Liquid crystal optical response dynamics of the flexoelectric effect in a spatially inhomogeneous electric field

An investigation of the flexoelectric effect in a spatially inhomogeneous field revealed the two specific features of the liquid crystal optical response. First the optical response occurs at frequencies up to 500 Hz testifying to possible response time for flexoelectric effect-devices from 2 to 5 ms. Secondly in a photosensitive structure a flexoelectric effect application allows the implementation of an optical analogue of synchronous detection as well as the subtraction of images.     

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.     

Optical measurement of flexoelectric polarisation change in liquid crystals doped with bent-core molecules using hybrid-aligned structure

We proposed an optical measurement method for determination of flexoelectric polarisation change in liquid crystals (LCs), which can be induced in highly distorted LC geometries. A hybrid-aligned nematic LC (NLC) mode was introduced to evaluate the direction and magnitude of the flexoelectric polarisation. We measured the DC offset amounts for equivalent brightness levels between forward and reverse bias vertical electric fields to estimate the sign and magnitude of e_s?e_b of flexoelectric coefficients. Additionally, the optical incident angle (α_max) for the maximum effective birefringence was investigated to predict the depth distribution of the LC director affecting the magnitude of the flexoelectric polarisation. The relationship between the variations of the DC offset and α_max by the flexoelectric polarisation changes was examined using the NLC mixtures doped with three selected bent-core LCs.     

Electric field induced birefringence in a ferroelectric liquid crystal

We have measured the d.c. electric field dependence of the birefringence and conoscopic images for the smectic C* phase of a partially racemized ferroelectric chiral smectic liquid crystal CE-8. The experiments were performed using 50mu m thick homeotropic cells with lateral electrodes which created a d.c. electric field parallel to the smectic layers. The observed field induced birefringence shows a characteristic step-like behaviour which is due to the stepby-step unwinding of the helical structure in a sample with finite dimensions along the helical axis. In conoscopic observations we observe that these steps are associated with moving disclination lines that traverse the sample in the direction of the smectic layers. The observed electric field dependence of the birefringence is discussed in terms of the soliton-like unwinding of helical smectic structures and compared with the predictions of the Landau theory. A qualitatively good agreement is obtained.     

Rubbing-induced surface textures in nematic MBBA layers and their behaviour under applied d.c. or a.c. voltages

Surface irregularities (for example, rubbing-induced domains, and bumps) have been observed in MBBA nematic cells after special treatment of the electrodes using a conventional soap. Various techniques such as polarizing microscopy, the shadowgraph technique and computer processing of the images have been used. The behaviour of the rubbing-induced domains under a.c. or d.c. electric fields has been studied. A new flexoelectric effect has been observed leading to the dividision of the rubbing-induced domains. A simple model has been proposed (a modification of the Saupe model), which explains the structure and dividision of the rubbing-induced domains.     

Rubbing-induced surface textures in nematic MBBA layers and their behaviour under applied d.c. or a.c. voltages

Surface irregularities (for example, rubbing-induced domains, and bumps) have been observed in MBBA nematic cells after special treatment of the electrodes using a conventional soap. Various techniques such as polarizing microscopy, the shadowgraph technique and computer processing of the images have been used. The behaviour of the rubbing-induced domains under a.c. or d.c. electric fields has been studied. A new flexoelectric effect has been observed leading to the dividision of the rubbing-induced domains. A simple model has been proposed (a modification of the Saupe model), which explains the structure and dividision of the rubbing-induced domains.     

Deformation of isotropic and anisotropic liquid droplets dispersed in a cellulose liquid crystalline derivative

In this work we study the strain-induced deformation of both isotropic and anisotropic liquid droplets dispersed in a liquid crystalline cellulose matrix. We have produced two types of acetoxypropylcellulose (APC) solid films one with a droplet dispersion of the commercial liquid crystal E7 from Merck, and another with a droplet dispersion of silicone oil. To produce the solid films a solution of APC (60%wt) in dimethylacetamide (DMAc) with 15%wt of either the commercial nematic liquid crystal E7 or the silicone oil was prepared. After homogenization the phase separated solutions were submitted to a shear flow mechanical field and casted onto a Teflon plate. We performed mechanical uniaxial stress-strain tests in the free standing films recording continuously the strain and images of the deformed droplets. The mechanical tests were carried out using a mini stress-strain testing machine apparatus and an Olympus optical polarizing microscope with an attached CCD camera. The images obtained from the mechanical tests for each value of the imposed strain were then analyzed comparing the images of deformed droplets with those of the undeformed ones, extracting in this way the local strain field. The droplet deformation data obtained show, as expected, significant differences in the local strain field when stretching parallel and perpendicular to the initial shear direction. No significant differences were found in the local strain fields obtained from the silicone oil and the E7 droplets films. The local strain fields variation with the imposed strain are compared with the predictions of the theory developed for nematic elastomers by Warner and Terentjev (Liquid crystal elastomers. Clarendon Oxford Press, Oxford, 2003).     

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.     

Quantitative conoscopic imaging of cholesteric thin films

The periodic helical structure of an aligned polymerized cholesteric liquid crystal (ChLC) film gives rise to circular Bragg reflection within a narrow wavelength range, such that circularly polarized light of the same handedness as the helix is reflected, while counter circularly polarized light is transmitted. The ChLC is also strongly optically active with opposite rotatory power at either side of the circular Bragg zone. Both the selective reflection of circularly polarized light within the Bragg zone, as well as the optical activity of the cholesteric liquid crystal, are imaged with a new conoscopic technique based on a microscope equipped with the rotating polarizer-circular analyser MetriPol imaging system. The conoscopic images reveal the off-axis Bragg zone as an annulus at wavelengths below normal selective reflection. The annulus converges into a disk before disappearing at wavelengths above the region for normal selective reflection. The technique allows clear identification of the Bragg zone and the sign of the optical activity.     

