Threshold flexoelectric deformations in homeotropic nematic layers

Elastic deformations of nematic liquid crystal layers subjected to a d.c. electric field were studied numerically. The flexoelectric properties of the nematic material and the presence of ionic space charge were taken into account. Homeotropic alignment with finite surface anchoring strength was assumed. The director orientation and the electric potential distribution were calculated; the space charge density was also determined. It was found that the threshold voltage strongly depended on the parameters of the system. In particular, a threshold as low as a few tenths of a volt occurred under suitable circumstances. In the case of a negative dielectric anisotropy, Δ ε, such low values of the threshold voltage existed when the ion concentration was sufficiently high, and given sufficiently large magnitudes of the flexoelectric coefficients and a sufficiently small anchoring energy. If the ion concentration was low or if the flexoelectric coefficients were small or if the surface anchoring was strong, the threshold was equal to several volts. In the case of positive dielectric anisotropy, the threshold amounted to several tenths of a volt for a weakly anisotropic and highly conductive material. If the dielectric anisotropy was sufficiently high or if the ion concentration was sufficiently low, the threshold voltage increased with Δ ε and reached tens of volts. These results can be explained as the effect of the inhomogeneous electric field arising in the vicinity of the surfaces, due to the ionic space charge redistributed by the external voltage. They are qualitatively consistent with earlier experiments which show the effect of the ion concentration on the elastic deformations in flexoelectric nematics. They correspond also with theoretical results concerning the effect of the electric field produced by the surface polarization or by the adsorption of ions.     

Threshold voltage for purely flexoelectric deformations of conducting homeotropic nematic layers

Elastic deformations induced by an electric field in homeotropic nematic layers with finite anchoring energy were studied numerically. A nematic material possessing flexoelectric properties and characterized by a positive dielectric anisotropy was considered. The ionic space charge and the ion transport across the layer were taken into account. The director orientation, the electric field strength and the ion concentrations were calculated as functions of the coordinate normal to the layer. The calculations show that the electric field distribution, which determines the form of the deformations, is influenced by the ionic current and therefore depends on the ionic content and on the properties of the electrodes. Several types of deformations were distinguished. When the electrode contacts are well conducting or when the ionic content is low, the threshold voltage is very close to the value U _f valid for an insulating nematic. When the electrodes are poorly conducting or blocking at high ion concentration, the threshold voltage decreases much below U _f. At moderate ion concentrations, i.e. between 10¹⁹ and 10²⁰ m^?3, two different behaviours were found depending on the sign of the sum of flexoelectric coefficients e ₁₁+e ₃₃. In the case of e ₁₁+e ₃₃<0, the threshold voltage decreases with the ionic content; in the case of e ₁₁+e ₃₃>0, the deformations occur in two separate voltage regimes. They arise above a certain threshold voltage, disappear at some higher voltage and reappear at an even higher threshold.     

Converse flexoelectric effect in homeotropic nematic layers with asymmetric surface anchoring

The dc electric field-induced deformations of conducting flexoelectric nematic layers were studied numerically. Asymmetric boundary conditions expressed by 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 the deformations and the director distributions in the deformed layers were calculated for low, moderate and high ion concentrations. The director distributions were also determined. The results show that asymmetry caused by difference between the anchoring strengths and by difference between mobilities of anions and cations lead to two threshold values for a given layer corresponding to two polarities of the bias voltage. Additionally, the values of both thresholds depend on the sign of the flexoelectric parameter. In every case under consideration, the threshold is significantly lowered when the ion concentration is high.     

Influence of the surface pretilt angle on spatially periodic deformations in nematic layers

The deformations induced by electric field in twisted or untwisted flexoelectric nematic layers can be homogeneous (i.e. one-dimensional) or spatially periodic (i.e. two-dimensional). The periodic deformations are undesirable from an applicative point of view since they destroy the homogeneous appearance of the area of an excited pixel of a display. They are particularly favoured when the nematic material possesses flexoelectric properties. In order to check whether the unwanted periodic deformations can be eliminated by means of suitable surface pretilt angle, the small deformations arising just above the corresponding threshold voltage were investigated numerically. The nematic materials exhibiting both weak and strong flexoelectricity were taken into account. The surface pretilt angles ranging from 0° to 30° were adopted. It was shown that the periodic patterns, arising in the case of planar surface alignment, disappear if sufficiently large surface pretilt angle is applied.     

