Electrohydrodynamic Modulated Structures

Kini [29] considered the electric field-induced static modulated structures of nematic liquid crystals. The electric field E was applied parallel to the sample, and the initial uniform director orientation was tilted with respect to the sample boundaries in the plane normal to E. The formation of modulated structures was shown to be favored when a stabilizing magnetic field H of sufficient strength was applied along the initial director orientation. This type of modulated instability was observed in experiment [30]. 

In nematic liquid crystals, subjected to an external electric field at a certain critical voltage, a periodic distribution of the space charge Q and the electric potential appears, resulting in the corresponding periodic variations of the initial director orientation L and the hydrodynamic fiow with the velocity v. This effect, known as the electrohydrodynamic instability (EHDI), could be visualized optically as a periodic pattern of domains. Fig. 5.5. In a screen, domains become visible as black and white stripes perpendicular to the distortion plane, where periodic director deformation and vortex liquid crystal movement is observed. These stripes are caused by the periodicity of the change in the refractive index for an extraordinary ray due to variations in the director. Fig. 5.6. These spatially periodic variations of the refractive index (domains) were first detected by Zvereva and Kapustin [32]. Then Williams [33] investigated transverse domains in detail, and it is current practice to call this type of instability Williams or Kapustin-Williams [34] domains. 

FIGURE 5.5. Electrohydrodynamic instability in nematic liquid crystals (a) the onset of the instabihty (b) the vortex motion of a Hquid crystal and (c) the picture of black-and-white stripes in the screen plane. 

If a monochromatic beam, for example, from a laser, is transmitted through a cell showing domain structure, a different pattern appears on a screen placed behind the cell. The diflEraction pattern takes the form of a chain of reflections arranged in the plane perpendicular to the domains [40, 41]. The angular distribution of the maxima and minima is described by the usual equation for diffraction from a grating with period w w is the period of the Kapustin-Williams domains)  

The nematic liquid begins to move with a velocity Vz under the action of the drug force proportional to —Q x)E, in accordance with the Navier-Stokes equation 

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Classification of the domain structures according to the physical origin of their appearance and the nature of the domain patterns. Two main types of modulated structures are discussed [4] orientational domains with pure director rotation without fluid motion, and electrohydrodynamic domains when the collective effect of the periodic director reorientation is observed together with regular vortices of the moving liquid. 

References [59] investigate the static and dynamic behavior of the electrohydrodynamic instability in fireely suspended layers of nematic liquid crystals. The existence of a domain mode was shown, which consists of adjacent elongated domains with a spatial period proportional to the thickness of the layer. This mode occurs only if the thickness of the layer exceeds a critical value 7 /x), and can be understood in terms of the same anisotropic mechanism as the Carr-Helfrich-type, as in the case of the Kapustin-WiUiams modulated structure. 

In this section we will consider another type of nonuniform liquid crystal structures in nematics. These structures are created by a spatially nonuniform electric field, and have nothing in common with the modulated orientational and electrohydrodynamic patterns discussed above which, in fact, were created as a result of self-organization. A spatially nonuniform electric field exists in an electrooptical cell in many important cases such as, photosensitive liquid crystal cells [152-154], spatial light modulators with matrix addressing [152], liquid crystal defectoscopy of surfaces [155], liquid crystal microlens [156], etc. By analyzing the liquid crystal electrooptical behavior in a nonuniform field we can estimate different characteristics of the layer, in particular, sensitivity (i.e., the intensity of the optical response at a given voltage), spatial resolution, etc. 

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