Large-scale periodic pattern in homeotropic liquid crystals induced by electric field

In-plane periodic modulation of the director field of an initially homeotropic liquid crystal layer with negative dielectric anisotropy is studied in external electric field with time varying amplitude envelope. Periodically turning a low frequency electric field on and off the cell, an in-plane periodic modulation of the director develops with a length scale that is orders of magnitude larger than the cell gap and can be as large as couple of centimetres. Doping the liquid crystal layer with low concentration of dichroic dye allows easy mapping of the director. We show that the periodic pattern is a periodic arrangement of +1 and ?1 point defects, so called ‘umbilics’. We argue that the in-plane direction of the director is governed by the local flow that accompanies the turn on and off of the electric field. The finite size and the shape of the cell, incompressibility constraint and the nature of the surface alignment material, all together with the flow, are ultimately responsible for the development of the observed periodic director modulation.     

Modelling of director equilibrium states in a nematic cell with relief surface

We study two-dimensional equilibrium configurations of nematic liquid crystal (NLC) director in a cell bounded by two parallel surfaces. One surface is planar and the other one is spatially modulated. The relief of the modulated surface is described by a smooth periodic sine-like function. The orientation of NLC director easy axis is assumed to be homeotropic at one cell surface and planar at the other one. The NLC director anchoring with cell surfaces is assumed to be strong. We consider the case where disclination lines occur in the bulk of NLC above the extrema of the modulated surface. These disclination lines run along the crests and troughs of the surface relief. If the orientation of director at both bounding surfaces is of the same type, then NLC director field is continuous. For both configurations mentioned above (with defects and without defects), we obtain analytical expressions for director distribution in the bulk of NLC in the approximation of planar director deformations. Equilibrium distances from disclination lines to the spatially modulated surface are calculated when the defects occur. The dependences of these equilibrium distances on the period and depth of surface relief and the cell thickness are investigated in detail.     

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.     

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.     

Tunable polarised fluorescence of quantum dot doped nematic liquid crystals

The concentration, excitation photon wavelength, and polarisation dependent fluorescence of quantum dot (QD)–liquid crystal (LC) mixtures has been studied at room temperature using high-resolution, steady-state fluorescence spectroscopy. The fluorescence of QD–LC mixture increases with increasing QD’s concentration but the spectral red shift of ~10 nm relative to the stock QD–Toluene solution remains independent of concentration. In vertical switching (VS) cells, an external electric field changes the LC alignment direction and enhances the apparent fluorescence intensity. The apparent fluorescence anisotropy compared to that at zero applied electric field monotonically increases up to ~27% at an applied electric field of 0.6 V/µm. These results are consistent with the formation of disc-like assemblages of QDs oriented on planes perpendicular to the director of the nematic liquid crystal (NLC). These findings have important utility in polarisation sensitive photonic devices.     

Analysis of electro-optical and dielectric parameters of TiO2 nanoparticles dispersed nematic liquid crystal

The present investigation is focused on to find out the role of TiO₂ nanoparticles (NPs) on altering the dielectric and electro-optical parameters of nematic liquid crystal (NLC). In addition to this, we also optimized the concentration of dopant (0.25 wt%) for a saturation value of permittivity and dielectric anisotropy in the doped system. Dielectric spectroscopy has been performed with the variation of frequency and temperature to investigate the various dielectric parameters, which demonstrate that the investigated NLC is of positive dielectric anisotropy; the observed result shows a decrement in the value of relative permittivity and dielectric anisotropy; however, the permittivity value increases for higher concentration of dopant but remains less than that of pure NLC. Electro-optical measurements have also been performed to compute the optical response of pure and dispersed NLC. It is found that optical response decreases for the NP-doped systems. This optimized concentration of NPs in NLC matrix can have various credential applications in the field of active matrix display and holography.     

Field quenching of director fluctuations in thin films of nematic liquid crystals

The continuum theory of director fluctuations in nematic liquid crystals is extended to take account of finite sample size which more accurately describes experiments on thin films. The effect of external fields on director fluctuations is considered for two cell geometries: (i) the field parallel to the director for materials of positive susceptibility anisotropy, and (ii) the field perpendicular to the director for materials of negative susceptibility anisotropy. In the latter geometry, quenching of fluctuations leads to induced biaxiality. Comparison with experimental results shows that even allowing for the finite size of the sample, there is still a significant disagreement between theory and experiment, especially from thin samples.     

