Director Tilt Angle Research Articles

Electrically Induced Structural Transformations of a Chiral Nematic under Tangential-Conical Boundary Conditions

In this study, structural transformations induced by an electric field in the chiral nematic under tangential-conical boundary conditions have been considered. The composition influence of the orienting polymer films on the director tilt angles, the formation of orientational structures in the LC layer, as well as the electro-optical response and relaxation processes have been studied. It has been shown that the poly(tert-butyl methacrylate) concentration change in the orienting polymer mixture allows for smoothly controlling the director tilt angle without fixing its azimuthal orientation rigidly.

Nematic Structures under Conical Anchoring at Various Director Tilt Angles Specified by Polymethacrylate Compositions.

Dependence of the director tilt angle of nematic liquid crystal (LC) under conical anchoring from the two-component polymer mixture composition has been studied. We varied the ratio of poly(isobutyl methacrylate) (PiBMA), which specifies a conical anchoring for the nematic liquid crystal LN-396, and poly(methylmethacrylate) (PMMA) assigning a tangential alignment for the same nematic. An oblique incidence light technique to determine a tilt angle has been used. It has been shown that the tilt angle increases from to when PiBMA:PMMA ratio changes in the range 30:70 to 100:0. The specific optical textures viewed under the polarizing microscope and proper orientational structures have been considered for various compositions of the polymer films. An electric field action on the formed orientational structures has been investigated. The obtained results are promising for the application in various electro-optical LC devices with a conical anchoring in which the director tilt angle is a crucial parameter: a controlled diffraction gratings, an electrically operated achromatic rotators of linear light polarization, etc.

Oblique light incidence method to study topological defects in nematic layers with conical boundary conditions

A polarization microscopy method to investigate the orientational structures and boojums formed in the chiral and achiral nematic layers under conical (tilted) boundary conditions has been developed. Oblique light incidence on nematic layer is used, due to which the phase difference between the ordinary and extraordinary waves depends on the director’s azimuthal angle. The phase difference gets maximal when the director azimuthal angle of achiral nematic varphi (x,y) = 0 and an azimuthal angle at the center of the chiral nematic layer varphi _0(x,y) = 0 independently of the total twist angle varphi _{TOTAL}. It has been found that the m=+1 boojums with the phase xi = pm 90^circ and xi = (-90^circ + varphi _{TOTAL}/2) are formed in achiral and chiral nematics, respectively, at the director tilt angle theta _{d/2} cong 40^circ at the interface. In addition, the defectless structure of chiral nematic with the periodically variable azimuthal director angle on the substrates has been studied.

Polar anchoring energy and tilt angle measured by magneto-optical technique in nematic doped with ionic surfactant

ABSTRACT The surface anchoring of a nematic doped with the ionic surfactant has been investigated and compared with the one in the undoped sample. The director tilt angle at the substrates coated with the orienting polymer film has been determined by the null method in a rotating magnetic field. The Frederiks transition in a magnetic field has been chosen as a convenient technique to measure the polar anchoring energy W θ. The temperature dependences of anchoring energy have been obtained for the various nematic cells. The W θ values for nematic doped with the ionic surfactant are less than for the undoped one. The factors affecting the measurement accuracy have been discussed. The accuracy is higher for the thinner nematic layers and weaker anchoring energy.

Analytical Approach of Director Tilting in Nematic Liquid Crystals for Electronically Tunable Devices

This paper presents an analytical expression that models the tilt angle of directors in a nematic liquid crystal (LC), depending on its elastic properties, its dielectric anisotropy, and the quasi-static electric field applied. The analytical solution obtained is fast and easily computable in comparison with numerical estimations and is of special interest in radiofrequency; for instance, for the LC modeling in full-wave electromagnetic simulators in the design process of electronically tunable devices, such as microwave phase shifters or electronically steerable antennas for satellite communications. Subsequently, a comparison is made between numerical approaches (self-implemented shooting method) and the analytical formulas when varying the parameters of the LC, being demonstrated its usefulness. The average LC director is then obtained and used to form the full permittivity tensor that completely characterizes the electrical properties of the material. Finally, an electromagnetic simulation is carried out to show the capabilities of the LC as a tunable phase shifter. It is shown that only 5 cm of a commercial 200-μm LC mixture is necessary to achieve 360° of the maximum variable phase shift at the 30-GHz band.

