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.     

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.     

Structure and elastic properties of a nematic liquid crystal: A theoretical treatment and molecular dynamics simulation

The Frank elasticity constants which describe splay (K ₁), twist (K ₂), and bend (K ₃) distortion modes are investigated for 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic liquid crystal. The calculations rest on statistical-mechanical approaches where the absolute values of K _i (i=1,2,3) are dependent on the direct correlation function (DCF) of the corresponding nematic state. The DCF was determined using the pair correlation function by solving the Ornstein-Zernike equation. The pair correlation function, in turn, was obtained from molecular dynamics (MD) trajectory. Three different approaches for calculations of the elasticity constants were employed based on different level of approximation about the orientational order and molecular correlations. The best agreement with experimental values of elasticity constants was obtained in a model where the full orientational distribution function was used. In addition we have investigated the approximation about spherical distribution of the intermolecular vectors in the nematic phase, often used in derivation of various mean-field theories and employed here for the construction of the DCF. We found that this assumption is not strictly valid, in particular a strong deviation from the isotropic distribution is observed for short intermolecular distances. Received 22 March 2000 and Received in final form 9 June 2000     

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.     

Surface electric-field-induced instabilities in a homeotropically oriented nematic liquid crystal sample

The effect of a surface electric field produced by ionic adsorption on the molecular orientation of a nematic liquid crystal sample is analyzed. The eigenvalue problem for a semi-infinite medium is analytically solved both for strong and weak anchoring situations. The threshold instabilities are numerically determined and it is shown that the homeotropic pattern can be destabilized also in the situation of strong anchoring. The dependence of the threshold field on the anchoring strength and on the surface polarization is determined by taking into account also the coupling of the quadrupolar component of the flexoelectric coefficient with the field gradient. Received 4 November 1999 and Received in final form 4 April 2000     

Theoretical investigations of rotational phenomena and dielectric properties in a nematic liquid crystal

The molecular dynamics (MD) simulation, based on a realistic atom-atom interaction potential, was performed on 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic phase. The rotational viscosity coefficients (RVCs) γ _i, (i = 1, 2) and the ratio of the RVCs λ = - γ ₂/γ ₁ were investigated. Furthermore, static and frequency-dependent dielectric constants and ε were calculated using parameters obtained from the MD simulation. Time correlation functions were computed and used to determine the rotational diffusion coefficient, D _⊥. The RVCs and λ were evaluated using the existing statistical-mechanical approach (SMA), based on a rotational diffusion model. The SMA rests on a model in which it is assumed that the reorientation of an individual molecule is a stochastic Brownian motion in a certain potential of mean torque. According to the SMA, γ _i are dependent on the orientational order and rotational diffusion coefficients. The former was characterized using: i) orientational distribution function (ODF), and ii) a set of order parameters, both derived from analyses of the MD trajectory. A reasonable agreement between the calculated and experimental values of γ _i and λ was obtained. Received 22 March 2000 and Received in final form 8 October 2000     

Director reorientation in twisted nematic liquid crystals due to thermomechanical effect

We have studied molecular director reorientation in a twisted nematic liquid crystal induced by a two-dimensional temperature gradient. We studied the effect of rate change between the temperature gradients in two directions. Our obtained director reorientations are in the range that can be observed experimentally very easily.     

An azo-isomerization-induced Freedericksz transition of a nematic liquid crystal

We observed an azo-isomerization-induced Freedericksz transition of the 5CB liquid crystal doped with 1% double-azo. In experiment, we found that the Freedericksz transition threshold occurred at optical intensity level of 0.3 mW/mm² for the 12.5 μm-thickness planar alignment doped 5CB, which is four orders of magnitude lower as that for the pure 5CB. Using optical phase retardation, we measured the relations between the Freedericksz transition threshold and the pump beam polarization. The maximum twist angle of liquid crystal molecules under different pump beam intensity is given. The experiment indicated that trans–cis isomerization plays an important role in the decrease of the Freedericksz transition threshold.     

