Investigation of Nematic Liquid Crystals Doped with Spherical Multiferroic Nanoparticles in the Presence of a Magnetic Field

Recently, multiferroic nanoparticles (MFNPs) have attracted significant attention as dopant in the nematic liquid crystal (NLC) medium. Here, behavior of the NLC molecules and MFNPs in the presence of a magnetic field is theoretically investigated in the framework of continuum theory, based on our knowledge. The electric field of the MFNPs is taken into account in the calculations. Freedericksz transition (FT) threshold field in the presence of spherical nanoparticles is determined. Dependence of the FT threshold to the diameter and volume fraction of the nanoparticles was studied. Also, the NLC director and nanoparticle reorientations for the magnetic field larger than the FT threshold field are studied. It was shown that the FT threshold of NLC is decreased by doping of spherical MFNPs. Migration of the nanoparticles to the central layers of the cell (segregation effect) is investigated.     

Inhomogeneous threshold director reorientation in a planar nematic flexoelectric cell with finite anchoring energy

The dependence of the threshold parameters and the period of the electric-field-induced spatially periodic reorientation of the director in a flexoelectric nematic liquid crystal (NLC) on the anchoring conditions at the surface of a planar NLC cell has been studied. The threshold electric field and the corresponding wave-number of the periodic structure of the director field have been numerically calculated for arbitrary values of the anchoring energy. In the case of strong anchoring, the corresponding analytical expressions are obtained in a single-constant approximation. A decrease in the azimuthal anchoring energy leads to an increase in the intervals of possible values of the flexoelectric parameter ν and the ratio K₂/K₁ of the Frank elastic constants. A decrease in the polar anchoring energy leads to narrowing of these intervals as compared to the case of infinitely strong anchoring at the NLC cell surface.     

Surface reorientation dynamics of nematic liquid crystals

In this paper we report an experimental investigation on the dynamics of the azimuthal director reorientation at a nematic-solid interface. Three qualitatively different kinds of substrates have been investigated: I) intrinsically anisotropic SiO-substrates (-evaporation), II) isotropic SiO-substrates (-evaporation) and III) rubbed PVA-substrates. In the case II), an in-plane anisotropy was induced cooling slowly the thermotropic nematic liquid crystal (NLC) from the isotropic phase in the presence of a 0.75 T magnetic field. The reorientation dynamic of the surface azimuthal director angle at the switching-on and off of a magnetic (or electric) field has been investigated. All the substrates show comparable azimuthal anchoring energies and two dynamic regimes: a fast dynamic response, driven by the bulk director reorientation and an extremely slow reorientation. The slow dynamics is explained in terms of anisotropic adsorption of NLC molecules on the solid substrate and is well represented by a stretched exponential. Received 7 December 1998     

Rotational reorientation of the director in twisted nematic liquid-crystal cells

The orientational relaxation of the director to its equilibrium orientation under electric, elastic, and viscous torques arising in twisted nematic liquid-crystal cells is investigated. It is shown that the relaxation time of the director depends strongly on the external electric field strength and weakly on the energy of anchoring of liquid-crystal molecules to the surfaces of the cell. The relaxation time of the director anomalously increases in electric fields close to the Fréedericksz threshold. It is established that, at specific strengths of the external electric field, the relaxation can occur in the form of traveling waves propagating from one edge to the other edge of the twisted nematic liquid-crystal cell. The calculations of the relaxation processes in the vicinity of the nematic-smectic A phase transition temperature demonstrate that the distortion of the director field is uniform over the entire cross section of the liquid-crystal cell and does not depend on the strength of anchoring of the liquid-crystal molecules to the surfaces of the cell.     

表面弹性项K13对液晶盒临界场强的影响和实验测定

以修正后的Rapini-Papoular公式为基础，得到了有表面弹性能K₁₃存在时，弱锚定向列液晶盒指向矢满足的方程和边界条件。用解析推导和数值计算的方法，详细研究了K₁₃对阈值场强和饱和场强的影响。在理论上给出了检验K₁₃是否存在的一种新方法及用沿面平行校列的弱锚定楔型液晶盒测定K₁₃值的实验方案，并通过数值实验证实了本文所给方法的可行性。     

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.     

挠曲电效应对向列相液晶盒电光效应的影响

研究挠曲电效应对向列相液晶盒电光效应的影响.通过变分理论得到液晶指向矢满足的微分方程和边界条件,利用差分迭代的方法计算强锚定和弱锚定液晶盒中液晶指向矢的分布情况.借助琼斯矩阵的方法,计算两种液晶盒电光特性曲线.此外,在计算中同时考虑了挠曲电表面和体积效应.     

Threshold property of a nematic liquid crystal cell with two grating surface substrates

A grating surface can drive the liquid crystal molecules to orientate along the direction parallel or vertical to the projected plane of the grating surface. The nematic liquid crystal (NLC) cell manufactured with two pre-treated grating surface substrates may realize the vertical display, parallel display and twist display. In this paper, the threshold property of this NLC cell is investigated systematically. With the Frank elastic theory and the equivalent anchoring energy formula of grating surface substrate, the analytic expressions of the threshold voltage related to three displays are obtained, which are dependent on their geometrical parameters such as amplitude δ and pitch λ of the grating surface substrate. For a certain anchoring strength, the threshold voltage increases or decreases with the increase of the value δ/λ of the different displays.     

