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.     

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.     

Flexoelectric deformations of homeotropic nematic layers in the presence of ionic conductivity

Elastic deformations of homeotropic nematic liquid crystal layers subjected to a d.c. electric field were studied numerically in order to find the dependence of threshold voltage on the properties of such a system. A nematic material characterized by a negative sum of flexoelectric coefficients and by a small negative dielectric anisotropy was considered. The flow of ionic current was taken into account. The electric properties are described in terms of a weak electrolyte model. Finite surface anchoring strength was assumed. The director orientation, the electric potential and the ion concentrations were calculated as functions of the coordinate normal to the layer. It was found that the threshold for the deformation depends on the distributions of the ions, governed by the generation constant and by the properties of the electrodes. The effects observed may be interpreted as a consequence of the separation of the ions. When the electrodes have pronounced blocking character, a high and non-uniform electric field, created by the subelectrode ion space charges, causes drastic decrease of the threshold voltage, much below the value U _f valid for the insulating nematic. On the other hand, the electric field gradient arising in the bulk at moderate concentrations has a stabilizing effect and remarkably enhances the threshold above U _f. When the electrodes are conducting there are no significant space charges and the threshold voltage remains close to U _f. These results indicate that phenomena related to the charge transport should be taken into account in the analysis of the elastic deformations of ion-containing flexoelectric nematics.     

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.     

Rod-shaped dopants for flexoelectric nematic mixtures

We report the synthesis and liquid crystalline behaviour of two series of para-substituted terphenyls as dopants with a rigid rod-like shape, rather than a wedge-, pear- or banana-shape, for guest–host nematic mixtures with flexoelectric properties. One series of liquid crystalline dopants is of low-to-strongly negative dielectric anisotropy and the other is of low-to-strongly positive dielectric anisotropy. The usefulness of apolar and polar rod-like dopants as components of flexoelectric nematic mixtures of positive dielectric anisotropy for use in LCDs is investigated in general and the dependence of the flexoelectric properties of the doped nematic mixtures on the polarity of the dopants is studied in particular. The correlation between the concentration of the dopant and the magnitude of the flexoelastic ratio of several guest–host nematic mixtures is investigated.     

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.     

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.     

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.     

Gradient flexoelectric switching response in a nematic phenyl benzoate

We report on the inverse flexoelectric effects observed in a nematic liquid crystal with a small positive dielectric anisotropy subject to static and very low frequency (<1 Hz) a.c. fields. The Bobylev–Pikin flexobands appear at a temperature‐dependent d.c. threshold. Under square wave excitation, a new type of transient optical response occurs soon after each polarity reversal, and we ascribe it to the gradient flexoelectric distortion explicable on the basis of the presence of intrinsic double layers. This instability is characterized by a threshold voltage that decreases with temperature. Its maximum amplitude increases linearly with voltage close to threshold, and occurs after polarity reversal at a time τ_m that scales inversely as the voltage; τ_m decreases exponentially with frequency and temperature. After each polarity change, the ionic current following the charging current decreases almost exponentially to a non‐zero value; the residual current increases monotonically with the applied bias.     

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.     

Nematic nanocomposites with enhanced optical birefringence

The proper performance of electro-optical devices utilising liquid crystals (LCs) requires materials with high diffraction efficiency, i.e. with high optical/dielectric anisotropy, low threshold voltage and fast switching. One can achieve increase of dielectric anisotropy by using chemical synthesis or mixing LC materials. However, in most cases, this causes an increase in the threshold voltage and switching times. Therefore obtaining materials with high dielectric anisotropy and keeping threshold voltage and switching times low is a challenging task. We achieved promising results by making binary mixtures of a polar nematic LC 4'-hexyl-4-biphenylcarbonitrile (HBPCN) with low percentage (1–10% by weight) gold nanoparticles. We report that for the mixtures with 1% and 2% gold the dielectric anisotropy increases by 100% and the birefringence by about 50% of their values for pure nematic. We also report that the increase of the dielectric anisotropy in the mixtures only slightly affects threshold voltage and switching times. We propose that this increase is caused by cluster formation in the mixtures.     

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.     

