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.     

A continuum description for cholesteric and nematic twist-bend phases based on symmetry considerations

ABSTRACT

The recently discovered twist-bend nematic phase, N_tb, is a non-uniform equilibrium nematic phase that presents a spontaneous bend with a precession of the nematic director, n, on a conical helix with a tilt angle θ and helical pitch P. The stability of the N_tb phase has been recently demonstrated from the elastic point of view by extending the Frank elastic energy density of the nematic phase to include the symmetry element of the helical axis, t. In the present article, we investigate the influence of an external bulk field (magnetic or electric) on the N_tb phase. Using symmetry arguments we derive the expression for the flexoelectric polarisation in twist-bend nematic phases. We show that, besides the standard contribution related to the spatial variation of the nematic director, two new contributions connected with the existence of the helical axis appear. In the ground state, where the nematic deformation is a pure heliconical deformation, the new contribution vanishes identically, and the total flexoelectric polarisation is perpendicular to the nematic director. Furthermore, as an example, we study the role of an external magnetic field applied parallel to the helical axis for a material with positive magnetic susceptibility anisotropy. We show that the field modifies the range of values of the coupling parameter between the director and the helical axis, thus shifting the interval of values for which this coupling results in the N_tb phase.     

Director distribution in field-induced undulated structures of cholesteric liquid crystals

Structures with a periodic in-plane liquid crystal director field modulation induced by an electric field are studied in cholesteric liquid crystals (CLCs). A phenomenon of the electric-field-induced instability in a planarly aligned cholesteric cell is used to create these undulated structures. The initial field-off state is planarly aligned with the cholesteric helix axis oriented perpendicular to the cell substrates. The interaction of the CLC with an electric field results in modulation of the refractive index, which is visualised as stripe domains oriented either along or perpendicular to the rubbing direction at cell alignment surfaces. The threshold electric field for the undulation appearance and a period of stripes are measured experimentally for three Grandjean zones (ratio d/p ~ 0.5, 1.0, and 1.5, where d is a cell thickness and p is the natural cholesteric pitch). For the zone with d/p ~ 1.0 using numerical simulations, we describe in detail the director distribution at an applied electric field. It is found that the in-plane undulated structure is characterised by a conical director rotation on moving along the alignment direction. The conical axis is tilted with respect to the alignment axis. The sign of the tilt angle depends on the handedness of CLC.     

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.     

Experimental determination of the flexoelectric coefficients of some nematic liquid crystals

Abstract

We report measurements of the temperature variation of the flexoelectric coefficient (e ₁–e ₃) of a number of nematic liquid crystals like phenylcyclohexanes, cyanobiphenyls, etc. We have also measured (e ₁+e ₃) of a few systems using appropriate methods of applying an electric field gradient to the sample. In most of the systems, (e ₁–e ₃)/k, where k is a curvature elastic constant, is found to be positive and independent of temperature, as expected. However, in 4-heptyl-1-(4-cyanocyclohexyl)cyclohexane and a few other compounds with relatively flexible parts, |(e ₁–e ₃)/k| increases with temperature. We discuss the possible molecular origin of the sign and temperature dependence of the flexoelectric coefficients of the systems studied.     

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.     

Improvement of the crystal rotation method to measure the flexoelectric difference (e1–e3) in achiral materials using AC electric fields

We show that the crystal rotation method for measuring the difference between splay and bend flexoelectric coefficients (e₁–e₃) [Outram and Elston, Liq. Cryst. 39, 149 (2012)] can be improved by using AC instead of DC fields. The field frequency is small (~0.05 Hz), yet sufficient to get rid of the difficulties connected with the migration of charge carriers. The method is sensitive enough so as to use fields with amplitudes as small as 1 V/mm. This has the advantage of avoiding the consideration of the interaction due to the dielectric anisotropy, and greatly simplifies the analysis of data. The results are extracted from a simple fitting scheme, which involves two parameters. In particular (e₁–e₃) is obtained from a scale factor in a one-parameter fit. Measurements of the temperature dependence of (e₁–e₃) are presented for two classical nematic materials.     

Nematic twist-bend phase under external constraints

ABSTRACT

The recently discovered twist-bend nematic phase, N_TB, has short-pitched heliconical structure with doubly degenerate handedness. In contrast to the classic nematic, in the N_TB phase the director is spontaneously distorted, resulting in unusual elastic properties. The response of the N_TB phase to external stimuli, like chiral doping or applied fields might provide further information about its structure and can find utilisation in practical applications. Here, the N_TB behaviour is theoretically investigated under chiral doping and strong electric fields. We show that the chiral doping removes the N_TB degeneration and modifies the conical tilt angle, leaving the pitch unchanged. Thus, the N_TB helical twisting power is very high and strongly non-linear. Under electric field, we consider separately the ferroelectric, flexoelectric and dielectric couplings. We show that the experiments reported so far disagree with the ferroelectric behaviour, indicating that the N_TB phase is not spontaneously polarised. On the contrary, the observed polar effects fit well with the flexoelectric coupling, confirming the degenerated heliconical structure of the phase. Under very strong fields, we predict a second-order twist-bend nematic – nematic phase transition due to the dielectric torque on the director.     

