Flexoelectric polarization and second order elasticity for nematic liquid crystals

The flexoelectric properties of nematic liquid crystals are analysed. It is shown that in the frame of the usual elasticity two coefficients characterize completely the flexoelectric properties of the liquid crystal. These coefficients, in the limit of small scalar order parameter, i.e. near the clearing point, are approximately equal. More precisely they have the same linear term in the scalar order parameter, and differ for terms quadratic in this parameter. Their difference behaves, hence, as the usual nematic liquid crystal elastic constants, whereas their sum depends on the temperature, like the mixed splay-bend elastic constant. It is shown furthermore that in the frame of a second order elastic theory in the flexoelectric polarization there are no terms from the second order spatial derivatives of the nematic director, or the nematic tensor order parameter. Consequently also in the frame of the second order elasticity the flexoelectric polarization is given by the usual expression. This conclusion is important in connection with the surface polarization recently discovered in pretilted nematic liquid crystal samples.     

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.     

Giant flexoelectricity of bent-core nematic liquid crystals

Flexoelectricity is a coupling between orientational deformation and electric polarization. We present a direct method for measuring the flexoelectric coefficients of nematic liquid crystals (NLCs) via the electric current produced by periodic mechanical flexing of the NLC's bounding surfaces. This method is suitable for measuring the response of bent-core liquid crystals, which are expected to demonstrate a much larger flexoelectric effect than traditional, calamitic liquid crystals. Our results reveal that not only is the bend flexoelectric coefficient of bent-core NLCs gigantic (more than 3 orders of magnitude larger than in calamitics) but also it is much larger than would be expected from microscopic models based on molecular geometry. Thus, bent-core nematic materials can form the basis of a technological breakthrough for conversion between mechanical and electrical energy.     

Flexoelectric effect modelling

A statistical theory of dipole flexoelectric (FE) polarization in liquid crystals is used to calculate temperature dependence of order parameters, elastic constants and FE coefficients. Two systems with polar wedge-shaped and banana-shaped molecules are investigated. In both cases, the FE coefficients are proportional to the dipole moment component parallel to the molecule symmetry axis. It results from the symmetries of interactions and of the Mayer function. The origin of the FE effect and microscopic pictures of the distorted phases are discussed.     

Flexoelectric blue phases

We describe the occurrence and properties of liquid crystal phases showing two dimensional splay and bend distortions which are stabilized by flexoelectric interactions. These phases are characterized by regions of locally double splayed order separated by topological defects and are thus analogous to the blue phases of cholesteric liquid crystals. We present a mean-field analysis based upon the Landau-de Gennes Q-tensor theory and construct a phase diagram for flexoelectric structures using analytic and numerical results. We stress the similarities and discrepancies between the cholesteric and flexoelectric cases.     

Flexoelectric origin of oblique-roll electrohydrodynamic instability in nematics

We develop the theory of electrohydrodynamic instability in nematic liquid crystals by incorporating the flexoelectric terms. Using a one-dimensional linear analysis of the problem for an applied DC field, we demonstrate that for the usual materials the rolls have an oblique orientation as has been found experimentally. We also provide an experimental evidence for the strong flexoelectric influence on the director profile in the rolls.     

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.     

Viewing angle characteristics of a nematic liquid crystal cell with two crossed-grating surface substrates

Liquid crystal in a nematic liquid crystal cell surface with two crossed-grating surface substrates can be oriented along the normal grating direction with given geometric parameters of groove and anchoring strength. This display is equivalent to multi-domain vertical-alignment mode. It has a relatively wide viewing angle. In this letter, we investigate the viewing angle characteristics of this kind of cell. The viewing angle dependence of contrast ratio is obtained using the extended Jones matrix method, which also considers the flexoelectric effect. The viewing angle is dependent on the geometric parameter of grating surface, the flexoelectric coefficients, and the anchoring strength. Therefore, appropriate value for each factor needs to be selected to obtain a better viewing angle of this cell.     

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.     

液晶盒中挠曲电效应的计算

负性液晶MBBA在液晶盒中垂面排列,沿面外加电场后产生挠曲电效应.基于液晶弹性理论研究这一效应,基于变分理论得到了液晶指向矢满足的微分方程及边界条件.应用差分迭代方法进行了数值求解.在小角度近似下,得到了指向矢分布的解析解,与数值解和专著结果进行了比较.     