Ion adsorption and its influence on direct current electric field induced deformations of flexoelectric nematic layers

The influence of ion adsorption on the behavior of the nematic liquid crystal layers is studied numerically. The homeotropic flexoelectric layer subjected to the dc electric field is considered. Selective adsorption of positive ions is assumed. The analysis is based on the free energy formalism for ion adsorption. The distributions of director orientation angle, electric potential, and ion concentrations are calculated by numerical resolving of suitable torques equations and Poisson equation. The threshold voltages for the deformations are also determined. It was shown that adsorption affects the distributions of both cations and anions. Sufficiently large number of adsorbed ions leads to spontaneous deformation arising without any threshold if the total number of ions creates sufficiently strong electric field with significant field gradients in the neighborhood of electrodes. The spontaneous deformations are favored by strong flexoelectricity, large thickness, large ion concentrations, weak anchoring, and large adsorption energy.     

Polarized states of hybrid aligned nematic layers

Electric polarization arising in hybrid aligned nematic liquid crystal layers with rigid boundary conditions is studied numerically by solving the torques equation and Poisson equation. Three phenomena that give rise to the polarization are taken into account: flexoelectricity, surface polarization and adsorption of ions. The director orientation within the layer, as well as the distribution of electric potential and space charge density are calculated for layers deformed by an external magnetic field. The role of the ionic space charge is investigated. For a particular set of parameters of a model substance, the voltage arising between the layer surfaces varies from 10^-1 V (in an extremely pure nematic) to 10^-3 V (in material with a typical ion concentration). The surface polarization yields an additional voltage (of the order 10^-2 V) nearly independent of the ion concentration. The effect of simultaneous flexoelectric polarization and ion adsorption is evidently different from a linear superposition of their separate contributions. The flexoelectric polarization leads to partial separation of ions of opposite signs. In the case of positive flexoelectric coefficients, a thin sublayer of positive charge arises at the planar-orienting boundary plate. The negative charge is displaced towards the homeotropically aligning plate. The magnitude of this effect increases with the magnetic field. The surface phenomena introduce additional subsurface charges.     

Dynamics of electric field induced deformations in flexoelectric nematic layers

The dynamics of deformations induced by DC electrical fields in homeotropically aligned layers containing a flexoelectric nematic material with negative dielectric anisotropy has been studied numerically. The rise time constants, characterising the development of deformations after switching on the external voltage, and the decay time constants, describing the decay of deformation after switching off the voltage, were calculated as a function of the parameters essential for the behaviour of the layer. In particular, the influence of flexoelectricity was studied. It was found that the stronger the flexoelectric properties of the nematic, the lower is its viscosity, the higher is the bias voltage, the weaker is the surface anchoring, the thinner is the layer and the higher is the ion concentration, the more rapid was the onset of deformation. Similarly, the lower the viscosity, the thinner is the layer, the stronger the anchoring and the larger the ion content, the more rapid was the decay of deformation. Neither the voltage previously applied nor the flexoelectric properties were found to affect the decay time.     

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.     

Influence of anchoring at a nematic cell surface on threshold spatially periodic reorientation of a director

We have analysed the influence of surface director anchoring in a planar flexoelectric nematic cell on the threshold spatially periodic reorientation of the director in an external dc electric field. By minimizing the free energy of the nematic cell we obtained the equations for a director and numerically solved them in the one elastic constant approximation. The dependences of the threshold electric field and the spatial period of director structure on the azimuthal and polar anchoring energy, as well as the flexoelectric parameters, are determined. It is shown that the domain of the flexoelectric parameter values, at which the spatially periodic reorientation of a director takes place, increases with decreasing azimuthal anchoring energy and increasing polar anchoring energy.     

Continuum modelling of hybrid-aligned nematic liquid crystal cells: optical response and flexoelectricity-induced voltage shift

A continuum model is employed to study systematically the optical response of hybrid-aligned nematic (HAN) liquid crystal cells under the application of an external electric field. The influence of the flexoelectric effect is discussed for a large range of anchoring strengths at the homeotropic alignment layer. It is shown that the optical response of HAN cells is governed by a complicated interplay between the flexoelectric coefficient and homeotropic anchoring strength. In particular, the calculations reveal that, for weak homeotropic anchoring, the flexoelectric effect leads to a non-linear voltage shift of the optical transmittance as a function of flexoelectric coefficient, and gives rise to an asymmetry in the transmittance–voltage curve. Finally, a comparison of the continuum-model simulations with recent experimental observations indicates that both the flexoelectric coefficient and the anchoring strength of the nematic liquid crystal MBBA on a homeotropic polyimide alignment layer are significantly lower than previously reported.     

