Analytical approach to V-shaped characteristics in antiferroelectric liquid crystal displays

Not only in ferroelectric liquid crystal displays (LCDs), but also in antiferroelectric LCDs, grey levels are possible by actively addressing the ‘continuous director rotation mode’. For ferroelectric LCDs this was shown qualitatively and quantitatively in previous articles. In this article it is shown that an exact analytical approach is also possible for antiferroelectric LCDs. In two consecutive layers the director orientations are symmetric, and at zero voltage they are in a splayed state. The conditions on alignment layer thickness and interaction coefficients are related to those of ferroelectric liquid crystal but are easier to fulfill.     

Optical and electrooptical properties of homeoplanar layers of cholesteric liquid crystals

Abstract

A wedge shaped layer of a cholesteric liquid crystal, with the director surface orientations first planar and the other homeotropic, shows two distinctive textures depending on the relation between the local thickness, d, and the equilibrium pitch, P ₀. If d/P ₀ < 1, the texture does not show any domains; the director distribution is reminiscent of a corkscrew. If d/P ₀ > 1, there are linear periodic domains. The domain direction rotates as the thickness of the layer increases. The voltage dependence of light transmission of the homeoplanar cholesteric layer placed between crossed polarizers is less pronounced and more linear than the corresponding dependence for the twisted nematic effect.     

A liquid crystal microlens obtained with a non-uniform electric field

Abstract

A homogeneously aligned nematic liquid crystal cell with a hole-patterned electrode and with an indium-tin oxide (ITO-) coated counter-electrode has been prepared. A non-uniform electric field can be produced by the asymmetrical electrode structure. The liquid crystal director can be reoriented by applying a voltage across the electrodes, and this produces an axially symmetrical profile of the refractive index. This liquid crystal cell is expected to have a lens effect and so its optical properties have been investigated. The profile of the output light intensity was measured by using a detecting system with an optical fibre. Some relationships between the lens properties, the diameter of the hole and the thickness of the liquid crystal layer have been examined. The liquid crystal cell becomes a convex (converging) lens with a relatively low voltage. A focal length of several millimetres can be obtained by applying voltages of 3-4 V. As the applied voltage increases, the focal length becomes longer, and the cell changes to a concave (diverging) lens when a high voltage is applied (? 20 V). These properties are discussed from the viewpoint of the director orientation effects resulting from the non-uniform electric fields in the cell.     

Analytical approach to V-shaped characteristics in antiferroelectric liquid crystal displays

Not only in ferroelectric liquid crystal displays (LCDs), but also in antiferroelectric LCDs, grey levels are possible by actively addressing the 'continuous director rotation mode'. For ferroelectric LCDs this was shown qualitatively and quantitatively in previous articles. In this article it is shown that an exact analytical approach is also possible for antiferroelectric LCDs. In two consecutive layers the director orientations are symmetric, and at zero voltage they are in a splayed state. The conditions on alignment layer thickness and interaction coefficients are related to those of ferroelectric liquid crystal but are easier to fulfill.     

Simulations of energy and switching in AFLCDs with different boundary conditions

Using standard expressions for the various terms in the Gibbs free energy, the switching in antiferroelectric liquid crystal (AFLC) displays is simulated and the time evolution of various energy terms and of the liquid crystal director distributions are calculated. It is shown that when returning from a strong positive voltage to zero, one can reach two types of antiferroelectric state: the normal alternating state with the two bulk polarizations perpendicular to the electrodes and opposite to each other, and the alternative splayed symmetric state with two bulk polarizations parallel to the electrodes and again opposite to each other. The former case gives rise to tri-state switching characteristics, the latter to V-shaped switching. In general strong polar interaction with the alignment layer favours V-shaped switching while weak or no polar interaction give rise to tri-state switching characteristics. Since the V-shaped characteristic has so far only been demonstrated experimentally in ferroelectric liquid crystals (or antiferroelectric liquid crystals being in the ferroelectric state), the difference in AFLCs is discussed and the conditions for continuous switching are modelled. The simulations show that the switching characteristics of the antiferroelectric display can be controlled by the surface parameters.     

Fast switching and luminance-controlled fringe-field switching liquid crystal device for vehicle display

ABSTRACT

Liquid crystal displays (LCDs) for vehicle displays should exhibit a fast response time in wide temperature range and wide-viewing angle in horizontal and downward directions without grey-scale inversion but limited brightness in the upward direction because the display images can be reproduced in the front window glass of a vehicle, affecting driver’s front visibility. Currently, fringe-field switching (FFS) liquid crystal device is widely commercialised for high resolution and wide-viewing-angle LCD; however, it needs to improve response times and limit the display brightness in the upward direction. As a solution, we propose a homogeneously aligned liquid crystal device in which liquid crystal director does tilt as well as twist deformation in a confined area by both vertical- and fringe-electric fields, exhibiting about two times faster decay response time than that of conventional FFS mode with suppressed luminance in the upward direction. The proposed liquid crystal device can be applied to LCDs for vehicle displays.     