Effect of an electric field on defects in a nematic liquid crystal with variable surface anchoring

We report experimental studies on defects in a nematic liquid crystal with negative dielectric anisotropy mounted in a cell with perfluoropolymer-coated surfaces. The sample exhibits a discontinuous anchoring transition from planar to homeotropic on cooling at zero or a small electric field, and above a cross-over voltage a continuous ‘inverse Freedericksz transition’, at which the director starts tilting in opposite directions at the two surfaces. Defects of strength ±1/2 are either annihilated or expelled when the director tilts. On the other hand, disclination lines of ±1 which end in partial point defects (boojums) at the surfaces in the planar alignment regime acquire point defects of strength ±1 at the midplane of the cell when the director tilts. At a low enough temperature, the homeotropic anchoring becomes strong, and an electric field above the Freedericksz threshold generates the usual umbilic defects, which follow the dynamic scaling laws found in earlier studies.     

Strong deformations induced by a DC electric field in homeotropic flexo-electric nematic layers

Elastic deformations of homeotropic nematic liquid crystal layers subjected to a DC electric field were studied numerically in order to determine their development under increasing voltage. Both signs of the dielectric anisotropy, Δ?, and of the sum of flexo-electric coefficients, e ₁₁ + e ₃₃, were considered, as were also low, moderate and high ion concentrations. The electrical properties of the layer are described in terms of a weak electrolyte model. Quasi-blocking electrode contacts and a finite surface anchoring strength were adopted. Director orientation, the electric potential and the ion concentrations were each calculated as a function of the coordinate normal to the layer. The director distributions turned out to depend not only on the sign of Δ? but also on the sign of e ₁₁ + e ₃₃, due to the difference in the mobility of anions and cations. The importance of ion content was also confirmed.     

Instabilities in electric fields of nematic liquid crytals with positive dielectric anisotropy: domains,loop domains and reorientation

Instabilities in electric fields are reported for p,p′-di-n-butyl azoxybenzene (DIBAB), a new room temperature nematic with a positive dielectric anisotropy. The threshold voltage is found to be almost independent of the frequency up to 100 kHz. However, unlike in nematics with negative dielectric anisotropy usually no normal domains are observed. The instabilities take the form of a reorientation, while loop domains are observed as a transiet effect. These loop domains indicate that the instability is not purely dielectric in origin.     

Ferroelectric Particles in Nematic Liquid Crystals with Soft Anchoring

A theoretical evaluation of the electric Freedericksz transition threshold and saturation field is proposed for a liquid crystals composite with ferroelectric particles. Existing models consider a strong anchoring of nematic molecules on the glass support of the cell, but in this paper a soft molecular anchoring of molecules on the glass support and also on the ferroelectric nanoparticle’s surface is assumed. Thus, a finite saturation field was obtained in agreement with real systems. Calculations are made for planar configuration of positive dielectric anisotropy liquid crystals. The results are compared with data obtained on similar systems from different publications and the differences are discussed.     

Instabilities across the isotropic conductivity point in a nematic phenyl benzoate under AC driving

We characterize the sequence of bifurcations generated by ac fields in a nematic layer held between unidirectionally rubbed ITO electrodes. The material, which possesses a negative dielectric anisotropy epsilona and an inversion temperature for electrical conductivity anisotropy sigmaa, exhibits a monostable tilted alignment near TIN, the isotropic-nematic point. On cooling, an anchoring transition to the homeotropic configuration occurs close to the underlying smectic phase. The field experiments are performed for (i) negative sigmaa and homeotropic alignment, and (ii) weakly positive sigmaa and nearly homeotropic alignment. Under ac driving, the Freedericksz transition is followed by bifurcation into various patterned states. Among them are the striped states that seem to belong to the dielectric regime and localized hybrid instabilities. Very significantly, the patterned instabilities are not excited by dc fields, indicating their possible gradient flexoelectric origin. The Carr-Helfrich mechanism-based theories that take account of flexoelectric terms can explain the observed electroconvective effects only in part.     

Dielectric and electro-optic behaviour of nematic-SWCNT nanocomposites under applied bias field

We have prepared the composites of a room temperature Nematic Liquid Crystals and Single-Walled Carbon Nanotubes. Effect of dispersion of nanotubes on various dielectric and electro-optic parameters on host nematic liquid crystals were investigated. The changes in dielectric and electro-optic parameters (viz: relative permittivity, dielectric anisotropy, switching threshold voltage and splay elastic constant) were observed for composite systems. The composites filled in the cells have been probed under applied bias electric field and it enhanced the nematic ordering of the liquid crystal molecules in the composites which results overall improvement of dielectric and electro-optic parameters of the prepared composites.