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.     

Volume-stabilized ULH structure for the flexoelectro-optic effect and the phase-shift effect in cholesterics

Flexoelectric coupling gives rise to a linear electro-optic response in cholesterics (flexoelectrooptic effect) with a uniformly lying helix (ULH) structure and this electro-optic effect is strongly reliant on the homogeneity and quality of the texture. The ULH structure, unfortunately, is complicated in itself and may be perturbed by factors such as dielectric coupling, surface/liquid crystal interactions and phase transitions, and often there is a tendency for relaxation into the Grandjean texture (standing helix structure) with time. Hence, in order to exploit the flexoelectro-optic effect in cholesterics any instability of the ULH structure must be ruled out. We have overcome these problems by incorporating a polymer network by means of photopolymerization of a reactive monomer added to the cholesteric. The volume stabilized ULH structure still exhibits the flexoelectro-optic effect, it is stable and it is also retained after heating to the isotropic phase and going back to the cholesteric phase. In addition to the flexoelectro-optic mode, the ULH structure is of interest in an electro-optic mode characterized by a pure phase-shift with no change in amplitude (transmittance). This mode, which has obvious applications in spatial light modulators, optical computing devices and electrically controlled kinoforms and phase holograms working without polarizers, is also briefly discussed.     

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.     

Achiral Dichroic Dyes-mediated Circularly Polarized Emission Regulated by Orientational Order Parameter through Cholesteric Liquid Crystals

It is noteworthy that cholesteric liquid crystal (CLC) platforms have been witnessed in high-performance circularly polarized luminescence (CPL) behaviors through the highly organized chiral co-assembled arrangement of achiral dyes. However, most CPL-active design strategies are closely relative to the helix co-assembly structure of CLC rather than achiral dyes. Herein, we developed an intriguing regulation strategy for CPL-active CLC materials. They were regulated using the orientational order parameter (S_F) of achiral dichroic dyes as an incisive probe for the order arrangement degree of achiral dyes in CLC media. The I-shaped phenothiazine derivative PHECN dye (S_F=0.30) emitted a strong CPL signal (|g_lum|=0.47). In contrast, the T-shaped derivative (PHEBen) dye (S_F=0.09) showed a weak circular polarization level (|g_lum|=0.07) at similar CLC textures. Most interestingly, this kind of dichroic PHECN dye with a higher S_F could greatly improve the contrast ratio of CPL (Δg_lum=0.47) and emission intensity (ΔFL=46.0 %) at direct-current electric field compared with the T-shaped PHEBen (Δg_lum=0.07 and ΔFL=1.0 %) in CLC. This work demonstrates that an induced CPL emission can be mediated using achiral dichroic dye, which will open a new avenue for developing excellent CPL-active display materials.     

Chiral periodic mesoporous organosilica in a smectic-A liquid crystal: source of the electrooptic response

Chiral periodic mesoporous organosilica (PMO) materials have been shown to deracemise a configurationally achiral, but conformationally racemic liquid crystal in which the PMO is embedded. In particular, application of an electric field E in the liquid crystal’s smectic-A phase results in a rotation of the liquid-crystal director by an angle proportional to E, which is detected optically – this is the so-called ‘electroclinic’ effect. Here we present results from electroclinic measurements as a function of frequency and temperature, which allow us to distinguish the component of optical signal that arises from liquid-crystal chirality induced within the PMO’s chiral pores from that induced just outside the silica colloids. Our central result is that the overwhelming source of our electrooptic signal emanates from outside the PMO, and that the contribution from the liquid crystal embedded in the chiral pores is much smaller and below the noise level.     

Relationship between lens properties and director orientation in a liquid crystal lens

Lenses with a homogeneously aligned liquid crystal having a Fresnel structure have been prepared by using a nematic with a positive dielectric anisotropy. Their focal length can be varied continuously from the value f_e for an extraordinary ray to f _o for an ordinary ray by applying an electric field across the lens cell. The effective refractive index of the lens where the director is aligned perpendicular to the grooves of the Fresnel structure becomes smaller than when the director is aligned parallel to the grooves. Then the liquid crystal lens has a characteristic aberration which could not be observed in a conventional glass lens; that is, the focal length of the lens becomes different according to the incidence of rays on the different parts of the lens. The properties of the liquid crystal lens can be improved by making the director orientation axially symmetric, in the form of a concentric circle, but the polarization component rotated 90° from the incident extraordinary ray appears when the voltage is applied across the lens cell. This phenomenon is discussed in relation to the optical properties and the director orientation in a liquid crystal prism cell.     

