Influences of surface and flexoelectric polarization on the effective anchoring energy in nematic liquid crystal

The physical effects on surface and flexoelectric polarization in a weak anchoring nematic liquid crystal cell are investigated systematically. We derive the analytic expressions of two effective anchoring energies for lower and upper substrates respectively as well as their effective anchoring strengths and corresponding tilt angles of effective easy direction.All of these quantities are relevant to the magnitudes of both two polarizations and the applied voltage U. Based on these expressions, the variations of effective anchoring strength and the tilt angle with the applied voltage are calculated for the fixed values of two polarizations. For an original weak anchoring hybrid aligned nematic cell, it may be equivalent to a planar cell for a small value of U and has a threshold voltage. The variation of reduced threshold voltage with reduced surface polarization strength is also calculated. The role of surface polarization is important without the adsorptive ions considered.     

Flexoelectric-Induced Voltage Shift in Hybrid Aligned Nematic Liquid Crystal Cell

Flexoelectric-induced voltage shift in a weak anchoring hybrid aligned nematic liquid crystal cell is investigated theoretically. Based on the elastic theory of liquid crystal and the variation method, the equations for the bulk and the boundary of the cell are derived. By computer simulation, the dependence of the
shift voltage on the sum of the flexoelectric coefficients and the anchoring energy strength is obtained. As a result, a novel method to determine the sum of the flexoelectric coefficients by measuring the shift voltage is put forward.     

Threshold property of a nematic liquid crystal cell with two grating surface substrates

A grating surface can drive the liquid crystal molecules to orientate along the direction parallel or vertical to the projected plane of the grating surface. The nematic liquid crystal (NLC) cell manufactured with two pre-treated grating surface substrates may realize the vertical display, parallel display and twist display. In this paper, the threshold property of this NLC cell is investigated systematically. With the Frank elastic theory and the equivalent anchoring energy formula of grating surface substrate, the analytic expressions of the threshold voltage related to three displays are obtained, which are dependent on their geometrical parameters such as amplitude δ and pitch λ of the grating surface substrate. For a certain anchoring strength, the threshold voltage increases or decreases with the increase of the value δ/λ of the different displays.     

Anchoring properties of substrate with a grating surface

The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal (NLC) in a grating surface originates from two mechanisms, thus the anchoring energy consists of two parts. One originates from the interaction potential between NLC molecules and the molecules on the substrate surface, and the other stems from the increased elastic strain energy. Based on the two mechanisms, the expression of anchoring energy per unit area of a projected plane of this grating surface is deduced and called the equivalent anchoring energy formula. Both the strength and the easy direction of equivalent anchoring energy are a function of the geometrical parameters (amplitude and pitch) of a grating surface. By using this formula, the grating surface can be replaced by its projected plane and its anchoring properties can be described by the equivalent anchoring energy formula.     

Analysis of deformations of flexoelectric homeotropic liquid crystal layers with various anchoring strengths

Deformations of homeotropic layers of nematic liquid crystal possessing flexoelectric properties and subjected to external dc voltage were studied numerically. The influence of the anchoring strengthWwas investigated. The calculations were performed for two types of layers, one with positive dielectric anisotropy and positive sum of flexoelectric coefficients and the other with opposite signs of these parameters. Strongly blocking electrodes were assumed. The threshold voltages for deformations were computed for several anchoring strength values and for low, moderate, and high ion contents. The director distributions were also determined. They were influenced by joined effects of anchoring strength and space charge of ions. For increasing ion contents and increasing anchoring strength, remarkable change of deformation character was noticed. In the case of negative dielectric and flexoelectric parameters, the threshold was nearly proportional to W for low anchoring strength and saturated at some high value of W. In the case of positive dielectric and flexoelectric parameters, the threshold voltage increased strongly with W. In the range of enhanced ion concentrations, the deformation arose in two voltage ranges. The increasing anchoring strength damped the deformations in the whole layer, however, this effect was minor at high ion content.     

栅状表面液晶盒的光学属性

基于栅状表面等效锚定能公式和弹性理论,对Bryan-Brown等人提出的混和排列向列相液晶盒进行研究.通过变分理论得到指向矢倾角和扭曲角满足的方程和边界条件.根据这些方程和边界条件,利用差分迭代方法计算出指向矢倾角和扭曲角对应某一个δ/λ值在不同电压下的分布.应用琼斯矩阵方法,研究这种液晶盒的电光效应.这些结果都与栅状表面的几何参数有关,即与周期λ和振幅δ有关.     