Temperature and external field-driven microrelief at free surface of smectic-A liquid crystal

A homeotropically oriented smectic-A film on a solid substrate with periodical microrelief is considered. Periodical distortions of the free surface of the film induced by this microrelief are theoretically investigated. The dependence of these distortions on the film thickness, the temperature, and external magnetic (electric) field is obtained. It is shown that, for a certain choice of the shape of the substrate surface microrelief, one can realize a temperature and external magnetic (electric) field control on the microrelief at the free surface of the smectic-A film.     

Optical storage effect in a platinum orthometalated liquid crystal

Received: 24 June 1997     

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.     

Optical visualization of deformations with nematic liquid crystals

Nematic liquid crystals are shown to be able to visualize elastic deformations even if no dynamic scattering is present. At low values of the elastic energy density, by observing the excited birefringence it is possible to map the normal modes of the elastic disturbance. At higher energy density a cellular motion (rolls) is produced which, in the homeotropic geometry, gives rise to a domain pattern which allows to visualize the velocity field. Work supported by Gruppo Nazionale di Struttura della Materia (GNSM) of CNR.     

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.     

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     

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.     

Soliton-like solutions of certain types of nonlinear diffusion-reaction equations with variable coefficient

With a view to exploring new soliton-like solutions of certain types of nonlinear diffusion-reaction (DR) equations with a variable coefficient, we demonstrate the viability of a method which is the combination of both the symbolic computation technique of Gao and Tian [Y.T. Gao, B. Tian, Comput. Phys. Commun. 133 (2001) 158] and auxiliary equation method of Sirendaoreji [Sirendaoreji, Phys. Lett. A 356 (2006) 124] and used recently for the KdV equation. In particular, the DR equations with quadratic and cubic nonlinearities with a time-dependent velocity in the convective flux term are studied and the existence of soliton-like solutions is shown.     

Effect of surface electric field on the anchoring of nematic liquid crystals

We analyse the influence of adsorbed ions and the resulting surface electric field and its gradient on the anchoring properties of nematics with ionic conductivity. We take into account two physical mechanisms for the coupling of the nematic director with the surface electric field: (i) the dielectric anisotropy and (ii) the coupling of the quadrupolar component of the flexoelectric coefficient with the field gradient. It is shown that for sufficiently large fields near saturated coverage of the adsorbed ions, there can be a spontaneous curvature distortion in the cell even when the anchoring energy is infinitely strong. We also discuss the director distortion when the anchoring energy of the surface is finite. Received: 29 September 1997 / Received in final from: 10 November 1997 / Accepted: 18 November 1997     

Operadic deformations as a tool for cogravity

The deformation equation and its integrability condition (Bianchi identity) of a non-(co)associative deformation in operad algebra are found. Based on physical analogies, two ideas ofcogravity equations are proposed. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.     

Twist deformations for algebras of motion

We study the twist deformations of algebras of motiong ^H ⊂ sl(N) with the Cartan subalgebraH(g^H) equal toH(sl(N)). The proposed deformations are maximal in the sense that their carrier algebrasg _c coincide withg ^H. The algebraic properties are demonstrated forg ^H ⊂ sl(5). Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. This work has been partially supported by the Russian Foundation for Fundamental Research under the grant N 00-01-00500.     

Electrically controlled liquid crystal fiber

We consider a cylindrical fiber whose core is a liquid crystal (LC) subject to the action of a low frequency field applied parallel to the axis of the cylinder and having initially the escaped configuration. We find the distorted textures of the nematic inside the cylinder by assuming arbitrary anchoring boundary conditions. In the optical limit we calculate the ray trajectories followed by a low intensity beam along the fiber parametrized by a low frequency electric field. Finally, we calculate exactly the spatial dependence of the transverse magnetic modes distribution in the guide, on the electric field, by using a numerical scheme. We summarize our paper and discuss our results.