Tunable transmission of a nematic liquid crystal as defect in a 1D periodic structure of dielectric materials by orientation and re-orientation of liquid crystal molecules.

In this paper, we investigate tunable transmission characteristics of a one-dimensional periodic structure (1DPS), designed with periodic dielectric materials containing a nematic liquid crystal (NLC) as a defect layer, on the basis of orientation and re-orientation of LC molecules. The nonlinear differential equation for the director of the liquid crystal under the light field is solved numerically. The relation between the liquid crystal director and the intensity of the electromagnetic wave (EMW) is derived. Transmittances of the liquid crystal defect layer in the 1DPS are calculated with the variation of the intensity of the incident wave and liquid crystal director tilt angles. By varying the director tilt angle of the liquid crystal molecules as well as the incident angle of the EMW, the shifting of the transmitted defect mode wavelengths is studied. Such study is helpful to understand how orientation and reorientation of the molecules affect the transmittance of the considered periodic structure when the EMW interacts with an embedded liquid crystal as a defect layer in the 1DPS of dielectric materials. Such photonic structure of dielectric materials with the liquid crystal layer as a defect layer can be used to fabricate bistable switches, optical filters, feedback lasers, etc.

Cholesterol-Based Grafted Polymer Brushes as Alignment Coating with Temperature-Tuned Anchoring for Nematic Liquid Crystals.

Novel alignment coating with temperature-tuned anchoring for nematic liquid crystals (NLCs) was successfully fabricated in three step process, involving polymerization of poly(cholesteryl methacrylate) (PChMa) from oligoproxide grafted to the glass surface premodified with 3-aminopropyltriethoxysilane. Molecular composition, thickness, wettability of the PChMa coating and its alignment action for a NLC were examined with time of flight-secondary ion mass spectrometry, ellipsometry, contact angle measurements, polarization optical microscopy and commercially produced PolScope technique allowing for mapping of the optic axis and optical retardance within the microscope field view. We find that the PChMa coating provides a specific monotonous increase (decrease) in the tilt angle of the NLC director with respect to the substrates normal upon heating (cooling) referred to as anchoring tuning.

Director configurations in nematic droplets with tilted surface anchoring

ABSTRACTThe polymer dispersed nematic liquid crystal (LC) with the tilted surface anchoring has been studied. The droplet orientational structures with two point surface defects – boojums and the surface ring defect – are formed within the films. The director tilt angle α = 40° ± 4° at the droplet interface and LC surface anchoring strength Ws ~ 10–6 (J m−2) have been estimated. The bipolar axes within the studied droplets of oblate ellipsoidal form can be randomly oriented are oriented randomly relatively to the ellipsoid axes as opposed to the droplets with homeotropic and tangential anchoring.

Position-Dependent Three-Dimensional Diffusion in Nematic Liquid Crystal Monitored by Single-Particle Fluorescence Localization and Tracking.

Anisotropic mass diffusion in liquid crystals (LCs) is important from the point of both basic LC physics and their applications in optoelectronic devices. We use super-resolution fluorescence microscopy with astigmatic imaging to track 3D diffusion of quantum dots (QDs) in an ordered nematic LC. The method allowed us to evaluate the diffusion coefficients independently along the three spatial axes as well as to determine the absolute position of the QD with respect to the cell wall. We found variations of the diffusion coefficient along the different directions across the cell thickness and explained these as being due to changes of a tilt angle of the LC director. Close to the surface, the diffusion is slowed down due to the confinement effect of the cell wall. Overall, the QD diffusion is much slower than expected for a corresponding particle size. This phenomenon is suggested to originate from reorientation of the LC director in the vicinity of the particle.

Optical properties of hybrid liquid-crystal cells for various angles of incidence of light

A theoretical and computer model has been developed for the dependence of the phase-lag difference on the pretilt angle of the liquid-crystal director in cells with an inhomogeneous distribution of the director over the cell thickness and with different angles on the opposing substrates of the cell. A method is described for calculating how the normalized phase-lag difference depends on the distribution law of the director tilt angle over the thickness of the cell. The method can be used for various types of liquid-crystal cells, with positive or negative dielectric or optical anisotropy. A method is proposed for measuring the tilt angle on one of the substrates of a hybrid cell when the pretilt angle of the liquid crystal on the other substrate is known. The model thus developed can be used in designing optical compensators.

