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.     

Effect of Disclination Lines on Free Energy of Nematic Liquid Crystals

In the light of φ-mapping method-and topological current theory, the effect of disclination lines on the free energy density of nematic liquid crystals is studied. It is pointed out that the total Frank free energy density can be divided into two parts. One is the distorted energy density of director field around the disclination lines. The other is the saddle-splay energy density, which is shown to be centralized at the disclination lines and to he topologically quantized in the unit of kπ/2 when the Jacobian determinant of the director field does not vanish at the singularities of the director field. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director field at the disclination lines, i.e., the disclination strengthes. When the Jacobian determinant vanishes, the generation, annihilation, intersection, splitting and merging processes of the saddle-splay energy density are detailed in the neighborhoods of the limit points and bifurcation points, respectively. It is shown that the disclination line with high topological quantum number is unstable and will evolve to the low topological quantum number states through the splitting process.     

Disclination motion in liquid crystalline films

We theoretically study a single disclination motion in a thin free-standing liquid crystalline film. Backflow effects and the own dynamics of the orientational degree of freedom (bond or director angle) are taken into account. We find the orientation field and the hydrodynamic velocity distribution around the moving disclination, which allows us to relate the disclination velocity to the angle gradient far from the disclination. Different cases are examined depending on the ratio of the rotational and shear viscosity coefficients.     

Topological Aspect and Bifurcation of Disclination Lines in Two—Dimensional Liquid Crystals

Using φ-mapping method and topological current theory,the topological structure and bifurcation of disclination lines in two-dimensional liquid crystals are studied.By introducing the strength density and the topological current of many disclination lines,the total disclination strength is topologically quantized by the Hopf indices and Brouwer degrees at the singularities of the director field when the Jacobian determinant of director field does not vanish.When the Jacobian determinant vanishes,the origin,annihilation and bifurcation processes of disclination lines are studied in the neighborhoods of the limit points and bifurcation points,respectively.The branch solutions at the limit point and the different directions of all branch curves at the bifurcation point are calculated with the conservation law of the topological quantum numbers.It is pointed out that a disclination line with a higher strength is unstable and it will evolve to the lower strength state through the bifurcation process.     

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.     

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.     

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     

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.     

Contribution of Disclination Lines to Free Energy of Liquid Crystals in Single-Elastic Constant Approximation

In the light of C-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kn/2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director l~eld at the disclination lines, i.e. the disclination strengths. From the Lagrange‘s method of multipliers, the equilibrium equation and the molecular field ofliquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density.     

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.     

Orientational optical torque in a nematic liquid crystal,caused by trans- and cis-isomers of low- and high-molecular compounds

The effect of light on the conformational composition of low- and high-molecular (fifth-generation dendrimer) azobenzene dyes in a nematic host is studied. The orientational optical response of the nematic liquid crystal (NLC), caused by the presence of these compounds in the nematic host, is measured. The contributions of isomers to the orientational optical torque affecting the NLC director are determined. The results obtained suggest that the increase in the optical orientation efficiency in NLCs when using high-molecular dopants instead of low-molecular ones is unrelated to the difference in their conformational composition in the light field, but is caused by deceleration of orientational motion of chromophores.     

Structural Transformations in Nematic Liquid Crystals with a Hybrid Orientation

Journal of Experimental and Theoretical Physics - The structural transformations in a nematic liquid crystal (NLC) layer with a hybrid orientation (planar director orientation is created on one...     

Topological Aspects of Liquid Crystals

Using -mapping method and topological current theory, the properties and behaviors of disclination points in three-dimensional liquid crystals are studied. By introducing the strength density and the topological current of many disclination points, the total disclination strength is topologically quantized by the Hopf indices and Brouwer degrees at the singularities of the general director field when the Jacobian determinant of the general director field does not vanish. When the Jacobian determinant vanishes, the origin, annihilation, and bifurcation of disclination points are detailed in the neighborhoods of the limit point and bifurcation point, respectively. The branch solutions at the limit point and the different directions of all branch curves at the first- and second-order degenerated points are calculated. It is pointed out that a disclination point with a higher strength is unstable and will evolve to the lower strength state through the bifurcation process. An original disclination point can split into at most four disclination points at one time.     

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.     

