Traveling waves in twisted nematic liquid crystal cells

We have described a novel reorientation mechanism in the form of the traveling waves, under influence of an external electric field, directed parallel to both glass plates, which occur in the twisted nematic cell (TNC). It is found that the slowest velocity of the traveling front is proportional to the field strength, and, approximately, in three times higher than the front velocity corresponding to the non-traveling solution. The value of the critical electric field Ecr$E_{\mathrm{cr}}$ which may excite the traveling waves in the TNC in π   times less than the value of the threshold electric field Eth$E_{\mathrm{th}}$ corresponding to the untwisted geometry.     

Monte Carlo simulation of joint density of states in one-dimensional Lebwohl-Lasher model using Wang-Landau algorithm

Monte Carlo simulation using the Wang-Landau algorithm has been performed in an one-dimensional Lebwohl-Lasher model. Both one-dimensional and two-dimensional random walks have been carried out. The results are compared with the exact results which are available for this model.     

Surface anchoring energy and the Freedericksz transitions in ferronematics

This paper analyzes the influence of anchoring conditions on the two-field-induced Freedericksz transition in ferronematics. Using the Euler-Lagrange analytical method we find a correlation between the threshold intensities of the magnetic and the laser fields, the anchoring strength, the material and device parameters. The threshold fields in our case are smaller than those obtained in the rigid anchoring limit. We show that for finite anchoring energy, the saturation transition is possible, and find the correlation between the saturation fields, the anchoring strength, the material and cell parameters. Our results can be useful in designing magneto-optical devices using ferronematics.     

Transient Reorientation of a Doped Liquid Crystal System under a Short Laser Pulse

The transient optical nonlinearity of a nematic liquid crystal doped with azo-dye DR19 is examined. The optical reorientation threshold of a 25-μm-thick planar-aligned sample of 5CB using a 50 ns pulse duration 532nm YAG laser pulse is observed to decrease from 800 mJ/mm^2 to 0.6 mJ/mm^2 after the addition of i vol% azo dopant, a reduction of three orders of magnitude. When using a laser pulse duration of 10ns, no such effect is observed. Experimental results indicate that the azo dopant molecules undergo photoisomerization from trans-isomer to cis-isomer under exposure to light, and this conformation change reorients the 5CB molecules via intermolecular coupling between guest and host. This guest-host coupling also affects the azo photoisomerization process.     

Magnetically induced Freedericksz transition and relaxation phenomena in nematic liquid crystals doped with azo-dyes

A static and dynamic investigation was performed on liquid crystal cells containing pure nematics and nematics doped with an azo-dye (Methyl Orange). It was found that the critical field for magnetic Freedericksz transition was decreased in samples containing the “trans” isomer and increased in those containing the “cis  ” isomer. Changes in the relaxation time _τA${\tau }_A$, _τB${\tau }_B$ intervening when switching on/off the magnetic field were also noticed. A theoretical model was elaborated to explain these phenomena.     

Universal growth laws in liquid crystals far from equilibrium

Universal growth laws were examined experimentally for the transition from an isotropic melt to the liquid-crystalline state as well as the liquid-crystal (LC) to crystal transition for a system, which can be largely super-cooled. For large quench depths the growth exponent of the growth law L(t) ∼tⁿ is given by n=1. On decreasing the quench depth, two phase-ordering processes can be resolved for the isotropic (Iso.)–LC transition, one with a decreasing growth exponent 1<n<1/2 and a long-time process with n=1, independent of quench depth. In the very vicinity of the transition, nucleus growth is described by a single process according to L(t) ∼t^1/2. This behavior is interpreted in terms of an Iso. to blue-phase (BP) to cholesteric (N*) transition. The crystallization from the liquid-crystalline state (monotropic smectic A*) can be super-cooled substantially and follows a linear-growth process L(t)∼t. Received: 3 July 2000 / Accepted: 17 October 2000 / Published online: 10 January 2001     

On spatial variations of nematic ordering

We present a theory of orientational order in nematic liquid crystals which interpolates between several distinct approaches based on the director field (Oseen and Frank), order parameter tensor (Landau and de Gennes), and orientation probability density function (Onsager). As in density-functional theories, the suggested free energy is a functional of spatially-dependent orientation distribution, however, the nonlocal effects are taken into account via phenomenological elastic terms rather than by means of a direct pair-correlation function. In illustration of this approach we consider a simplified model with orientation parameter on a circle and reveal its relation to the complex Ginzburg-Landau theory.     