Dielectric studies of the nematic mixture E7 on a hydroxypropylcellulose substrate

To study the influence of a polymeric substrate, hydroxypropylcellulose (HPC), on the dynamics of the nematic mixture E7, the real ( ε') and imaginary ( ε" ) parts of the complex dielectric permittivity of the unaligned composite system (polymeric substrate covered with liquid crystal) were measured as a function of frequency and temperature, and compared with those of unaligned pure E7. The temperature range was extended down to the supercooled region. Three superimposed processes were detected, related to different alignment states in relation to the electric field: (1) a main relaxation mechanism due to the hindered rotation of molecules about their short axis, corresponding to the case where the director is parallel to the electric field in an oriented sample, (2) a low frequency process attributed to molecular aggregates, and (3) a high frequency process due to the tumbling of molecules. Processes (2) and (3) correspond to the case when the director is perpendicular to the electric field in an oriented sample. In the composite system the main relaxation mechanism results in a faster process but the other two processes almost superimpose in the frequency window, the high frequency process being much more intense relative to pure E7. The enhancement of the high frequency process in HPC+ E7 can be interpreted as an increase in the number of dipoles whose director has a component aligned perpendicular to the electric field, due to surface effects. The temperature dependence of the main and high frequency relaxation mechanisms obeys the VFT law, which is a feature of glass-like systems.     

Droplet shape and reorientation fields in nematic droplet/polymer films

Polymer films containing droplets of nematic liquid crystal form an important class of new electro-optic light valves and displays. While previous work has shown that the nematic droplet size is an important factor in the electro-optic properties of these films, here we report that the droplet shape is equally important in determing the electro-optics of the film. Electron micrographs show that for films using polyvinyl alcohol as the polymeric binder the cavities formed by the polymer matrix are oblate in nature, and aligned with the minor axis perpendicular to the film plane. In oblate cavities the elastic-deformation free energy is minimized when the director field in the droplet is aligned along a major axis of the spheroid; the electric field performs work on the nematic in reorienting the nematic into a higher-energy state, equal to the elastic-free-energy difference between the two configurations. Calculations and experiment are used to estimate the elastic and electric field free-energy-density changes that occur upon reorientation of the nematic droplet. The general agreement between these two values is used to indicate that droplet shape anisotropy is a major factor in determining the electrooptic properties of these films.     

Droplet shape and reorientation fields in nematic droplet/polymer films

Polymer films containing droplets of nematic liquid crystal form an important class of new electro-optic light valves and displays. While previous work has shown that the nematic droplet size is an important factor in the electro-optic properties of these films, here we report that the droplet shape is equally important in determing the electro-optics of the film. Electron micrographs show that for films using polyvinyl alcohol as the polymeric binder the cavities formed by the polymer matrix are oblate in nature, and aligned with the minor axis perpendicular to the film plane. In oblate cavities the elastic-deformation free energy is minimized when the director field in the droplet is aligned along a major axis of the spheroid; the electric field performs work on the nematic in reorienting the nematic into a higher-energy state, equal to the elastic-free-energy difference between the two configurations. Calculations and experiment are used to estimate the elastic and electric field free-energy-density changes that occur upon reorientation of the nematic droplet. The general agreement between these two values is used to indicate that droplet shape anisotropy is a major factor in determining the electrooptic properties of these films.     

Novel alignment method for control of high pretilt angle by using a solvent dipping effect on polymer surfaces

A novel alignment method for control of high pretilt angle in nematic liquid crystals (NLC), using a solvent dipping effect on various alignment layers, was successfully investigated. The pretilt angle of a NLC is increased by dipping before rubbing treatment on three kinds of rubbed polyimide (PI) surfaces. The pretilt generated by the dipping after rubbing a PI surface with a short side chain is high compared with a PI surface with a long side chain. The pretilt generated by dipping before rubbing homeotropic layer of a positive type NLC (δε > 0) is lower than that of the negative type NLC (δε < 0). The generated NLC pretilt angle is attributed to the perpendicular component of the permittivity epsilon of the NLC.     

Two-dimensional director configurations in a nematic-filled cylindrical capillary with the hybrid director alignment on its surface

ABSTRACT

We analytically calculate two-dimensional equilibrium configurations of the nematic liquid crystal (NLC) director in a right cylindrical capillary with the hybrid director alignment on its inner surface. A part of this surface is treated to impose the strong homeotropic alignment, while on the remaining part the strong circular alignment, perpendicular to the capillary axis, is imposed. Owing to the system homogeneity along the capillary axis, a disclination line emerges in the bulk of the NLC, which runs parallel to the axis. It is shown that there exist either one or two equilibrium locations of the disclination line depending on the ratio of capillary surface parts with homeotropic and circular alignment. The technique that allows to obtain an analytical expression for the system free energy as a function of a disclination line location is presented. It considerably simplifies calculations and can be used while solving a variety of problems in which a defect location is sought.     