A guided wave study of the voltage dependent director configuration in a nematic liquid crystal layer with finite surface tilt

Prism coupling techniques have been used to excite optical modes in a thin nematic liquid crystal with finite surface tilt in order to study the voltage dependent director profile. The surface tilts are opposite in character and it is found that at zero applied volts the stable configuration is the substantially horizontal state. On applying the field this state is broken, probably transforming to the twisted vertical state. By modelling all the data obtained, the detailed behaviour of the director profile has been fully characterized yielding much information, including the change of surface tilt with applied voltage. For the nematic liquid crystal E7, this gives a voltage induced surface tilt of approximately 0.67° V^-1 for a 5.65 μm thick cell. Also using a boundary layer model, it has been possible to analyse the free energy in the cell and hence show that the observed twisted vertical state is the expected stable state under the field applied.     

Observations on the voltage response of a 90° twisted nematic cell using guided modes

Using prism coupling to guided modes and surface plasmons we have examined in detail the director response of a 90° twisted nematic liquid crystal cell as a function of applied voltage. By careful comparison of angle scan reflectivity data with theoretical predictions generated from a combination of liquid crystal continuum theory and multilayer optics theory it has been possible to establish how the surface tilt changes with voltage, and also to observe changes in the optic constants due to changes in the order parameter with applied field.     

Light diffraction studies on director arrangement in the polymer‐pinned striped pattern obtained via the electric field‐induced Fréedericksz transition of nematics

We have observed an anomalous pattern forming phenomenon in which a striped pattern in a nematic liquid crystal appeared after removing an electric field following a Fréedericksz transition, and this pattern was preserved even in the equilibrium state in zero‐electric field. The nematic director arrangement in the striped pattern was investigated by light diffraction measurements. The stripes are proposed to consist of a periodic distortion of the nematic directors, specifically, tilted directors with the same absolute value of tilt angle but of opposite sign are alternately arrayed. The proposed model of the stripes is in good accord with the experimental results of light diffraction dependence on polarizing direction and light incidence angle.     

Relationship between lens properties and director orientation in a liquid crystal lens

Lenses with a homogeneously aligned liquid crystal having a Fresnel structure have been prepared by using a nematic with a positive dielectric anisotropy. Their focal length can be varied continuously from the value f_e for an extraordinary ray to f_o for an ordinary ray by applying an electric field across the lens cell. The effective refractive index of the lens where the director is aligned perpendicular to the grooves of the Fresnel structure becomes smaller than when the director is aligned parallel to the grooves. Then the liquid crystal lens has a characteristic aberration which could not be observed in a conventional glass lens; that is, the focal length of the lens becomes different according to the incidence of rays on the different parts of the lens. The properties of the liquid crystal lens can be improved by making the director orientation axially symmetric, in the form of a concentric circle, but the polarization component rotated 90° from the incident extraordinary ray appears when the voltage is applied across the lens cell. This phenomenon is discussed in relation to the optical properties and the director orientation in a liquid crystal prism cell.     

A liquid crystal microlens obtained with a non-uniform electric field

A homogeneously aligned nematic liquid crystal cell with a hole-patterned electrode and with an indium-tin oxide (ITO-) coated counter-electrode has been prepared. A non-uniform electric field can be produced by the asymmetrical electrode structure. The liquid crystal director can be reoriented by applying a voltage across the electrodes, and this produces an axially symmetrical profile of the refractive index. This liquid crystal cell is expected to have a lens effect and so its optical properties have been investigated. The profile of the output light intensity was measured by using a detecting system with an optical fibre. Some relationships between the lens properties, the diameter of the hole and the thickness of the liquid crystal layer have been examined. The liquid crystal cell becomes a convex (converging) lens with a relatively low voltage. A focal length of several millimetres can be obtained by applying voltages of 3-4 V. As the applied voltage increases, the focal length becomes longer, and the cell changes to a concave (diverging) lens when a high voltage is applied (≳ 20 V). These properties are discussed from the viewpoint of the director orientation effects resulting from the non-uniform electric fields in the cell.     

Relationship between lens properties and director orientation in a liquid crystal lens

Lenses with a homogeneously aligned liquid crystal having a Fresnel structure have been prepared by using a nematic with a positive dielectric anisotropy. Their focal length can be varied continuously from the value f_e for an extraordinary ray to f _o for an ordinary ray by applying an electric field across the lens cell. The effective refractive index of the lens where the director is aligned perpendicular to the grooves of the Fresnel structure becomes smaller than when the director is aligned parallel to the grooves. Then the liquid crystal lens has a characteristic aberration which could not be observed in a conventional glass lens; that is, the focal length of the lens becomes different according to the incidence of rays on the different parts of the lens. The properties of the liquid crystal lens can be improved by making the director orientation axially symmetric, in the form of a concentric circle, but the polarization component rotated 90° from the incident extraordinary ray appears when the voltage is applied across the lens cell. This phenomenon is discussed in relation to the optical properties and the director orientation in a liquid crystal prism cell.     