Thermal diffusivity measurements in a lyotropic discotic nematic phase

The present work is focused on thermal diffusivity (D)$(D)$ measurements, via Z  -scan experiment, in a discotic nematic phase of the lyotropic mixture comprised of potassium laurate, decanol and D₂O${\text{D}}_2\text{O}$. In this experiment, the nematic sample is translated through the focal region of a focused Gaussian laser beam. The experimental data are analyzed according to the thermal lens model and the ratio between the thermal diffusivities parallel (D_∥)$(D_{\parallel })$ and perpendicular (D_⊥)$(D_{\perp })$ to the director of the nematic sample has been found to be smaller than one. The results are compared to others obtained with different liquid crystals and explained by using a simple model where this ratio is correlated to the shape anisotropy of the micelles.     

Geometry of nematic liquid crystals under shearing flow

In this work, an extended version of the Hess-Baalss conformal approach is used to propose a relation connecting the viscosity coefficients of the nematic liquid crystals. Starting from the well-known fact that, in its usual form, the conformal transformation leads to results which are not observed experimentally, it is shown that, when the director field of an ordered nematic phase under sheared motion is taken as a three-dimensional surface with torsion, the resulting theory describes the observed experimental data efficiently. Moreover, this model predicts that the five viscosity coefficients of the Leslie ah hoc model are not independent, but connected. A comparison of the deduced relationship with experimental data is performed and an excellent agreement is obtained.     

Phase transition in liquid crystal elastomers—A Monte Carlo study employing non-Boltzmann sampling

We investigate nematic-isotropic transition in liquid crystal elastomers employing a variant of Wang-Landau sampling. This technique facilitates calculation of the density of states from which other thermodynamic properties can be obtained. We consider a lattice model of a liquid crystal elastomer and a Hamiltonian which accounts for interactions among liquid crystalline units and interaction of local nematics with global strain. We investigate the effect of varying the strength of coupling between nematic and orientational degrees of freedom. When the local director is coupled strongly to the global strain, the transition is strongly first order. When the strength of the coupling decreases the transition becomes weakly first order. The transition temperature decreases when the coupling becomes weaker. We also report for the first time results on variation of free energy as a function of average energy at different temperatures and coupling constants.     

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.     

Elastic constants of a nematic liquid crystal: Quadrupole-quadrupole interaction in the ellipsoidal approximation

The elastic constants of a nematic liquid crystal are calculated by means of a pseudo-molecular method that considers the quadrupolar intermolecular interaction with a screening length governing the range of the forces. The bulk as well as the surface-like elastic constants are determined as functions of the eccentricity of the interaction volume of ellipsoidal shape. It is shown that the elastic constants become negative for some values of the eccentricity, and, therefore, that the screened quadrupolar interaction could be the source of instabilities in the nematic phase and should be taken into account to interpret threshold phenomena in these systems.     

Depletion effects in smectic phases of hard-rod-hard-sphere mixtures

It is known that when hard spheres are added to a pure system of hard rods the stability of the smectic phase may be greatly enhanced, and that this effect can be rationalised in terms of depletion forces. In the present paper we first study the effect of orientational order on depletion forces in this particular binary system, comparing our results with those obtained adopting the usual approximation of considering the rods parallel and their orientations frozen. We consider mixtures with rods of different aspect ratios and spheres of different diameters, and we treat them within Onsager theory. Our results indicate that depletion effects, and consequently smectic stability, decrease significantly as a result of orientational disorder in the smectic phase when compared with corresponding data based on the frozen-orientation approximation. These results are discussed in terms of the τ parameter, which has been proposed as a convenient measure of depletion strength. We present closed expressions for τ, and show that it is intimately connected with the depletion potential. We then analyse the effect of particle geometry by comparing results pertaining to systems of parallel rods of different shapes (spherocylinders, cylinders and parallelepipeds). We finally provide results based on the Zwanzig approximation of a fundamental-measure density-functional theory applied to mixtures of parallelepipeds and cubes of different sizes. In this case, we show that the τ parameter exhibits a linear asymptotic behaviour in the limit of large values of the hard-rod aspect ratio, in conformity with Onsager theory, as well as in the limit of large values of the ratio of rod breadth to cube side length, d, in contrast to Onsager approximation, which predicts τ ∼ d ³. Based on both this result and the Percus-Yevick approximation for the direct correlation function for a hard-sphere binary mixture in the same limit of infinite asymmetry, we speculate that, for spherocylinders and spheres, the τ parameter should be of order unity as d tends to infinity.     