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.     

Slow relaxation processes in nematic liquid crystals at weak surface anchoring

We present new results of experimental investigations of azimuthal director reorientation dynamics for a nematic liquid crystal on solid substrates. Two types of substrate with weak anchoring were studied: glass/polystyrene and glass/UV-activated dye. Slow and fast relaxation processes were observed in both cases under the action of a strong 'in-plane' electric field. The slow surface reorientation and memory effects were controlled by two parameters: the electric voltage and the excitation time. It was established that the increase of the excitation time results in a slowing of the relaxation of the system to the initial state after turning off the electric field. A phenomenological model of a gliding of easy axes is proposed to explain the slow relaxation process.     

Orientational Behaviour of the Nematic Director upon Macroscopic Rotation at the Magic Angle

The ¹⁹F N.M.R. spectrum of 1,2,2,2-tetrachloro-l,l-difluoroethane has been studied in the nematic liquid crystal ZLI1167 (Merck) upon rotation at the magic angle. The director of the liquid crystal is oriented perpendicular to the spinning axis when the angle between the rotation axis and the magnetic field is less than the magic angle and parallel when this angle is more than the magic angle. It is shown that exactly at the magic angle the spectrum corresponds to a frequency modulated powder pattern. This powder pattern leads to an understanding of the orientational behaviour of the director when a nematic is spun at the magic angle.     

The effect of replacing a benzene ring with a saturated six-membered ring on the mesomorphic properties of 4,4′-disubstituted diphenyldiacetylenes

We present new results of experimental investigations of azimuthal director reorientation dynamics for a nematic liquid crystal on solid substrates. Two types of substrate with weak anchoring were studied: glass/polystyrene and glass/UV‐activated dye. Slow and fast relaxation processes were observed in both cases under the action of a strong ‘in‐plane’ electric field. The slow surface reorientation and memory effects were controlled by two parameters: the electric voltage and the excitation time. It was established that the increase of the excitation time results in a slowing of the relaxation of the system to the initial state after turning off the electric field. A phenomenological model of a gliding of easy axes is proposed to explain the slow relaxation process.     

Preparation and magnetic properties of Cu-ferrite nanorods and nanowires

An aqueous solution method has been developed for preparing Cu-ferrite nanorods (NRs) array and nanowires (NWs) on Cu substrate. The Cu-ferrite NRs exhibit a clear uniaxial anisotropy with the easy axis along rods. The decrease of the reduced remanence from 0.24 in the parallel magnetic field to almost zero in the perpendicular field shows a strong effect of the demagnetizing field perpendicular to the rod axis. The weaker uniaxial anisotropy makes NWs the lower saturation magnetization.     

Convective director structures upon continuous rotation of nematic side group polymers

We present the first study of convective director structures in nematic side group polymers. A thin liquid crystal cell (10-500 μm) was continuously rotated about an axis perpendicular to the field of a 7T NMR magnet. The director behaviour was followed by deuteron NMR as well as by polarization microscopy. While by optical studies the development of periodic director structures can be directly monitored, the analysis of the NMR lineshape gives detailed information about the director distribution in these structures. The development of the structures depends sensitively on the rotation frequency and is discussed in terms of non-linear amplification of long wavelength director fluctuations due to the coupling between director rotation and viscous flow of the nematic.     

Generalised technique for calculation of plane director profiles in bounded nematic liquid crystals

We propose an improved conformal mapping technique for analytical calculation of two-dimensional profiles of the nematic liquid crystal (NLC) director in a cell with a simply connected cross-sectional region. We consider the case of the strong anchoring and the piecewise constant director pretilt on the piecewise smooth curve which bounds the region. Obtained expressions for the director profile explicitly depend on the conformal mapping which maps the region onto the upper half plane of a complex plane. An advantage of our method in comparison with the standard conformal mapping technique is that it does not require the knowledge of the inverse mapping and the calculation of the integral in the Poisson formula. Proposed technique allows to take into account topological defects in the bulk of the NLC on the symmetry axis of the region. As an example of how the method can be used, we find an analytical expression for the director profile in a horizontal cylindrical groove partly filled with the NLC. We consider the case where a disclination line parallel to the axis of the groove occurs in the bulk of the NLC. The equilibrium position of the disclination line is found.