表面序电极化、挠曲电极化与向列液晶盒饱和点的双稳态

理论分析和数值模拟相结合,研究了表面序电极化、挠曲电极化对非对称弱锚定向列液晶盒在饱和点双稳态的影响,得到了两种极化共存时液晶指向矢满足的方程和边界条件.通过引入新的状态参量,从能量的角度对两种极化的物理效应进行了分析.结果表明,在一定条件下,两种极化耦合,在饱和点通过改变锚定能影响边界条件,从而诱导双稳态.文中给出了判断是否存在双稳态的一般条件,此条件与数值计算结果符合. 关键词： 表面序电极化 挠曲电极化 饱和点 双稳态     

Surface electric-field-induced instabilities in a homeotropically oriented nematic liquid crystal sample

The effect of a surface electric field produced by ionic adsorption on the molecular orientation of a nematic liquid crystal sample is analyzed. The eigenvalue problem for a semi-infinite medium is analytically solved both for strong and weak anchoring situations. The threshold instabilities are numerically determined and it is shown that the homeotropic pattern can be destabilized also in the situation of strong anchoring. The dependence of the threshold field on the anchoring strength and on the surface polarization is determined by taking into account also the coupling of the quadrupolar component of the flexoelectric coefficient with the field gradient. Received 4 November 1999 and Received in final form 4 April 2000     

Nematic ordering in a cell with modulated surface anchoring: effects of flexoelectricity

We have analyzed molecular ordering in a nematic sample sandwiched between two parallel substrates, characterized by a periodically varying anchoring easy axis. If the periodicity lambda is smaller than the Debye screening length l(D) and the nematic material possesses flexoelectric properties, it is necessary to take into account also the electrostatic and flexoelectric contributions in the thermodynamical potential when the actual director field is determined. In this framework, for small deviations from the homeotropic alignment we have derived analytical expressions for the tilt angle (theta) and the electrical potential. To establish a connection with experimentally observable quantities, we have related the theta profile to the average and investigated its behavior for different values of lambda, the flexoelectric coefficient, and the anchoring strength w. Our results indicate that in a nematic with pronounced flexoelectric properties for small enough lambda, a kind of subsurface deformation appears, which substantially decreases . Therefore, effects of flexoelectricity cannot be neglected in treating nematic cells with modulated anchoring which allows bistable ordering.     

Inhomogeneous threshold director reorientation in a planar nematic flexoelectric cell with finite anchoring energy

The dependence of the threshold parameters and the period of the electric-field-induced spatially periodic reorientation of the director in a flexoelectric nematic liquid crystal (NLC) on the anchoring conditions at the surface of a planar NLC cell has been studied. The threshold electric field and the corresponding wave-number of the periodic structure of the director field have been numerically calculated for arbitrary values of the anchoring energy. In the case of strong anchoring, the corresponding analytical expressions are obtained in a single-constant approximation. A decrease in the azimuthal anchoring energy leads to an increase in the intervals of possible values of the flexoelectric parameter ν and the ratio K₂/K₁ of the Frank elastic constants. A decrease in the polar anchoring energy leads to narrowing of these intervals as compared to the case of infinitely strong anchoring at the NLC cell surface.     

Theoretical analysis of the influence of flexoelectric effect on the defect site in nematic inversion walls

Based on the experimental phenomena of flexoelectric response at defect sites in nematic inversion walls conducted by Kumar et al., we gave the theoretical analysis using the Frank elastic theory. When a direct-current electric field normal to the plane of the substrate is applied to the parallel aligned nematic liquid crystal cell with weak anchoring, the rotation of ± 1 defects in the narrow inversion walls can be exhibited. The free energy of liquid crystal molecules around the +1 and-1 defect sites in the nematic inversion walls under the electric field was formulated and the electric-field-driven structural changes at the defect site characterized by polar and azimuthal angles of the local director were simulated. The results reveal that the deviation of azimuthal angle induced by flexoelectric effect are consistent with the switching of extinction brushes at the +1 and-1 defects obtained in the experiment conducted by Kumar et al.     

挠曲电效应对向列相液晶盒电光效应的影响

研究挠曲电效应对向列相液晶盒电光效应的影响.通过变分理论得到液晶指向矢满足的微分方程和边界条件,利用差分迭代的方法计算强锚定和弱锚定液晶盒中液晶指向矢的分布情况.借助琼斯矩阵的方法,计算两种液晶盒电光特性曲线.此外,在计算中同时考虑了挠曲电表面和体积效应.     

Influence of Surface Geometry of Grating Substrate on Director in Nematic Liquid Crystal Cell

The director in nematic liquid crystal cell with a weak anchoring grating substrate and a strong anchoring planar substrate is relative to the coordinates x and z. The influence of the surface geometry of the grating substrate in the cell on the director profile is numerically simulated using the two-dimensional finite-difference iterative method under the condition of one elastic constant approximation and zero driven voltage. The deepness of groove and the cell gap affect the distribution of director. For the relatively shallow groove and the relatively thick cell gap, the director is only dependent on the coordinate z. For the relatively deep groove and the relatively thin cell gap, the director must be dependent on the two coordinates x and z because of the increased elastic strain energy induced by the grating surface.     