Surface transitions in nematic liquid crystals oriented with Langmuir-Blodgett films

In this paper two types of surface transitions in nematic liquid crystals are theoretically analyzed with a simple model in which the anchoring energy is the result of both steric and electric interactions. The physical model is proper to explain both the transition temperature experimentally observed in homeotropically aligned nematic liquid crystals, and the change in the mean molecular direction due to the variation of the number of surfactant films, piled on the boundary surfaces with the Langmuir-Blodgett technique.Partially supported by the TEMPUS program     

Effect of aerosil dispersions on the nematic-to-isotropic interface

The effect of silica aerosils on the kinetics of the first-order nematic-isotropic (NI) phase transition is phenomenologically described in the framework of the time-dependent Landau-Ginzburg equation. A steady-state solution to the equation is presented such that the NI interface may propagate with a solitary-like wave profile under constant quenching. The results provide a plausible basis for the interpretation of the dynamical effects of quenched disorder in the liquid-crystal systems, caused by randomly interconnected porous media, such as aerosils. In the low silica aerosil ρ_s ( ≤0.1 g/cm^3) regime, the calculated values of the interface velocity v(T,ρ_s), the interface thickness κ(T,ρ_s), and the critical radius of a spherical nucleus of new nematic phase in a bulk isotropic environment, composed of polar molecules, such as 4-n-octyl- 4^′- cyanobiphenyl and 4-n-heptyl- 4^′- cyanobiphenyl shows that the effect of silica aerosils on the kinetics is reflected in a shifting of the set of temperature-dependent curves to lower temperature values.-1     

Peculiarities of biphasic regions at phase transitions in oriented textures of 4-cyano-4′-n-pentylbiphenyl

Peculiarities of the biphasic regions at the direct and reverse phase transitions between homeotropic oriented nematic mesophase and isotropic liquid have been investigated in detail in this work. The shift of phase transition temperatures to the low temperatures by the reverse phase transitions have been observed for this mesophase. Nonlinearity of thermotropic and thermo-optical properties at the phase transitions between nematic mesophase and isotropic liquid have been found.     

Nonlinear molecular deformations and solitons in a nematic liquid crystal

We studied nonlinear molecular deformations in a nematic liquid crystal with homeotropically aligned molecules and hard boundaries. As the basic dynamical equation for the director axis of the liquid crystal resembles the Landau-Lifshitz equation representing spin dynamics in a one dimensional classical continuum isotropic Heisenberg ferromagnetic spin chain, we invoke here the space curve formalism and the stereographic projection technique used in the case of the Heisenberg spin chain. Under space curve mapping, the director dynamics with elastic deformation is found to be governed by a perturbed nonlinear Schrödinger equation. A multiple-scale perturbation analysis brings out perturbed solitons to represent molecular deformations in the nematic liquid crystal. However, when a constant electric field is applied, the director dynamics is expressed under stereographic projection and the molecular deformations are found to be governed by periodic and localized static planar director configurations. A linear stability analysis on the static planar configurations shows that the system exhibits stable deformations.     

Soliton-like molecular deformations in a nematic liquid crystal film

We study the nature of molecular deformations in a nematic liquid crystal film with elastic energy under homeotropic boundary conditions. The deformation in terms of splay, twist and bend fields of the director axis is found to be governed by the completely integrable Davey-Stewartson-I (DS-I) equation in (2+1) dimensions. Using the line soliton and breather solutions of the DS-I equation, the director axis is constructed, the components of which exhibit damped spatial oscillations. However, the splay and bend fields of the director axis exhibit localized structures of deformation.     

Langmuir-Blodgett film and nematic interface

The orientation induced by a Langmuir-Blodgett film on a Nematic Liquid Crystal (NLC) is theoretically analyzed. We show that the effective surface energy is due to different contributions connected with steric and van der Waals interactions between the nematic and the solid substrate. The analysis shows that the Langmuir-Blodgett film orientation depends on the surface density of the molecules. The initial homeotropic orientation may become unstable giving rise to a tilted film. The average orientation of the nematic molecules is also analyzed. We show that, in the event in which the steric interaction Nematic-Langmuir-Blodgett film is very large with respect to the dispersion interaction Nematic-Substrate, the nematic orientation coincides with the one of the film. On the contrary, when the two interactions are comparable, the orientation of the two media may differ. In particular, we analyze how the stable orientation depends on the surface molecular density of the film.     

Induced ferrielectricity in antiferroelectric liquid crystals

The behaviour of the antiferroelectric SmC_A liquid crystal phase under applied electric field is discussed theoretically. The phase diagram involving the SmA, SmC_A and SmC _A ^* phases is worked out and shown to exhibit a Lifshitz critical point. The deformation of the bilayer structures induced by the field transforms the SmC_A phases into a ferrielectric phase whose specific configuration is described. Received: 23 October 1997 / Revised: 8 April 1998 / Accepted: 14 July 1998