Nematic director reorientation at solid and liquid interfaces under flow: SAXS studies in a microfluidic device.

In this work we investigate the interplay between flow and boundary condition effects on the orientation field of a thermotropic nematic liquid crystal under flow and confinement in a microfluidic device. Two types of experiments were performed using synchrotron small-angle X-ray-scattering (SAXS). In the first, a nematic liquid crystal flows through a square-channel cross section at varying flow rates, while the nematic director orientation projected onto the velocity/velocity gradient plane is measured using a 2D detector. At moderate-to-high flow rates, the nematic director is predominantly aligned in the flow direction, but with a small tilt angle of ∼±11° in the velocity gradient direction. The director tilt angle is constant throughout most of the channel width but switches sign when crossing the center of the channel, in agreement with the Ericksen–Leslie–Parodi (ELP) theory. At low flow rates, boundary conditions begin to dominate, and a flow profile resembling the escaped radial director configuration is observed, where the director is seen to vary more smoothly from the edges (with homeotropic alignment) to the center of the channel. In the second experiment, hydrodynamic focusing is employed to confine the nematic phase into a sheet of liquid sandwiched between two layers of Triton X-100 aqueous solutions. The average nematic director orientation shifts to some extent from the flow direction toward the liquid boundaries, although it remains unclear if one tilt angle is dominant through most of the nematic sheet (with abrupt jumps near the boundaries) or if the tilt angle varies smoothly between two extreme values (∼90 and 0°). The technique presented here could be applied to perform high-throughput measurements for assessing the influence of different surfactants on the orientation of nematic phases and may lead to further improvements in areas such as boundary lubrication and clarifying the nature of defect structures in LC displays.

A Review of Polymer-Stabilized Ferroelectric Liquid Crystals.

The polymer stabilized state of ferroelectric liquid crystals (FLC) is reviewed; and the effect of a dispersed polymer network in an FLC outlined and discussed. All fundamental material aspects are demonstrated; such as director tilt angle; spontaneous polarization; response time and viscosity; as well as the dielectric modes. It was found that the data can largely be explained by assuming an elastic interaction between the polymer network strands and the liquid crystal molecules. The elastic interaction parameter was determined; and increases linearly with increasing polymer concentration.

Enhancing transmittance of fringe-field switching liquid crystal device by controlling perpendicular component of dielectric constant of liquid crystal

In this paper, we briefly report the effect of the magnitude of the perpendicular component (ε⊥) of the dielectric constant of liquid crystals with a positive dielectric anisotropy on the transmittance of a fringe-field switching liquid crystal device. The larger the ε⊥, the more the tilt angle of the liquid crystal director near the edges of electrodes is reduced, thereby increasing the twist angle above the center of electrodes. Consequently, the transmittance of the device is significantly improved by controlling ε⊥ of the liquid crystal.

Numerical modeling of electromagnetic wave propagation in a liquid crystal cell at oblique incidence

This paper presents a robust numerical method for the analysis of wave propagation in nematic liquid crystals. The structure is excited by a plane wave incident at an oblique angle with respect to the normal to the liquid–crystal cell. The underlined formulation is based on an eigenvalue problem which is solved analytically in order to obtain the governing field expressions inside a homogeneous, thin crystal layer. The liquid–crystal cell is comprised of N such layers. Enforcing the continuity of the tangential electric and magnetic fields at the interfaces formed by the various layers, a matrix system is generated. Solution of the linear system of equations results in the light intensity inside the liquid crystal, which is coupled to a non-linear differential equation for the director tilt angle. This equation is solved using either an explicit or implicit finite-difference scheme. An iteration process continues until convergence is reached for the coupled problem. The proposed numerical method was validated against published results that were generated by approximate analytical methods. Further simulations and studies were conducted emphasizing on the physics of the problem and related interesting phenomena.

The influence of surface polarization on the saturation behaviour of a weak anchoring NLC cell

Based on the modified Rapini-Papoular formula for surface anchoring energy, the saturation behaviour of a weak anchoring nematic liquid crystal cell is studied. The mathematical equations of solving director distribution are obtained. A parameter reflecting the characteristic of director distribution is introduced. Expressions for saturation voltage and the parameter reflecting the characteristic of director distribution are obtained for the second order transition. The methods of calculating the two quantities for the first order transition are also given. The influences of surface polarization on the two quantities are discussed in detail. The results show that whether the second or the first order transition, the position of the maximal tilt angle of director will shift towards the substrates with the increase of surface polarization. The influences of surface polarization on saturation voltage for the second and the first order are reverse. The saturation voltage will increase for the second order but decrease for the first order with the increase of surface polarization.

