Relaxation of the director field in the form of a traveling wave in twisted nematic cells

The orientational relaxation of the director field toward its equilibrium orientation in the form of a traveling wave is investigated. It is shown that the nonlinear relaxation can occur in the form of a traveling wave in a twisted nematic cell under specific conditions for the external electric field and material parameters characterizing the nematic liquid crystal. The calculations of the relaxation processes in the form of traveling waves have demonstrated that these nonlinear processes in the twisted nematic cell proceed more easily when the initial perturbation of the director is induced in the vicinity of one of the bounding cell surfaces.     

Optical response from dual-frequency hybrid-aligned nematic liquid crystal cells

Dual-frequency hybrid-aligned nematic liquid crystal cells and the influence of the parameters of a control electric field on their optical response are studied. It is found that the harmonic oscillations of the optical transmission in such cells are observed in the interval between low frequency-to-high frequency voltage switchings unlike in conventional twisted nematic cells. A V-shaped bistable optical response is obtained by successively applying sinusoidal electric fields with frequencies of 1 and 30 kHz to a twisted nematic cell. For a liquid crystal layer 8 ??m thick and an applied voltage of 50 V, the response time is 10 ms. In a hybrid-aligned twisted-nematic cell with a large initial tilt angle of the director (about 70°), the V-shaped optical response is observed when the inclined homeotropic state is switched to the twisted state by applying a 30-kHz field. The initial structure of the layer recovers as a result of natural elastic relaxation, and the response time increases roughly fourfold.     

Inverse regime of ionic modification of surface anchoring in nematic droplets

It was found that the effect of the ionic modification of anchoring in liquid-crystal droplets can be implemented in the inverse regime. Droplets of 4-n-pentyl-4′-cyanobiphenyl nematic doped with ionic cetyltrimethylammonium bromide surfactant were dispersed in polyvinyl alcohol and investigated. In the initial state, nematic droplets have a radial structure with homogeneous homeotropic anchoring typical of the surfactant used. In the presence of a dc electric field, the boundary conditions become tangential in the surface area left by the cations. That results in the transformation of an orientational structure following by various scenarios. For the new states of nematic droplets, the distribution of the director field was analyzed and the corresponding textural patterns were numerically calculated.     

Dielectric relaxation of <Emphasis Type="Italic">trans</Emphasis>-4-propyl-(4-cyanophenyl)-cyclohexane liquid crystals

The frequency dependences of the permittivity of a trans-4-propyl-(4-cyanophenyl)-cyclohexane (3PCH) liquid crystal in the nematic phase are measured in the frequency range 1–2000 MHz for different orientations of the director of liquid-crystal molecules with respect to the polarization of an ac electric field. The temperature dependences of the dielectric and optical characteristics are compared in the range of the transition from the nematic phase to the isotropic liquid phase. The dielectric spectra are approximated numerically, and the times of dipole relaxation upon rotation of the molecules about the short and long axes are determined. It is demonstrated that intramolecular motions make a significant contribution to the relaxation. The activation enthalpies are calculated.     

Critical exponents for Fréedericskz transition in nematics between concentric cylinders

The equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals is determined for strong homeotropic anchoring at the surfaces. The anchoring condition is such that the nematic director is perpendicular to the cylinder axes and a radial nonuniform electric field is applied to investigate a Fréedericksz transition. The distortions induced by the field remain in the plane perpendicular to the cylinder axes, and a threshold field is analytically determined indicating a transition from a pure splay to a splay-bend conformation of the director. It is shown that this transition can be induced by the thickness of the region between the two cylinders, and can be detected even in the absence of an external field. If the maximum value of the tilt angle is assumed as an order parameter, its behavior near to the transition can be used to obtain the critical exponent, which is the same as the one obtained in the mean field approximation. These results are indications that nontrivial consequences may occur when complex fluids are subject to non-planar geometries.     

The influence of external fields on the orientational relaxation of nematic liquid crystals

The relaxation of the director field n, the velocity field v, and the shear and normal components of the stress tensor is theoretically investigated by numerically solving the system of nonlinear hydrodynamic equations. These equations describe the director reorientation with allowance made for the field of velocities induced by the rotation of the director field. The relaxation time and the influence of the velocity field on the relaxation processes are analyzed for a number of hydrodynamic regimes, which arise in a liquid-crystal cell under the effect of external electric and magnetic fields.     

Phase-shift error as a result of molecular alignment distortions in a liquid-crystal point-diffraction interferometer

We report the observation of nematic director distortions around the diffracting element of a liquid-crystal point-diffraction interferometer. The observed director field distortions are similar to those reported in the literature for other liquid-crystal guest-host systems. We show how the alignment distortion changes as a function of the voltage applied to the liquid-crystal cell, leading to an observed phase-shift error. Tailoring of surface anchoring conditions and judicious choice of phase-shift algorithm can improve device accuracy.     