Dynamic photorefractivity in nematic liquid crystal cells with photoconductive orienting layers

A new mechanism of photorefractivity in nematic liquid crystal cells with photoconductive orienting layers, referred to as dynamic photorefractivity, is proposed. The essence of this mechanism is as follows: an external ac electric field excites quasi-periodic subgratings at the interface between a liquid crystal and a photoconductive orienting layer. The interference optical field, inducing a charge distribution on the surface of the orienting layers, modulates the surface anchoring force and the penetration depth of the external field into the liquid crystal layer. As a result, the surface charge grating azimuthally reorients subgratings according to its structure and stabilizes their period. Since the amplitude of the subgratings is determined by the strength of the applied electric field and the cell parameters, the wave mixing efficiency in the dynamic mode may significantly exceed that in the classical orientational effect.     

挠曲电效应对向列相液晶盒响应时间的影响

应用液晶动力学理论和差分迭代方法,考虑上液晶挠曲电特性情形下研究强锚泊混合排列向列相液晶盒撤掉电压时的动态响应过程,数值计算得到液晶盒透过率随时间的变化.结果表明:随展曲和弯曲挠曲电系数和的绝对值|e₁₁+e₃₃|的增加,液晶盒的响应时间逐渐减小,当|e₁₁+e₃₃|=50 pC·m^-1时,响应时间与忽略挠曲电效应的情况相比缩短了一半.     

液晶表面锚定能的温度依赖性研究

通过测量扭曲液晶盒中的液晶分子的实际扭曲角及摩擦方向与液晶分子的界面指向矢之间的方位偏角，用自行建立的液晶方位表面锚定能的测量方法，测定了５ＣＢ液晶与摩擦的聚酰亚胺界面的锚定能及其温度依赖性，并用热力学理论进行了分析．实验结果表明，随着温度的增加液晶的表面锚定能Ｅ_ａ是减小的，从２５.５℃时的５.０×１０^－5Ｊ／ｍ²减小到３５℃时的５.０×１０^－6Ｊ／ｍ²；同时，外推长度ｄ_e随 关键词：     

弱锚泊对液晶微波相位调制的影响

液晶对微波的调制取决于外加电压作用下液晶分子的取向, 而基板的锚泊对液晶取向有重要影响, 必然导致微波调制的变化. 本文研究了无手性掺杂的弱锚泊90°扭曲向列相液晶的微波调制特性. 基于液晶弹性理论和变分原理得到了液晶盒系统的平衡态方程和边界条件, 采用差分迭代方法数值模拟了不同锚定强度大小和不同预倾角下单位长度相移随电压的变化. 结果表明: 1)预倾角对微波相移的影响与施加电压有关. 当液晶盒施加电压为0.5–1.6 V之间时, 随预倾角增大, 单位长度微波相移及其与强锚泊0°预倾角90°扭曲液晶相移差均增大, 且相移差达到最大时的电压值也随倾角增大而减小; 1.6–3.0 V之间, 单位长度微波相移及相移差随预倾角增大而减小; 1.6 V附近及3.0 V之后, 相移基本没有变化. 2)表面锚定强度大小对微波相移的影响非常大. 随锚定强度减小, 单位长度微波相移及相移差均会增大, 微波相移的可调范围也增大, 且增加越来越明显. 此研究为液晶微波调制器件的设计提供了理论依据.     

Exploration of the sum of flexoelectric coef ficients of nematic liquid crystals

We present a theoretical calculation of the dependence of reflectivity Rpp of the improved fully leaky waveguide geometry,which comprises pyramid,matching fluid,and strongly anchored hybrid aligned nematic liquid crystal(NLC) cell on the internal angle.The calculation is based on the multi layer optical theory and the elastic theory of liquid crystals.For different sums of flexoelectric coefficients e11 and e33,the curve of Rpp moves a distance to the left or the right relative to the case of ignoring the flexoelectric effect and the distance of the movement varies with different flexoelectric coefficients.Consequently,the sum of flexoelectric coefficients can be explored by measuring the distance of the movement.     

Effect of surface electric field on the anchoring of nematic liquid crystals

We analyse the influence of adsorbed ions and the resulting surface electric field and its gradient on the anchoring properties of nematics with ionic conductivity. We take into account two physical mechanisms for the coupling of the nematic director with the surface electric field: (i) the dielectric anisotropy and (ii) the coupling of the quadrupolar component of the flexoelectric coefficient with the field gradient. It is shown that for sufficiently large fields near saturated coverage of the adsorbed ions, there can be a spontaneous curvature distortion in the cell even when the anchoring energy is infinitely strong. We also discuss the director distortion when the anchoring energy of the surface is finite. Received: 29 September 1997 / Received in final from: 10 November 1997 / Accepted: 18 November 1997     

液晶盒视角对比度曲线的实验测量

设计了一种测量液晶盒视角的实验装置,通过固定的水平角度和竖直角度扭曲向列相液晶盒光透过率的测量,得到了视角-对比度曲线。不同的水平和竖直视角,其对比度也是不同的。无论竖直视角的大小,水平视角为0°时对比度最大;当对比度大于某一数值（例如50）时,随着竖直视角从20°增加到20°,水平视角的范围先增大后减小。