Continuum modelling of hybrid-aligned nematic liquid crystal cells: optical response and flexoelectricity-induced voltage shift

A continuum model is employed to study systematically the optical response of hybrid-aligned nematic (HAN) liquid crystal cells under the application of an external electric field. The influence of the flexoelectric effect is discussed for a large range of anchoring strengths at the homeotropic alignment layer. It is shown that the optical response of HAN cells is governed by a complicated interplay between the flexoelectric coefficient and homeotropic anchoring strength. In particular, the calculations reveal that, for weak homeotropic anchoring, the flexoelectric effect leads to a non-linear voltage shift of the optical transmittance as a function of flexoelectric coefficient, and gives rise to an asymmetry in the transmittance-voltage curve. Finally, a comparison of the continuum-model simulations with recent experimental observations indicates that both the flexoelectric coefficient and the anchoring strength of the nematic liquid crystal MBBA on a homeotropic polyimide alignment layer are significantly lower than previously reported.     

The influence of the flexoelectric effect on the electrohydrodynamic instability in nematics

A rigorous three-dimensional linear analysis of the electrohydrodynamic instability in nematic liquid crystals including the flexoelectric effect is presented for the case of an applied d.c. voltage. The flexoelectric effect leads to an appreciable reduction of the threshold and to the appearance of oblique rolls at threshold for the standard material MBBA. We discuss the influence of a magnetic field and test several approximations against the rigorous results     

Calculation of the surface charge and potential and of the structural component of disjoining pressure in an interlayer in KCl solutions between glass samples

The dependence of the Stern potential, ψ₁, of glass samples on the distance between these, H, has been theoretically calculated, while taking into account the Stern isotherm and the electroneutrality equation. Comparison of the theoretical dependences ψ₁(C)_H→∞ with those previously experimentally obtained enables one to calculate the energy of adsorption of OH ions on glass and, further, the dependence ψ₁(H). It has been shown that for pH 4–6 and C_KCl = 10^-2-10^-5 mol/L, the value of ψ₁ practically does not depend on H. The result obtained was used to calculate theoretically the ionic-electrostatic forces and to compute (from the experimental values of the interaction forces) structural forces U_s(H). The dependence thus obtained, U_s(H), is of exponential character.     

Investigation of flexoelectric properties of a palladium-containing nematic liquid crystal, Azpac, and its mixtures with MBBA

Flexoelectricity of pure Azpac (an HOAB-palladium complex) was studied using planar nematic layers under an in-plane electric field. Longitudinal domains were observed with a period inversely proportional to the applied d.c. electric field. These domains were considered as a first experiment manifestation of the theoretical prediction of R. B. Meyer (1969) and their study has permitted the evaluation of the difference in flexo-coefficientse_1z - e_3x. Their appearance can also be followed for the non-complexed HOAB, using instant video-microscopy frames.

Mixtures of Azpac, up to 10wt%, and MBBA were oriented homeotropically and band flexoelectric deformations were observed, both in d.c. and in a.c. (1 to 1000 Hz) electric fields normal to the director. The dynamics of director reorientation were studied by the method of flexoelectric light modulation. A system comprising a He-Ne laser and a lock-in amplifier interfaced by a PC was developed. By operating this in a frequency sweep regime, viscoelastic spectra of director dynamics were recorded. These spectra were excited using a linear flexoelectric coupling mechanism. Breaks in the spectra were observed in the range 200 to 600 Hz, indicating a cross-over from bulk to surface dissipation of energy. For the first time, a surface viscosity of 2.6 × 10^-8Jsm^-2 was determined for MBBA homeotropically anchored on a DMOAP-coated glass surface.

In concentrations at low as 2.5 wt%, Azpac was found to cancel the bend flexo-coefficient of MBBA and at higher concentrations, a steep rise in the flexo-coefficient of the mixture was observed, but with an opposite sign. Thus, the application of Azpac as an effective additive for adjustment of the value and sign of the flexo-coefficient in flexoelectro-optic displays or light modulators could be suggested.     

Trapping of positronium in a size-dependent spherical square well potential

The real trapping potential energy U(r) of positronium in vacancy-type holes and self-sustaining bubbles in liquids is replaced by a spherical square well potential of finite energy depth U_m and the scaling procedure proposed by Yu et al. is applied. Available data for the ortho-positronium lifetime in molecular crystals and in liquids are re-examined and a unique relation is found between the potential energy depth U_m and the calculated radius R of the trapping site. The general form of a surface-enhanced real potential energy U(r) which is compatible with the behaviour of U_m is proposed.     

