Electro-disclinic effect in tilted smectic phases of banana-shaped liquid crystal materials

We give the first evidence that the director tilt angle can be reduced by electric fields in the tilted smectic phase of banana-shaped molecules. In these phases the value of polarization is determined by the molecular packing and no electro-clinic effect is expected. Our studies show that high electric fields eventually induce a meta-stable phase with zero director tilt. The tilted phase slowly recovers at low fields. We propose that the field-induced quenching of the layer fluctuations is responsible for the observed effects.     

Light diffraction studies on director arrangement in the polymer‐pinned striped pattern obtained via the electric field‐induced Fréedericksz transition of nematics

We have observed an anomalous pattern forming phenomenon in which a striped pattern in a nematic liquid crystal appeared after removing an electric field following a Fréedericksz transition, and this pattern was preserved even in the equilibrium state in zero‐electric field. The nematic director arrangement in the striped pattern was investigated by light diffraction measurements. The stripes are proposed to consist of a periodic distortion of the nematic directors, specifically, tilted directors with the same absolute value of tilt angle but of opposite sign are alternately arrayed. The proposed model of the stripes is in good accord with the experimental results of light diffraction dependence on polarizing direction and light incidence angle.     

Graphene and liquid crystal mediated interactions

ABSTRACT

The two-dimensional graphene-honeycomb structure can interact with the liquid crystal’s (LC) benzene rings through π–π electron stacking. This LC–graphene interaction gives rise to a number of interesting physical and optical phenomena in the LC. In this paper, we present a combination of a review and original research of the exploration of novel themes of LC ordering at the nanoscale graphene surface and its macroscopic effects on the LC’s nematic and smectic phases. We show that monolayer graphene films impose planar alignment on the LC, creating pseudo-nematic domains (PNDs) at the surface of graphene. In a graphene-nematic suspension, these PNDs enhance the orientational order parameter, exhibiting a giant enhancement in the dielectric anisotropy of the LC. These anisotropic domains interact with the external electric field, resulting in a non-zero dielectric anisotropy in the isotropic phase as well. We also show that graphene flakes in an LC reduce the free ion concentration in the nematic media by an ion-trapping process. The reduction of mobile ions in the LC is found to have subsequent impacts on the LC’s rotational viscosity, allowing the nematic director to respond quicker on switching the electric field on and off. In a ferroelectric LC (smectic-C* phase), suspended graphene flakes enhance the spontaneous polarisation by improving the tilted smectic-C* ordering resulting from the π–π electron stacking. This effect accelerates the ferroelectric-switching phenomenon. Graphene can possess strain chirality due to a soft shear mode. This surface chirality of graphene can be transmitted into LC molecules exhibiting two types of chiral signatures in the LCs: an electroclinic effect (a polar tilt of the LC director perpendicular to, and linear in, an applied electric field) in the smectic-A phase, and a macroscopic helical twist of the LC director in the nematic phase. Finally, we show that a graphene-based LC cell can be fabricated without using any aligning layers and ITO electrodes. Graphene itself can be used as the electrodes as well as the aligning layers, obtaining an electro-optic effect of the LC inside the cell.     

Light-controlled reorientation of nematic liquid crystal driven by an electric field

The joint influence of optical and (quasi-)static electric fields on the orientation of liquid crystal gives rise to peculiar effects. In this article we report on the generation of transient domains in liquid crystals, which are an order of magnitude larger than the size of the optical field profile. The formation of such a domain is due to the fact that the initially present optical field reverses the pre-tilt, and the voltage that is then applied gives rise to an amplification of the tilt angle. The resulting reorientation of the director strongly depends on the starting conditions of the preliminary present optical field. We demonstrate different switching conditions, depending on the relation between the incident angle of the beam and the pre-tilt angle. The resulting refractive index profiles give rise to lensing effects.     

Classical and quantum mechanics of diatomic molecules in tilted fields

We investigate the classical and quantum mechanics of diatomic molecules in noncollinear (tilted) static electric and nonresonant linearly polarized laser fields. The classical diatomic in tilted fields is a nonintegrable system, and we study the phase space structure for physically relevant parameter regimes for the molecule KCl. While exhibiting low-energy (pendular) and high-energy (free-rotor) integrable limits, the rotor in tilted fields shows chaotic dynamics at intermediate energies, and the degree of classical chaos can be tuned by changing the tilt angle. We examine the quantum mechanics of rotors in tilted fields. Energy-level correlation diagrams are computed, and the presence of avoided crossings quantified by the study of nearest-neighbor spacing distributions as a function of energy and tilting angle. Finally, we examine the influence of classical periodic orbits on rotor wave functions. Many wave functions in the tilted field case are found to be highly nonseparable in spherical polar coordinates. Localization of wave functions in the vicinity of classical periodic orbits, both stable and unstable, is observed for many states.     

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.     