Topological quantization of disclination points in three—dimensional liquid crystals

Using the φ-mapping method and topological current theory, we study the inner structure of disclination points in three-dimensional liquid crystals. By introducing the strength density and the topological current of many disclination points, it is pointed out that the disclination points are determined by the singularities of the general director field and they are topologically quantized by the Hopf indices and Brouwer degrees.     

Stability of Disclinations in Nematic Liquid Crystals

In the light of φ-mapping method and topological current theory, the stability of disclinations around a spherical particle in nematic liquid crystals is studied. We consider two different defect structures around a spherical particle: disclination ring and point defect at the north or south pole of the particle. We calculate the free energy of these different defects in the elastic theory. It is pointed out that the total Frank free energy density can be divided into two parts. One is the distorted energy density of director field around the disclinations. The other is the free energy density of disclinations themselves, which is shown to be concentrated at the defect and to be topologically quantized in the unit of (k-k₂₄)π/2. It is shown that in the presence of saddle-splay elasticity a dipole (radial and hyperbolic hedgehog) configuration that accompanies a particle with strong homeotropic anchoring takes the structure of a small disclination ring, not a point defect.     

Control of extraordinary light transmission through perforated metal films using liquid crystals

We calculate the effective dielectric tensor of a metal film penetrated by cylindrical holes filled with a nematic liquid crystal (NLC). We assume that the director of the NLC is parallel to the film, and that its direction within the plane can be controlled by a static magnetic field, via the Freedericksz effect. To calculate the effective dielectric tensor, we consider both randomly distributed holes (using a Maxwell-Garnett approximation) and a square lattice of holes (using a Fourier technique). Both the holes and the lattice constant of the square lattice are assumed small compared to the wavelength. The films are found to exhibit extraordinary light transmission at special frequencies related to the surface plasmon resonances of the composite film. Furthermore, the frequencies of peak transmission are found to be substantially split when the dielectric in the holes is anisotropic. For typical NLC parameters, the splitting is of order 5–10% of the metal plasma frequency. Thus, the extraordinary transmission can be controlled by a static magnetic or electric field whose direction can be rotated to orient the director of the NLC. Finally, as a practical means of producing the NLC-filled holes, we consider the case where the entire perforated metal film is dipped into a pool of NLC, so that all the holes are filled with the NLC, and there are also homogeneous slabs of NLC on both sides of the film. The transmission in this geometry is shown to have similar characteristics to that in which the NLC-filled screen is placed in air.     

Topological structure in polarization resolved conoscopic patterns for nematic liquid crystal cells

We investigate the polarization structure of coherent light, produced by a convergent light beam transmitted through nematic liquid crystal (NLC) cells with different director configurations. Employing solutions to the transmission problem for the case when plane wave propagates through an anisotropic layer, we analyze the arrangement of the topological elements, such as polarization singularities (C points with circular polarization and L lines with linear polarization), saddle points and extrema of polarization azimuth. We observe transformations of the topological structure under the variation of the incident light ellipticity and represent it by corresponding trajectories of topological elements in three-dimensional space. For the cells with uniform and non-uniform director configuration we describe the processes of creation/annihilation of C point pairs, which can be controlled precisely in the case of the cell with non-uniform director. Our experimental measurements for the homeotropically oriented NLC cells are in good agreement with the theoretical predictions.     

Optical bistability of the director field of the dendrimer-doped nematic liquid crystal

It was found that the second-generation carbosilane dendrimers with statistically distributed terminal aliphatic and azobenzene fragments induce negative orientational nonlinearity in nematic liquid crystals (NLC) (the NLC director turns perpendicular to the light field, decreasing the refractive index of an extraordinary wave). The light-induced Freedericksz transition in planar oriented NLCs is the first-order orientational phase transition characterized by a wide bistability region.     

Inclusions in Smectic C Films as Modeled by Disclinations

A simplified model of an inclusion represented by (+1)-wedge disclination and two accompanying (– 1/2)-wedge disclinations on the surface of inclusion in smectic C free standing films is used to describe the elastic interaction of inclusions. The orientation of the axis connecting positions of all three disclinations relatively to the director orientation at far distances due to elastic anisotropy is investigated. The configuration with the lowest director perturbations and the lowest anisotropy elastic energy is such that the axis connecting disclinations is parallel to the distant director orientation. The interaction between inclusions at far distances is quadrupolar. The chaining of inclusions is approximately described considering their repulsion due to molecular anchoring at inclusion surfaces.