed and qualitatively explained in terms of an analytical model within the one-constant approximation. Quantitatively accurate optical spectra are obtained by the full scale numerical simulations taking into account all relevant material parameters. The results pave the way for hybrid liquid-crystal-based metasurfaces with tunable optical transmission, diffraction, and lasing.