Threshold effects in homeotropically oriented nematic liquid crystals in an external electric field

The electric field-induced orientational transition in a homeotropically oriented nematic liquid crystal cell is investigated. The interaction with the field as a result of anisotropy of the permittivity and flexoelectric polarization is taken into account. For an arbitrary energy of interaction of the nematic with the substrate simple relations are derived for determining the threshold characteristics of the phase transition. It is shown that, in contrast with planar orientation, in fields above a critical value a periodic structure can occur only by virtue of the flexoelectric effect. The resulting dependences for the threshold parameters in the given geometry are exceptionally useful for determining experimentally the surface energy and the difference in the flexoelectric coefficients. Zh. éksp. Teor. Fiz. 116, 543–550 (August 1999)     

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.     

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.     

Surface and flexoelectric polarization in a nematic liquid crystal 5CB

The temperature dependence of the surface polarization has been measured for both the planar and homeotropic orientation of a nematic liquid crystal at a solid substrate. A conventional liquid crystal 5CB, pure and doped with an azo-dye, was used in cells with controlled asymmetry for light absorption. The measurements have been made by a pyroelectric technique using short pulses of a YAG laser to create a temperature increment. The latter, in turn, was measured independently by a novel time-resolved “optical thermometer” technique monitoring temperature-dependent birefringence by a He- Ne laser beam. In accordance with the symmetry of the order parameter, the surface polarization has different sign for the two orientations, its magnitude ranges from -4 to +2pC/m. The same technique has been used for the measurement of the flexoelectric polarization in hybrid cells. The sum of the flexoelectric coefficients is e ₁ + e ₃ = - 13pC/m at 25°C. Received 28 February 2000 and Received in final form 5 September 2000     

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     

Threshold voltages and optical retardation of deformed flexoelectric nematic layers with asymmetric surface anchoring

Deformations of homeotropically aligned flexoelectric nematic layers induced by dc electric fields were simulated numerically. Two different anchoring strengths on the limiting surfaces were assumed. Nematic material was characterised by negative dielectric anisotropy. Both signs of the sum of flexoelectric coefficients were taken into account. The electric properties of the layer were described in terms of a weak electrolyte model. Mobility of cations was assumed to be one order of magnitude lower than that of anions. Quasi-blocking electrode contacts were assumed. The threshold voltages for deformations were determined by means of calculations of the phase difference Φ between ordinary and extraordinary light rays passing through a layer placed between crossed polarisers. The threshold values depended on the polarity of the bias voltage U. When the threshold value was exceeded, the phase difference increased with the voltage. Two different Φ(U/U_threshold) dependencies for the two polarities of the voltage were found for each layer if the nematic possessed the flexoelectric properties. The possibility of using this effect to detect the flexoelectricity in the nematic was explored by simulated experiments. The effectiveness of the proposed method is discussed.     

Influence of Surface Energy on the Direct Flexoelectric Effect in a Plate

The influence the surface energy introduced earlier by Kretschmer and Binder has on flexoelectric polarization induced by bending a dielectric plate is studied in the context of phenomenological theory. In contrast to the familiar effect this energy has on permittivity, its influence on the flexoelectric response does not vanish within a thick plate.     

液晶界面物理效应研究及进展

液晶表面和与它接触的固体表面的相互作用，作为边界条件对液晶显示起着重要的控制作用，并影响着液晶表现出的各种物理效应．液晶表面和界面科学一直是液晶物理学研究的重要领域．这一领域内一个重要的课题是，从物理机理出发寻找正确反映界面作用规律的数学物理方程，以便完善发展液晶界面理论，指导界面诱导技术．文章就这一研究领域已取得的成果、未解决的问题、当前研究的热点(一级转变和挠曲电效应)及目前有争议的问题(表面弹性项是否存在等)进行了介绍。     

过热液氦均匀核化速率的确定

预测不同压力下过热液氦的均匀核化速率是十分重要的,它与液氦的极限过热度密切相关。文中通过回顾动力学理论、分子聚集理论、涨落理论等研究液体均匀核化的方法,对过热液氦的均匀核化速率进行了计算,并且对各种方法进行了比较与分析。结果表明,用能量涨落理论来计算过热液氦的均匀核化速率是一种比较合理的方法。     

Scaling effect of flexoelectric (Ba,Sr)TiO3 microcantilevers

The flexoelectric microcantilever offers an alternative approach for the development of micro/nano‐sensors. The transverse flexoelectric coefficients µ₁₂ of barium strontium titanate microcantilevers were measured at room temperature, and found to keep the same value of 8.5 µC/m for microcantilevers with thickness ranging from 30 µm to 1.4 mm. The calculated effective piezoelectric coefficient and electrical energy density of flexoelectric cantilevers are superior to those of their piezoelectric counterparts, suggesting that the flexoelectricity‐induced polarization can be significantly increased as structures are scaled down due to the scaling effect of strain gradient, holding promise for flexoelectric micro/nano cantilever sensing applications. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)