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 flexoelectro-optic effect in cholesterics

The flexoelectro-optic effect in short-pitch cholesterics [1] is analysed in terms of applied electric field strengths and material parameters such as the two flexoelectric coefficients es and eb and the three elastic constants. Starting from the free energy density of the uniformly lying-helix (ULH) configuration, including the flexoelectric polarization term, the equation describing the field-induced tilt angle of the bulk optic axis is derived. It is convenient to introduce the flexoelectric 'anisotropy' Deltae as the difference between the splay and bend flexoelectric coefficients, hence defined by Deltae es eb. Our results then show that Deltae is the essential material parameter controlling the sign and magnitude of the electrically induced tilt. In the region of linear approximation, the tilt is proportional to Deltae and to the electric field E, and inversely proportional to the helical wave vector k, as well as the effective elastic constant (K11 K33). The individual values of the elastic constants K11, K22 and K33 do have an influence on the magnitude of the effect, but not on its linearity. The Deltae dependence conforms in the simplest way to the physical requirement that the flexoelectro-optic effect must be particularly pronounced in the case that es and eb are of opposite sign.     

Quantitative conoscopic imaging of cholesteric thin films

The periodic helical structure of an aligned polymerized cholesteric liquid crystal (ChLC) film gives rise to circular Bragg reflection within a narrow wavelength range, such that circularly polarized light of the same handedness as the helix is reflected, while counter circularly polarized light is transmitted. The ChLC is also strongly optically active with opposite rotatory power at either side of the circular Bragg zone. Both the selective reflection of circularly polarized light within the Bragg zone, as well as the optical activity of the cholesteric liquid crystal, are imaged with a new conoscopic technique based on a microscope equipped with the rotating polarizer-circular analyser MetriPol imaging system. The conoscopic images reveal the off-axis Bragg zone as an annulus at wavelengths below normal selective reflection. The annulus converges into a disk before disappearing at wavelengths above the region for normal selective reflection. The technique allows clear identification of the Bragg zone and the sign of the optical activity.     

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.     

Dielectric enhancement of chiral flexoelectro-optic switching

The chiral flexoelectro-optic effect is a candidate for realising sub-millisecond electro-optic technologies. Here, we discuss how flexoelectro-optic switching in cholesteric structures can be enhanced by using the dielectric coupling of the field to materials with negative dielectric anisotropy. An experiment is described that can measure the dielectric effect on flexoelectric switching, and the technique is applied to a chiral nematic mixture E7+3.5%R5011. We explore numerically the optimal liquid crystal parameters to best exploit the effect. An enhancement of up to 1° is demonstrated numerically.     

Helix unwinding process in the chiral smectic C phase of MHPOBC as observed by conoscopy

Conoscopic studies have been made on the helix unwinding process in the chiral smectic C phase of MHPOBC. The unwinding process is rather unique in the sense that abrupt changes of the biaxiality and apparent tilt angle are followed by further gradual changes before the complete helix unwinding. The process is qualitatively explained by simulating the conoscopic images using the 4 ×4 matrix method with consideration of model molecular distributions, by taking account of both the ferroelectric and dielectric coupling between molecules and a field. The transmittance loss due to selective reflection was also measured under the application of a stepwise d.c. field. The shift of the dip position due to the loss, toward a longer wavelength region, was observed at low field. In contrast, the emergence of a transmittance loss at the same wavelength as that of an unperturbed state was observed. This phenomenon is explained by the ferroelectric deformation of a helix with the pitch unchanged.     

A further experimental study of parallel surface-induced flexoelectric domains (PSIFED) (flexo-dielectric walls)

Parallel surface-induced flexoelectric domains (flexo-dielectric walls) have been further studied using new tools—a shadowgraph technique and computer processing of the most important images. It was unambiguously proved that the domains are a manifestation of the quadrupolar flexoelectric effect arising in a non-homogeneous electric field created by injection or by double electric layers. In the latter case they began to form at a d.c. voltage of 0.3-0.5 V. Furthermore, they arose near the injecting electrode and interfered with rubbing-induced domains at the junctions of every two adjacent domains. Flexo-dielectric walls have been obtained for the first time in the liquid crystal p-n-butyl-p-methoxyazoxybenzene and new experimental facts have been discovered. A new model for their creation is proposed.     

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.     

Flexoelectro-optic effect in a hybrid nematic liquid crystal cell

W e analyse the influence of charged impurities and flexoelectric polarization on the optical transmission of a hybrid aligned nematic liquid crystal cell. The theoretical results obtained within the framework of the Poisson-Boltzmann equation and Frank elastic theory are compared with the observed optical response [N. V. Madhusudana and G. Durand,J. Phys.Lett. 46, L-195 (1985)]. We show that impurities can be very important for the behaviour of the system in the low field regime where the flexoelectric effect is relevant, and we determine the flexoelectric coefficient, the anchoring strength, and the concentration of impurities in the sample previously studied by Madhusudana and Durand.     

Orientability of the Minor Director of Homeotropically Aligned Smectic‐A Elastomers in External Mechanical Fields

We present studies on bulk smectic‐A copolymer networks with end‐on attached homeotropically oriented mesogens that show spontaneous optical biaxiality at room temperature. Orthoscopic and conoscopic investigations under uniaxial extension in the layer planes give first evidence of the orientability of the minor director in mechanical fields yielding biaxial monodomains with 3‐d orientational long‐range order of all three principle axes. This is an important step towards the synthesis of permanently oriented biaxial monodomain elastomers for which highly interesting mechanical and optical properties are expected.