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The dependence of the cut-off frequency of the conduction mode electrohydrodynamic instabilities, exhibited by homogeneously aligned negative dielectric anisotropy nematic liquid crystals, on the conductivity of the nematic material, the thickness of the nematic layer and the intensity of an orienting magnetic field, is examined. It is found that for sufficiently high conductivity and/or large layer thickness, the cut-off frequency is proportional to the conductivity of the material, and independent of the intensity of the orienting field. Lowering the conductivity and/or the thickness of the nematic layer results in smaller values of the ratio of the cut-off frequency to conductivity, until a critical limit is reached beyond of which no conduction mode of instability has to be observed. It is found also that for given values of conductivity and thickness, the effect of the orienting magnetic field is to lower the cut-off frequency of the instability and, also, to increase the critical conductivi...

Leading term approximative analytical formulas are derived for the powers of the fringes formed by a periodically distorted homogeneous nematic layer, illuminated by a monochromatic light beam at normal incidence. The agreement between the predictions of the derived formulas and those of the direct numerical computation for the odd-order fringes is restricted to very small distortions and, thus, to very low fringe power values. On the other hand, the respective comparison for the even-order fringes gives quite satisfactory results provided the sample is sufficiently thick and the order of the fringe is low.

The grating effect, observed when a homogeneously aligned and periodically distorted nematic liquid crystal layer (in the bend-spaly mode) is obliquely illuminated, is theoretically considered from a geometrical optics point of view. The basic characteristics of the effect, namely, the much more intense fringes obtained from a weakly distorted layer, compared with those formed in the normal incidence case, the asymmetry of the fringes, and the equal importance of the even- and odd-order fringes are revealed. Also, a formula is derived which satisfactorily predicts the dependence of the fringe power on the distortion amplitude of the nematic layer.

A formula has been derived for predicting the intensities of the first-order fringes that result from the illumination of a periodically reoriented nematic liquid-crystal layer that is excited electrohydrodynamically in the dielectric mode. The agreement between the predictions of the derived formula and those of the more rigorous theory is excellent. It turns out that the intensities of the first-order fringes are proportional to the square of the maximum angle formed between the director and its orientation direction in the undistorted state. It also turns out that these intensities are highly sensitive functions of the incidence angle of the monochromatic light beam that is illuminating the nematic layer; they exhibit two pronounced maxima that correspond to two different incidence angles that are determined by the material and distortion parameters as well as by the wavelength of the illuminating beam. The derived formula is an essential tool for monitoring the motion of the nematic director during electrohydrodynamic excitation in the dielectric mode.

A theoretical approach to the fascinating effect of the grating action of a periodically distorted nematic liquid crystal layer, under the realistic assumption of small distortion angles, is presented. The approach, being wave optical, equips us with tools that permit us (a) to test and fit data obtained during electrohydrodynamic instability experiments, (b) to furnish criteria for the extent of validity of the geometrical-optical methods, and (c) to have at our disposal easy-to-compute results for testing computational methods of more general validity.

The ability of homogeneously aligned nematics with a positive dielectric anisotropy to exhibit Williams Domain as a threshold effect is numerically investigated. A simplified two-dimensional model which has, already, given satisfactory results in the negative dielectric anisotropy case is used. The frequency dependence of the threshold fields obtained for materials with small dielectric anisotropies is in satisfactory qualitative agreement with the known experiments. The frequency dependence of the threshold spatial wavenumbers is calculated. In accordance with earlier work, a positive dielectric anisotropy nematic which normally does not exhibit Williams Domains, does so under the action of a stabilizing magnetic field. This effect is confirmed and the frequency dependence of the threshold fields as well as the assoiated threshold spatial wavenumbers, for various values of the stabilizing field, are calculated. In addition, the model predicts the existence of a class of positive dielectric aniso...

In a recent paper1 a method has been presented for the numerical computation of the electrohydrodynamic (EHD) instability limits and the corresponding director spatial wavenumbers (DSW) of a homogeneously aligned nematic cell, under the action of square-pulse electric field. The results obtained, using the physical constants of the room temperature nematic MBBA,2-5 was in satisfactorily good agreement with experiments. The aim of this note is to present the results of the application of the model used in Ref. 1 to the case where the exciting electric field is a sinusoidal one. Such an application has already been published for the one-dimensional model,6-8 as well as, for the two-dimensional one.9 It is well known, however, that the calculations based on the one-dimensional model do not permit the explicit calculation of the DSW at the conduction mode (CM) thresholds.10 On the other hand, the calculations of Ref. 9 are restricted to the CM of EHD instability under the, only approximately true, as...

A linear, two-dimensional formulation of the problem of the electrohydrodynamic instability limits of nematic liquid crystals is presented. The nematic is assumed to have negative dielectric anisotropy, homogeneous alignment, and to be excited by a square-pulsed electric field. The formulation enables one to determine, using digital computational techniques, the limiting values of the electric field for the instability and the respective spatial wavenumbers of the nematic director, at both, the conductivity and the dielectric, regimes. The method consists, essentially, in solving a system of two equations in terms of the applied electric field and the director wavenumber, so to retain, among the solutions, those giving the maximum and minimum values of the field. The program was applied to the case of the room temperature nematic N-(p-Methoxybenzylidene)-p-Butylaniline (MBBA). The results are found to be in good agreement with the known experimental facts.

The problem of the grating action of a periodically distorted nematic liquid crystal layer, in the geometrical optics ray approximation is considered, and a theory for the calculation of the fringe powers is proposed. A nonabsorbing nematic phase is assumed, and the direction of incidence is taken to be normal to the layer. The powers of the resulting diffraction fringes are related to the spatial and angular deviation of the rays propagating across the layer and to the perturbation of the phase of the wave associated with the ray. The theory is applied to the simple case of a harmonically distorted nematic layer. In the case of a weakly distorted nematic layer the results agree with the predictions of Carroll's model, where only even-order fringes are important. As the distortion becomes larger, odd-order fringes (with the exception of the first order) become equally important, and particularly those at relatively large orders (e.g., seven and nine) exhibit maxima greater than that of the even-order neighbors. Finally, the dependence of the powers of odd-order fringes on the distortion angle is quite different from that of the even-order fringes.