Numerical analysis of nematic liquid crystal alignment on asymmetric surface grating structures

The influence of an asymmetric periodic grooved cell surface on the 2D static director configuration of a nematic liquid crystal has been investigated. The minimum in the Frank-Oseen free energy was solved numerically with the Rapini-Papoular form of the surface anchoring energy at the nematic-grating interface. Results are presented for the variation of pretilt angle in the tilted bulk director field as a function of the surface groove depth, pitch and asymmetry and the bulk parameters. The simulations demonstrate the existence of two energetically degenerate high and low pretilted bulk alignment configurations. The pretilt values in these two regimes and also for the low tilt regime with finite surface anchoring are consistent with experimental results. An effective increase in the resolution of the model is obtained by using an irregular grid to describe the surface profile.     

Experimental characterization of hexatic smectic phases through electro-optic studies and dielectric relaxation spectroscopy

The electro-optic and complex dielectric behaviour of an antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)phenyl 4′-(n-butanoyloxyprop-1-oxy)biphenyl-4-carboxylate, having chiral SmC_A* and hexatic smectic phases, have been investigated. Complex dielectric permittivities were measured as a function of frequency, d.c. bias field and temperature. Spontaneous polarization was measured by the current reversal technique; tilt angle was measured under a polarizing microscope using a low frequency electric field. The electro-optic properties and dielectric behaviour of the material are compared with results obtained by DSC and polarizing optical microscopy. Dielectric relaxation processes in SmC_A* and hexatic smectic phases were determined. The dielectric strength at the SmC_A* to hexatic smectic phase transition is discussed in terms of coupling between the long range bond orientational order and smectic C director. It seems from the results of spontaneous polarization and dielectric relaxation spectroscopy that the material might possess an additional phase between the SmC_A* and hexatic smectic I* phases.     

Direct smectic A-smectic C*A phase transition

The anticlinic smectic CA phase belongs to the class of tilted smectic phases with an azimuthal angle alternating from one direction (theta=0) to the other (theta=pi) in successive layers. It occurs in general at lower temperature than the uniformly tilted smectic C phase, but may be obtained directly from the untilted smectic A phase. We use the chiral nCTBB9* series synthesized in this laboratory, in order to obtain a phase transition as close as possible to second order, as revealed by DSC. We measure the temperature behaviour of the birefringence and of the optical rotatory power across the transition in order to characterize the tilt angle. We finally study the optical response to a periodic electric field which excites separately the smectic C* and C*A soft modes. The main conclusion is that the only order parameter governing the critica Al behaviour of the phase transition is the tilt angle theta, as we get common divergence of both soft modes at the same temperature. This confirms previous high resolution calorimetric studies by Ema et al. that saw in MHPOBC an initial mean-field second order phase transition when the tilt appears, followed by sharp first order restructuring transitions between the tilted subphases.     

Direct smectic A-smectic C*A phase transition

The anticlinic smectic CA phase belongs to the class of tilted smectic phases with an azimuthal angle alternating from one direction (theta=0) to the other (theta=pi) in successive layers. It occurs in general at lower temperature than the uniformly tilted smectic C phase, but may be obtained directly from the untilted smectic A phase. We use the chiral nCTBB9* series synthesized in this laboratory, in order to obtain a phase transition as close as possible to second order, as revealed by DSC. We measure the temperature behaviour of the birefringence and of the optical rotatory power across the transition in order to characterize the tilt angle. We finally study the optical response to a periodic electric field which excites separately the smectic C* and C*A soft modes. The main conclusion is that the only order parameter governing the critica Al behaviour of the phase transition is the tilt angle theta, as we get common divergence of both soft modes at the same temperature. This confirms previous high resolution calorimetric studies by Ema et al. that saw in MHPOBC an initial mean-field second order phase transition when the tilt appears, followed by sharp first order restructuring transitions between the tilted subphases.     

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.     

Two distinct modulated layer structures of an asymmetric bent-shape smectic liquid crystal

We present chemical synthesis, polarising optical microscopy, electric current, and small-angle X-ray scattering measurements on a strongly anisotropic bent-shape liquid crystal material. We find that it has two layer-undulated ferroelectric phases, M1 and M2. In the higher temperature M2 phase the undulation amplitude and period increases on cooling, similar to other published materials. It can be identified with a tilted modulated phase. In the M1 phase the molecular plane is not tilted, and – in sharp contrast with all prior observations – the modulation amplitude and period decrease on cooling. These observations can be explained with a ‘leaning’ director structure, where the leaning angle is decreasing on cooling.     

Anchoring of a nematic liquid crystal on an anisotropic substrate

A nematic liquid crystal in contact with a flat solid substrate is studied by means of a mesoscopic Landau-de Gennes theory. It is assumed that the substrate is anisotropic, i.e. the directions x and y in the surface of the substrate are not equivalent, and the only symmetry is the mirror symmetry y ? - y. Assuming the simplest form of the bare surface free energy, where only the linear terms in the nematic order parameter are taken into account, we study anchoring directions induced by the interaction of the liquid crystal with the substrate. A phase diagram in terms of the surface fields and the temperature is obtained. Depending on the values of the surface fields we find four types of anchoring: the symmetric planar anchoring, with the director along x, the symmetric tilted anchoring, with the director in the xz plane, the antisymmetric planar anchoring, with the director along y, and the asymmetric tilted anchoring, with the director tilted with respect to all three axes.     