Formation of a temperature gradient in a hybrid-oriented liquid-crystal cell in response to shear stress

The orientational relaxation of the director, velocity, and temperature fields in a hybrid-oriented liquid-crystal cell in response to a shear stress applied to one of the cell surfaces has been investigated. The cases of the complete and partial thermal insulation of one of the cell surfaces have been considered under the condition where a constant temperature is maintained at the other cell surface. The relaxation time and the influence of the velocity field on the reorientation of the director field have been analyzed for a number of hydrodynamic regimes arising in the liquid-crystal cell under the effect of the shear stress and the temperature gradient formed over the cross section of the liquid-crystal cell.     

Reorientation effect on the current-voltage characteristics of a nematic cell

Possible mechanisms explaining the character of the relation I=I(V) for a nematic cell subjected to a large electric field are discussed, taking into account the reorientation effect of the nematic director induced by the external electric field. The analysis is performed in the quasi-static regime where the nematic orientation follows the time variation of the external field without delay. The time variation of the equivalent capacitance of the cell is equivalent to a pure resistance, and is responsible for a current peak when the applied voltage overcomes the threshold voltage for the transition of Fréedericksz.     

Micro- and nanostructures for the spatially periodic orientation of liquid crystals obtained by focused ion beam milling

Micro- and nanostructured surfaces creating spatially periodic boundary conditions of the alignment of nematic liquid crystals in two mutually orthogonal directions perpendicular and parallel to the surface are obtained by focused ion beam milling. It is shown that ion milling provides an easy axis along the normal and sufficiently strong anchoring energy. The value of this energy can noticeably exceed the energy of the planar anchoring of liquid crystals with typical orienting surfaces on the basis of polymer films. Using the numerical simulation, the anchoring energy values necessary for an implementation of a deep modulation of the director field with a spatial period of hundreds of nanometers are determined, which is important for creation of photonic liquid-crystal systems.     

Distribution function of relaxation times for a 4-<Emphasis Type="Italic">n</Emphasis>-pentyl-4′-cyanobiphenyl liquid crystal

The distribution function of relaxation times is reconstructed from the dielectric loss spectrum measured over a wide range of frequencies for a 4-n-pentyl-4′-cyanobiphenyl (5CB) liquid crystal. It is demonstrated that the distribution function for the isotropic and nematic phases is asymmetric in shape. Comparison shows that the reconstructed distribution function is in qualitative agreement with similar functions that are analytically derived from the Cole-Davidson and Havriliak-Negami empirical equations. The specific features observed in the behavior of the distribution function with a variation in the angle between the direction of polarization of a microwave electric field and the director of the liquid-crystal molecules are analyzed. A complex dependence of the permittivity for the liquid crystal in the range of ultrahigh frequencies is explained in terms of additional relaxation mechanisms associated with different motions of molecular fragments of alkyl chains.     

Smectic <Emphasis Type="Italic">C</Emphasis>* in an external electric field

A variational approach is used to derive equations describing orientation of molecules in a thin freely suspended ferroelectric smectic C* film in a constant electric field applied along the film surface. The equilibrium configuration of director orientations is determined from the solution of the Euler-Lagrange equation. It is shown that the external field reorients molecules in the liquid-crystal film in a nonthreshold manner.     

Behaviour of nematic liquid crystals doped with ferroelectric nanoparticles in the presence of an electric field

A planar nematic liquid crystal cell (NLC) doped with spherical ferroelectric nanoparticles is considered. Polarisation of the nanoparticles are assumed to be along the NLC molecules parallel and antiparallel to the director with equal probability. The NLC molecules anchoring to the cell walls are considered to be strong, while soft anchoring at the nanoparticles surface is supposed. Behaviour of the NLC molecules and nanoparticles in the presence of a perpendicular electric field to the NLC cell is theoretically investigated. The electric field of the nanoparticles is taken into account in the calculations. Freedericksz transition (FT) threshold field in the presence of nanoparticles is found. Then, the director and particles reorientations for the electric fields larger than the threshold field are studied. Measuring the onset of the nanoparticles reorientation is proposed as a new method for the FT threshold measurement.     

Study of the Effect of Pulsed-Periodic Electric Field and Linearly Polarized Laser Radiation on the Properties of Liquid-Crystal Waveguide

Integrated-optical waveguides with a nematic liquid-crystal 4-cyano-4’-pentylbiphenyl (5CB) waveguiding layer have been investigated for different polarizations of incident laser radiation and under a pulsed-periodic electric field. A dependence of the damping coefficient of waveguide modes and the sizes of quasi-steady-state irregularities of nematic liquid-crystal layer on the linear polarization of laser radiation and the strength of pulsed-periodic field has been found experimentally. The correlation length is estimated for waveguiding layer irregularities. The waveguide scattering method has provided a resolution in correlation length exceeding the classical resolution limit by approximately an order of magnitude. The observed decrease in the damping coefficient of waveguide modes and irregularity sizes under external field is explained by the decrease in the correlation length of director fluctuations.     

