Nematics in Spatially Nonuniform Fields

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. 

Until recently, there was no actual investigation of the electrooptical properties of liquid crystals in a spatially nonuniform field, due to the cumbersome calculations involved and difficulties in their experimental verification. Now the growing interest of experimental physicists to this problem is observed [152, 156], which stimulates theoretical investigations on the subject [157-161]. 

Theoretical investigations of the electrooptical phenomena in nonuniform fields were performed [157], for different boundary conditions (homogeneous, homeotropic, and twisted) and different types of spatially nonuniform field. It was shown that the sensitivity and spatial resolution of a liquid 

The approach [157] could be most easily demonstrated for the homeotropic orientation of a liquid crystal [163, 164]. The first step is to obtain the distribution of the nonuniform electric field. We suggest that 

78) take place, then the nonuniform electric field in a liquid crystal cell does not depend on the director distribution L and is defined by the Maxwell equation 

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Nematic and cholesteric liquid crystals can be used for the nondestructive study of electrical defects in transistors and integrated circuits [81, 82], for the detection defects in film capacitors prepared by vacuum deposition [83], for the visualization of electrically active defects or rapidly diffusing dopants, as well as for quality control at various stages of integrating circuits production [84-86]. The most suitable effect for this purpose would appear to be the B effect [85] and the fiexoelectric effect in spatially nonuniform field [84, 86], which permits the distribution of the electrical potential in operating the integrated circuits to be visualized. 

We should also note that the visualization of defects by a nematic liquid crystal, based on the flexoelectric effect in a spatially nonuniform field, is significantly more efiicient than in the dynamic scattering mode [81, 82], because of the higher contrast, the lower visualization voltages (3 to 4 times), and the lower leakage current (about 10 times) [84-86]. 

An extension of rubber elasticity (i.e. of the description of large, static and incompressible deformations) to nematic elastomers has been given in a large number of papers [52, 61-66]. Abrupt transitions between different orientations of the director under external mechanical stress have been predicted in a model without spatial nonuniformities in the strain field [52,63]. The effect of electric fields on rubber elasticity of nematics has been incorporated [65]. Finally the approach of rubber elasticity was also applied recently to smectic A [67] and to smectic C [68] elastomers. Comparisons with experiments on smectic elastomers do not appear to exist at this time. Recently a rather detailed review of the model of an-... 

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