松果状纳米氧化铁对液晶电光性能的影响

液晶材料被广泛应用于液晶显示器(LCD)中,但是由于液晶中杂质的存在,导致液晶的应用电压变大,增加了能耗。 为了降低应用中的阈值电压和饱和电压,通常向液晶中添加纳米颗粒来提高电光性能。 本文采用简单的化学沉淀法制备了形貌均一,大小尺寸均匀的松果状氧化铁(P-Fe₂O₃)纳米颗粒。 将其掺杂到向列相液晶4-氰基-4'-戊基联苯(4-cyano-4'-pentylbiphenyl,5CB)中,结果表明,掺杂质量分数为0.5%时,电光性能达到最优,阈值电压和饱和电压分别降低24.8%和45.2%,对比度增大46%,响应时间降低至17.6 ms,此性能优于相同条件下掺杂普通Fe₂O₃纳米颗粒的向列相液晶5CB,其阈值电压和饱和电压分别降低15%和16%。 这归因于松果状Fe₂O₃纳米颗粒可以在向列相液晶5CB中均匀分散,其粗糙的表面吸附了液晶中的杂质离子,减少了杂质离子的屏蔽效应,从而提高了电光性能。     

Solute alignment in liquid crystal solvents The Saupe ordering matrix for anthracene dissolved in uniaxial liquid crystals

We have described a theory for U, the potential of mean torque of rigid solutes at infinite dilution in a uniaxial liquid crystal phase; this may be used to calculate (S_xx - S_yy) and S_zz, the principal elements of the Saupe ordering matrix. In its simplest form U(ω) contains only second-rank terms and the dependence of the biaxiality (S_xx - S_yy) is determined by ω, a parameter which describes the departure of the potential of mean torque from cylindrical symmetry, and is predicted to be temperature independent. If dispersion forces are responsible for the magnitude of the orientational order parameter then ω should be independent of the solvent and depend only on the anisotropy in the electric polarizability of the solute. Indeed, this independence should result for any pair potential which can be factorized into a product of solute and solvent properties. These predictions are tested here by determining values of S_zz and (S_xx - S_yy) for anthracene-d₁₀ as a solute in several liquid crystal solvents, from the quadrupolar splittings obtained from the deuteron N.M.R. spectra. It is found that ω has a strong dependence on the nature of the solvent, which demonstrates that the solute ordering cannot be determined primarily by dispersion forces, or by a factorizable potential. There is also a weaker temperature dependence of λ observed for each binary mixture, and we show how this might be caused by a dependence of ω on solvent ordering, or by the inclusion of a fourth-rank term in U(ω).     

ZIF-8对向列相液晶电-光性能的提升

ZIF-8（沸石咪唑酯骨架结构材料）是一种金属有机物骨架结构材料,因其极高的比表面积、出色的热稳定性而被广泛应用于各种性质研究中。ZIF-8通过传统的水热法在甲醇溶液中合成,其颗粒尺寸约为250nm,形貌为菱形十二面体。研究发现,合成的ZIF-8材料具有良好的热稳定性及相当大的比表面积。将其掺杂进液晶中会增强液晶的电-光性能,增强效果与掺杂浓度有关。在向列相液晶4-氰基-4'-戊基联苯（5CB）中,ZIF-8可以吸附杂质离子,抑制屏蔽效应,最终使液晶驱动电压降低,响应加快。在掺杂浓度为0.05%（w,质量分数）时,液晶体系的电-光性能改善最明显,阈值电压（V_th）最小达到0.92 V,饱和电压（V_sat）达到1.31 V,响应时间仅为10.04 ms。而当掺杂浓度大于0.05%（w）时,ZIF-8在液晶盒中发生团聚,影响液晶分子的有序排布,同时吸附杂质离子减少,不利于液晶电-光性能的改善。     

Theory of the effect of small ions on the electrical admittance of macroion solutions

A general theory is given on the electrical admittance of a parallel plate capacitor filled with a conductive medium containing charged particles by considering both their electric atmospheres and the electric field due to charges induced on the electrodes. The theory is applied to a dilute macroion solution with added salt and it is found that the low frequency dielectric response of the solution reflects the motions of the macroion and bound small ions and the effect of motion of the ion atmosphere around the macroion is canceled out by the current due to the induced charges on the electrodes.