Dielectric properties of liquid crystals in polycapillary matrices

This paper reports on the results of investigations into the dielectric properties of liquid crystals embedded in polycapillary matrices and describes a technique for their measurement. It has been revealed that the chemical structure of the rigid core and the length of mobile alkyl groups of liquid-crystal molecules of the alkylcyanobiphenyl group substantially affect the equilibrium configuration of the liquid-crystal director in capillaries. The reorientation of liquid-crystal molecules embedded in capillaries in the nematic phase under the influence of an external magnetic field has been investigated.     

First-order Fréedericksz transition at the threshold point for weak anchoring nematic liquid crystal cell under external electric and magnetic fields

Based on the modified formula of Rapini-Papoular, the equilibrium equation and boundary condition of the director have been obtained and the behaviour of the Fréedericksz transition at the threshold point has been studied for weak-anchoring nematic liquid crystal cells under external electric and magnetic fields with the methods of analytical derivation and numerical calculation. The results show that, except for the usual second-order transition, the first-order Fréedericksz transition can also be induced by a suitable surface anchoring technique for the liquid crystal cell given in the paper. The conditions for the existence of the first-order Fréedericksz transition are obtained. They are related to the material elastic coefficient k_{11}, k_{33} the thickness of the liquid crystal cell, the external electric field and the strength of surface anchoring, etc.     

Branching of colloidal chains in capillary-confined nematics

We report on the observation of colloidal chain assembly and branching inside capillaries filled with a nematic liquid crystal. Because of the homeotropic anchoring of liquid crystalline molecules on the capillary and colloidal droplet surfaces, the assembly of droplets along the capillary axis is expected, producing a transformation of the nematic director field from an escape-radial to quasiradial configuration. However, the subsequent over time branching of the straight colloidal chains is counterintuitive. By numerical simulations, we demonstrate that chain branching can occur by overcoming an energy barrier and can at least dwell as a metastable configuration. Moreover, manipulation of colloidal chains by electric fields and their gradients demonstrates various regimes of chain behavior in electric fields.     

Surface controlled nematic bistability

One discusses phenomenologically the statics and dynamics of surface anchoring of nematic liquid crystals. In statics, for symmetrical situations, one can induce, under the action of an external field, a surface breaking with a bifurcation between two opposite orientations of the director. In dynamics, one shows that the surface director relaxation is intrinsically fast, and accompanied by a transient surface shear flow. In thin cells with planar anchorings, filled by cyanobiphenyl materials which orient normal to the plates under a strong electric field, there are now two effects which couple the relaxation of the surface director: a static one, which favors parallel orientation and a uniform cell texture, and a transient dynamical coupling from the surface flow, which forces π-twisted texture. With suitable electric signals, one can control the surface bifurcations to give at will one of these two bistable textures. Results are presented which show that these mechanisms could lead to a new class of surface controlled, fast nematic bistable displays. Reproduced from ‘Liquid Crystals Today’ (Vol. 8, p. 1–7, 1998) by permission from Taylor and Francis.     

Dynamics of domain-wall motion in ferroelectric liquid crystals in an electric field

The director reorientation in smectic liquid crystals with ferroelectric properties has been considered in the case where the interaction of liquid-crystal molecules with the surface leads to a partial unwinding of the helical structure of the liquid crystal and the reorientation occurs as a result of the domain-wall motion. The dependences of the velocity of domain-wall motion on the electric field strength, electric field variation frequency, boundary conditions, spontaneous polarization, and viscosity of the liquid crystal have been determined. It has been demonstrated that an increase in the electric field variation frequency or the polar part of the anchoring energy and the spontaneous polarization of the liquid crystal at a constant field frequency results in an increase of the velocity of domain-wall motion. As a consequence, the time of the electro-optic response of the liquid crystal in weak electric fields (from 0.4 to 2.0 V/μm) decreases by a factor of more than three.     

Relation between the microscopic and macroscopic descriptions of the effect of a solid-substrate surface on a homeotropically aligned nematic liquid crystal

A simple microscopic mean-field model is proposed for a homeotropically aligned planar nematic liquid crystal (NLC) in contact with a solid-substrate surface. The intermolecular interaction in the NLC is simulated with the anisotropic McMillan potential, and the orienting effect of the substrate surface on the molecules in the NLC is described as that of an external field acting only on the first surface molecular layer of the sample. This model is used to describe the deformation of the director field of the sample caused by the external field and to determine the anchoring strength coefficient W, which is employed to macroscopically describe the orienting effect of the solid substrate on the NLC. The dependence of this coefficient on the strength of the short-range orienting field of the substrate surface used in the proposed microscopic model is found, and a unique correspondence between W and the profile of the orientational order parameter near the substrate surface is established. The temperature dependence of the anchoring strength coefficient is derived and found to agree well with experimental data for the MBBA NLC.