Horizontal chevron configurations in ferroelectric liquid crystal cells induced by high electric fields

Application of a high electric field to a S*_c ferroelectric liquid crystal cell may cause the formation of horizontal chevron configurations with the smectic layers tilted by the amount of the chevron angle (in the case of the present investigation equal to the director tilt angle) with respect to the normal to the rubbing direction of the cell substrates. The layer structure resembles that of the well-known vertical chevron configuration, but in the plane of the substrate instead of perpendicular to it, and is similar to that recently reported for the stripe-shaped texture. Between crossed polarizers, the two domain types appear to switch in opposite directions when an a.c. electric field is applied. The temperature dependence of the observation of horizontal chevron structures was investigated and an explanation is proposed analogous to that for the stripe texture model.     

First Examples of de Vries‐like Smectic A to Smectic C Phase Transitions in Ionic Liquid Crystals

In ionic liquid crystals, the orthogonal smectic A phase is the most common phase whereas the tilted smectic C phase is rather rare. We present a new study with five novel ionic liquid crystals exhibiting both a smectic A as well as the rare smectic C phase. Two of them have a phenylpyrimidine core whereas the other three are imidazolium azobenzenes. Their phase sequences and tilt angles were studied by polarizing microscopy and their temperature‐dependent layer spacing as well as their translational and orientational order parameters were studied by X‐ray diffraction. The X‐ray tilt angles derived from X‐ray studies of the layer contraction and the optically measured tilt angles of the five ionic liquid crystals were compared to obtain their de Vries character. Four of our five mesogens turned out to show de Vries‐like behavior with a layer shrinkage that is far less than that expected for conventional materials. These materials can thus be considered as the first de Vries‐type materials among ionic liquid crystals.     

Orientational instability of nematic liquid crystal in a homeotropic cell with boundary conditions controlled by an electric field

We study the orientational instability of the director in a homeotropic nematic liquid crystal (NLC) cell in a DC electric field. The electric field is applied along or perpendicular to a cell surface depending on whether anisotropy of dielectric permittivity of NLC is positive or negative. The easy axis on one of the cell polymer substrates is allowed to deviate in perpendicular to the substrate plane due to the influence of the NLC and the electric field. It was established that the orientational instability of the director can have a threshold as well as be thresholdless which depends on the character of the coupling of the easy axis with the electric field. The temporal behaviour of a director and the easy axis during transition to the stationary state after turning on electric field and returning to the initial homogeneous state after turning off the field was investigated. In the case of the negative anisotropy of the static permittivity, the comparison of experimental and calculated time dependences of the easy axis reorientation angle let us to estimate values of the mobile easy axis viscosity coefficient and coupling parameter describing the coupling between the easy axis and the electric field.     

A blue-phase liquid crystal lens array based on dual square ring-patterned electrodes

We propose a blue-phase liquid crystal (BPLC) lens array based on dual square ring-patterned electrodes. A high dielectric constant layer is used to smoothen out the horizontal electric field and reduce the operating voltage. By creating a potential difference between the dual square ring-patterned electrodes, gradient electric fields are generated and lens-like phase profile is obtained. Besides, the focal length of the BPLC lens is adjustable with voltage changes and all simulation results indicate that the BPLC lens array is polarisation-insensitive.     

Director configurations in nematic droplets with tilted surface anchoring

The polymer dispersed nematic liquid crystal (LC) with the tilted surface anchoring has been studied. The droplet orientational structures with two point surface defects – boojums and the surface ring defect – are formed within the films. The director tilt angle α = 40° ± 4° at the droplet interface and LC surface anchoring strength W_s ~ 10^–6 (J m^?2) have been estimated. The bipolar axes within the studied droplets of oblate ellipsoidal form can be randomly oriented are oriented randomly relatively to the ellipsoid axes as opposed to the droplets with homeotropic and tangential anchoring.     

A modified Langevin-Debye model for investigating the electro-optic behaviour of de Vries smectic liquid crystals

An external electric field applied across a planar-aligned cell in Smectic A* phase of de Vries smectic liquid crystal induces director redistribution over a cone, resulting in a substantial increase in the birefringence and the apparent optical tilt angle. Such an electro-optic response is modelled by Shen et al. [Y. Shen et al., Phys. Rev. E 88, 062504 (2013)], who modified their previous hollow cone with a diffuse cone model by introducing the molecular distribution function limited over a range of tilt angles, that lie in between θ_min and θ_max. The limits in these two tilt angles are assumed to be temperature independent though the tilt angle in between the two values can be temperature dependent. However, the high resolution measurements of birefringence and the layer thickness indicate the presence of temperature dependent diffuse cone angle in SmA* phase.. In the proposed model, we replace θ_min by θ_T, a temperature dependent fitting parameter and the change shows that a better fit of the experimental data to the model is obtained. We determine the temperature dependence of θ_min and show that this angle increases as SmA* to SmC* phase transition temperature is approached.     

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.