The elastic distortion and stability of biaxial nematic liquid crystal on the surface grooves

Fukuda et al. reexamined the Berreman's model which attributes the surface anchoring to the elastic distortion of the uniaxial nematic liquid crystal induced by the grooves of a surface. They showed that at the variance with the assumption made in the original approach of Berreman, the azimuthal distortion of the director cannot be considered as negligibly small. Now this method is generalized to the biaxial nematic liquid crystals, with some approximations for the elastic constants. We obtain an additional term in the elastic distortion energy per unit area which depends on the second power of the cosine of the angle made between the main director n at infinity and the direction of the surface grooves. This additional term describes the distortion energy of the minor director m induced by the surface grooves when the n director is anchored exactly along the grooves. We have studied the stability of the n director around the grooves, and in one-constant model for each director the stability condition is that the elastic constant of the n director is the maximum.     

Characterization of the alignment of a nematic liquid crystal using half leaky guided modes

The excitation of half leaky guided optical modes to characterize fully the optical tensor profile in a thin liquid crystal layer has been used to evaluate the effect of rubbed polyimide aligning layers on the alignment of a nematic liquid crystal. A cell fabricated with rubbed polyimide alignment surfaces was studied at a wavelength of 632.8 nm. The liquid crystalline layer is sandwiched between a high refractive index top glass plate and a low refractive index glass substrate. Angular dependent reflectivities are recorded using a coupling prism and matching fluid with the same index as the top glass plate. Careful fitting of the predictions from multilayer optics theory to the observed angle dependent polarization conversion and reflectivity data yields the director profile within the liquid crystal layer in great detail.     

The alignment of nematic liquid crystals on photolithographic micro-groove patterns

Abstract

The alignment of nematic liquid crystals on micro-groove patterns was studied. It has been found that the order of the alignments is determined by the edge shape, spacing, and line pitch of the micro-groove patterns. On coarse patterns, with pitches greater than 2 μm, striped patterns of the liquid crystal alignment were observed using polarized light which manifested different orientations of the liquid crystals on the top, edge, and bottom of the grooves, respectively. On fine patterns, with pitches less than 2 μm, a uniform device-quality alignment has been realized, with which twisted nematic cells were constructed in combination with the rubbed alignment layer on the opposite substrate. Their viewing angle characteristics and tilt orientations of the director were also investigated.     

The influences of surface polarization on NLC cells

The influence of the surface polarization, P_s , on a nematic liquid crystal (NLC) cell is investigated analytically. Flexoelectric polarization is considered, but selective ion absorption is ignored. The differential equations are derived for tilt angle, θ, of director n and the corresponding boundary conditions based on Gibbs free energy, and their solutions discussed. Equations for the reduced threshold voltage, u_th , and the reduced saturation voltage, u_sat , are deduced and the relationships between u_th , u_sat and reduced strength of surface polarization, p, derived.     

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

ABSTRACT

We 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.     

Modelling of director equilibrium states in a nematic cell with relief surface

We study two-dimensional equilibrium configurations of nematic liquid crystal (NLC) director in a cell bounded by two parallel surfaces. One surface is planar and the other one is spatially modulated. The relief of the modulated surface is described by a smooth periodic sine-like function. The orientation of NLC director easy axis is assumed to be homeotropic at one cell surface and planar at the other one. The NLC director anchoring with cell surfaces is assumed to be strong. We consider the case where disclination lines occur in the bulk of NLC above the extrema of the modulated surface. These disclination lines run along the crests and troughs of the surface relief. If the orientation of director at both bounding surfaces is of the same type, then NLC director field is continuous. For both configurations mentioned above (with defects and without defects), we obtain analytical expressions for director distribution in the bulk of NLC in the approximation of planar director deformations. Equilibrium distances from disclination lines to the spatially modulated surface are calculated when the defects occur. The dependences of these equilibrium distances on the period and depth of surface relief and the cell thickness are investigated in detail.     

Molecular director and layer response of chevron surface stabilized ferroelectric liquid crystals to low electric field

Recent papers on chevron surface stabilized ferroelectric liquid crystal cells claim that the chevron layer structure can be reversibly uprighted by application of the low to moderate electric fields typically employed to produce director reorientation. In this paper we show, using optical microscopy and X-ray scattering, that there is no significant change in the smectic layer thickness or chevron layer structure of our chevron surface stabilized ferroelectric liquid crystal cells under typical director switching conditions. Furthermore, we present arguments, based on the known elastic properties of smectics, that there is not likely to be a significant elastic layer response to these levels of applied electric field in any surface stabilized ferroelectric liquid crystal cell with anchored layers. Both the switching and observed continuous optical response to applied field can be understood on the basis of electric field induced reorientation of a non-uniform molecular director distribution. We further show that the typically observed broad distribution of layer orientations about the mean chevron structure arises from localized layering defects.