Influence of the alignment surface on the characteristics of optically addressed liquid-crystal modulators

Two optically addressed transmission-type liquid-crystal modulators based on a nematic liquid crystal-a-Si: C: H photoconductor structure are studied. The modulators differ in the initial tilt angle of the director and in the barrier height at the interface. It is shown that these parameters influence the dependence of the diffraction efficiency on the feed conditions, recording pulse repetition rate, and spatial frequency of the recorded grating. The spatial resolution of the modulators at a level of half the diffraction efficiency is equal to 75 mm−1. The maximal diffraction efficiency is high, 69%, owing to the asymmetric profile of the grating, which arises at a large initial tilt angle of the liquid crystal director.

The influence of chirality on the difference in flexoelectric coefficients investigated in uniform lying helix, Grandjean and twisted nematic structures

Measurements of the difference in flexoelectric coefficients (e 1 – e 3), using the sign convention as originally defined by Meyer, are reported from three experiments employing the flexoelectro-optic effect in different geometries. The uniform lying helix (ULH) structure is used to measure the tilt angle of the liquid crystal director with respect to the helix axis for an applied electric field, in order to infer a value for (e 1 – e 3). Alternatively, measurements of the flexoelectric difference can be made by considering the transmission through a device with an in-plane electric field aligned in either the Grandjean structure for highly chiral materials, or a twisted nematic (TN) structure for largely achiral materials. The results from the Grandjean and ULH structures show the equivalence of the measurement techniques with helix axis either perpendicular or parallel to the substrates. Further comparison of these results with the measurement from the achiral TN device shows that the difference in flexoelectric coefficients displays no dependence on chirality, demonstrating that flexoelectricity is purely associated with splay and bend director deformations, as expected from symmetry considerations.

Shear flow in smectic A liquid crystals

This paper considers the onset of a shear-induced instability in a sample ofsmectic A liquid crystal. Unlike many previous models, the usual directorn need not necessarily coincide with the local smectic layer normala; the traditional Oseen constraint () is not imposed when flow is present. A recent dynamic theory for smectic A (Stewart 2007Contin. Mech. Thermodyn. 18 343–60) will be used to examine a stationary instability in asimple model when the director reorientation and smectic layer distortions are, firstly,assumed not to be coupled to the velocity and, secondly, are supposed coupled to thevelocity. A critical shear rate at which the onset of the instability occurs will be identified,together with an accompanying critical director tilt angle and critical wavenumber for theassociated smectic layer undulations. Despite some critical phenomena beinglargely unaffected by any coupling to the flow, it will be shown that the influenceof some material parameters, especially the smectic layer compression constantB0 and the couplingconstant B1, upon the critical shear rate and critical tilt angle can be greatly affected byflow.

Ellipsometric study of vertically aligned nematic liquid crystals

The director tilt angle distribution in vertically aligned nematic liquid crystal displays has been investigated by means of variable angle spectroscopic ellipsometry. Liquid crystal vertical alignment has been realized by thermal evaporation of SiOx. By changing the deposition angle, it is possible to control the pretilt angle. The director profile inside the sample was inferred by reflection and transmission ellipsometric measurements. The tilt angle distribution inside the cell versus the applied voltage is reported and eventually, comparing it with the simulations from the elastic theory, the anchoring energy has been obtained.

Determining the helical tilt of membrane peptides using electron paramagnetic resonance spectroscopy

Theoretical calculations of hyperfine splitting values derived from the EPR spectra of TOAC spin-labeled rigid aligned α-helical membrane peptides reveal a unique periodic variation. In the absence of helical motion, a plot of the corresponding hyperfine splitting values as a function of residue number results in a sinusoidal curve that depends on the helical tilt angle that the peptide makes with respect to the magnetic field. Motion about the long helical axis reduces the amplitude of the curve and averages out the corresponding hyperfine splitting values. The corresponding spectra can be used to determine the director axis tilt angle from the TOAC spin label, which can be used to calculate the helical tilt angle due to the rigidity of the TOAC spin label. Additionally, this paper describes a method to experimentally determine this helical tilt angle from the hyperfine splitting values of three consecutive residues.