Disclinations in nematics in the presence of flexoelectricity

The stability problems of wedge disclinations (with pure splay and bend distortions) in nematic liquid crystals (NLC) are considered in the presence of flexoelectricity. We write NLC director equations in the cylindrical coordinate system, taking into account flexoelectricity. These equations allow us to solve many interesting problems on the influence of flexoelectricity on the orientational structures of NLC. In particular, it is shown that the line of disclination with radial distribution of director can be stabilized in the presence of flexoelectricity even far from nematicsmectic phase transition point. For the disclination with azimuthal distribution of director for all physical sizes the line is not stable and escapes in the third dimension.     

Some features of second harmonic generation in the nematic liquid crystal 5CB in the pulsed-periodic electric field

Second harmonic generation (SHG) induced by an external pulsed-periodic electric field in a 5CB nematic liquid crystal (NLC) is investigated. Deformation of the NLC under this field is analyzed, and a possibility of its accumulation is established. The observed SHG features are due to the domains with quite different director orientations emerging in the NLC.     

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     

Destabilizing effect of a surface electric field generated by ionic adsorption on the molecular orientation of nematic liquid crystals

The destabilizing effect of a surface electric field, produced by selective ionic adsorption, on the molecular orientation of a nematic-liquid-crystal sample is analyzed for a cell in the shape of a slab of thickness d. The electric-field distribution considered in the analysis is the one obtained in the limit in which essentially all the positive ions are adsorbed. Because of the coupling of this surface field with the nematic director, the surface anchoring energy depends on the thickness of the sample as well as on the adsorption energy characterizing the surfaces. A relation connecting the threshold field for the destabilization of the homeotropic pattern to the adsorption energy and to the thickness of the sample is established in closed form, after solving a set of two coupled non-linear equations determining the electric-field distribution across the sample. It is shown that the values of surface electric field generated by adsorbed ions that can lead to a destabilization of the homeotropic alignment can be attained by real samples.     

Electric method for studying reorientation dynamics of the nematic liquid crystal director

A method has been proposed for studying the reorientation dynamics of the nematic liquid crystal (NLC) director using the results of measurements of the electric response of an LC cell. The simulation of the time dependences of the current in an LC cell with a homogeneous orientation is carried out upon variation of the applied voltage, the initial tilt angle of the director, dielectric anisotropy, and the elasticity coefficient, as well as the dynamic viscosity, density, and ion mobility in the NLC. A comparison of the experimental and computational curves of the electric response for NLC 5CB shows their good agreement. The method makes it possible to monitor the steady-state current, the density, and the ion mobility in NLCs.     

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.     

Improvement of turn-on time of liquid-crystal phase retarder by using an additional control voltage

We investigate theoretically and experimentally the process of turn-on time control of a nematic liquid crystal (NLC) based phase retarder by means of an additional control voltage. We propose a theoretical model of reorientation of NLC molecules in crossed electric fields (conventional transverse field and additional longitudinal field). The dynamics of reorientation of NLC molecules is considered depending on the ratio of amplitudes of control voltages. We show the possibility to reduce the turn-on time in NLC-based phase-retarder management by means of two control voltages.     

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.     

Investigation of the influence of external electric field on the anisotropy of nematic liquid crystals by X-Ray interferometry

The influence of external electric field on the anisotropy of a layer of nematic liquid crystal (NLC) was investigated by means of X-Ray interferometric method. It was shown that in Xray range of the spectrum NLC E7 is a positive anisotropic medium. The decrements of a layer of NLC subjected to the electric field were calculated. As a result of reorientation of NLC molecules perpendicular to the cell substrate, the decrements prove equal for cases when the optical axis of a sample was initially perpendicular or parallel to the X-ray beam polarization vector.     

Rayleigh–Benard Convection in the homeotropic nematic liquid crystal by a Gaussian laser beam absorption

The Rayleigh–Benard Convection (RBC) were studied theoretically in the homeotropic nematic liquid crystal (NLC) cell due to the absorption of a normally incident Gaussian light beam from upper side of the cell. It was shown that a convection of hydrodynamic motion in the NLC can be induced and eventually the molecular director coupling with hydrodynamics reorients the director. An external magnetic field parallel to the director decreases the director reorientation and the radial flow velocity, while the velocity in the z direction is unaffected. The results were found to be in a range that can easily be checked experimentally.     

Threshold and saturation properties of the field-induced twist cell with two parameters weak anchoring boundaries

On the basis of two-parameter formula of weak surface coupling anchoring energy of nematic liquid crystals proposed by Zhao et al recently, the general torque equilibrium equation and boundary conditions of the director have been obtained and the threshold field as well as the saturation field of the field-induced twist cell have been analysed for three kinds of configurations, i.e. homogeneous, splay and Pi cells formed by different rubbing conditions and pretilt angles. The results indicated that the polar anchoring has no effect on the threshold field. It is determined only by the twist anchoring and pretilt angle. But, the polar anchoring and twist anchoring are coupling with each other and have a great influence on the saturation field. The formulae for calculating the threshold field and saturation field are given. These results will be very useful in understanding surface physics and the design of liquid crystal cells.