Polar electro-optic switching in droplets of an achiral nematic liquid crystal

A polar electro-optic response is observed in droplets of an achiral nematic liquid crystal in coexistence with the isotropic phase. Between crossed polarizers each pancake-shaped droplet shows extinction brushes in the form of a centred cross aligned with the polarizer axes. An applied electric field E induces a rotation of the crosses about the field direction, with about half the droplets switching clockwise and the other half anticlockwise. The sense of rotation in each droplet changes when E is reversed. We propose that a twisted bipolar director structure is stabilized in the droplets by a relatively large splay elastic constant and tangential boundary conditions. The molecules twist along the diameter of the droplets, perpendicular to the applied field, which results in a linear rotation of the director by the inverse flexoelectric effect. Since the molecules are achiral, the handedness of the twist, and hence the sense of the switching, in any droplet is arbitrary.     

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.     

Polar electro-optic switching in droplets of an achiral nematic liquid crystal

A polar electro-optic response is observed in droplets of an achiral nematic liquid crystal in coexistence with the isotropic phase. Between crossed polarizers each pancake-shaped droplet shows extinction brushes in the form of a centred cross aligned with the polarizer axes. An applied electric field E induces a rotation of the crosses about the field direction, with about half the droplets switching clockwise and the other half anticlockwise. The sense of rotation in each droplet changes when E is reversed. We propose that a twisted bipolar director structure is stabilized in the droplets by a relatively large splay elastic constant and tangential boundary conditions. The molecules twist along the diameter of the droplets, perpendicular to the applied field, which results in a linear rotation of the director by the inverse flexoelectric effect. Since the molecules are achiral, the handedness of the twist, and hence the sense of the switching, in any droplet is arbitrary.     

Flexoelectric response at defect sites in nematic inversion walls

Electric field experiments have been carried out on +1 and ?1 defects formed in alignment inversion walls, in a planarly aligned nematic phenyl benzoate. The results show that the defects are non‐singular in the core and exhibit a flexoelectric response to an applied d.c. or low frequency a.c. field. When the c‐director flux lines are circular, as in a +1 defect in a wall parallel to the easy axis, flexoelectro‐optic switching characterized by an azimuthal angle variation is observed. When the c‐director flux is radial, the response is seemingly through polar angle variations involving no rotation of the extinction brushes due to crossed polarizers. This conclusion follows from the field‐induced structural distortions observed at a ?1 defect having a combination of radial and tangential c‐director fields.     

Second-harmonic generation and the influence of flexoelectricity in the nematic phases of bent-core oxadiazoles

Second-harmonic generation (SHG) in the nematic phase of bent-core oxadiazole-based liquid crystals (LCs) was studied and compared to that for the rod-like compound 4-cyano-4?-n-octylbiphenyl (8CB). Weak, isotropically scattered second-harmonic (SH) light was observed for all materials, consistent with SHG by nematic director fluctuations. The SH intensity produced by the bent-core materials was found to be up to ~ 3.4 times that of 8CB. We discuss this result in terms of the dependence of SH intensity on temperature, elastic constants and flexoelectric coefficients. We have calculated the latter by using a molecular field approach with atomistic modelling, thus demonstrating how molecular parameters contribute to the flexoelectric coefficients and illustrating the potential of this method for predicting the flexoelectric behaviour of bent-core LCs. We show that the increased SH signal in the bent-core compounds is partly due to their nematic phases being at a much higher temperature, and also potentially due to them having greater flexoelectric coefficients, up to ~1.5 times those of 8CB. These estimates are consistent with reports of increased flexoelectric coefficients in bent-core compounds in comparison to rod-like compounds.     

Deformed helix ferroelectric liquid crystal display: A new electrooptic mode in ferroelectric chiral smectic C liquid crystals

Abstract

A new electrooptic mode of operation of ferroelectric chiral smectic C liquid crystal displays (LCDs) is proposed and demonstrated. The effect, which is called the deformed helical ferroelectric (DHF) effect, is based on the deformation of the helical structure by weak electric fields. In the unbiased device the smectic layers are arranged in the bookshelf geometry with the helix axis parallel to the electrodes [1]. Systems with a very small pitch (<1 μm) and a large tilt angle are especially well suited for this mode. The key characteristics of DHF-LCDs are: (a) low driving fields (1 V_p-pμm^?1 for maximum contrast); (b) grey scale which is approximately linear with the applied electric field; (c) easy alignment even for thick cells using standard wall-aligning methods; and (d) response times at room temperature of 300 μs.