Liquid crystal director escape

For a disclination with the strength S, as one approaches the center of the disclination, the elastic energy diverges, as shown by Equation (1.124). In reality this will not occur. The liquid crystal will transform either into isotropic phase at the center of the disclination or a different deformation where there is no singularity. Here we only discuss the cases of cylindrical confinements (two-dimensional confinement) where it is possible to obtain analytical solutions. The mechanism of liquid crystal director escape in spherical confinement (three-dimensional confinement) is similar to that of two-dimensional. 

Figure 1.21 Liquid crystal director configurations in the cylinder (a) escape from splay to isotropic phase, (b) escape from splay to bend, and (c) escape from bend to twist.

The second possibility to avoid the singularity at the center of the cylinder is to escape from the splay deformation to the bend deformation, as shown in Figure 1.21(b) [30-32]. The liquid crystal director tilts to the z direction and is given by... 

For most liquid crystals, the twist elastic constant is smaller than the bend elastic constant Therefore it is possible to reduce the total elastie energy by escaping fi om the bend deformation to the twist deformation as shown in Figure 1.21(c). The liquid crystal director is no longer on the r-z plane but twists out of the plane and is given by... 

The sensitivity of deuteron NMR to the molecular orientational order and to director field configurations turned out to be extremely useful in studies of liquid crystals confined into snbmicrometer pores. Moreover, the large surface-to-volume ratio of these composite systems render the interfacial and surface phenomena, induced by the liquid crystal-surface interactions, accessible even to an essentially integrative technique like NMR. Since the discovery of polymer dispersed liquid crystals (PDLCs) in 1986 [4], NMR of selectively deuterated liquid crystals was used to discriminate unambiguously among various director structures in cavities, resulting from an interplay between elastic forces, morphology and size of the cavity, and surface interactions. These structures include the escaped-radial, planar axial, planar-polar, and... 

Another example is formation of boodjooms at the cell surfaces. Now we are interested not in the linear disclinations responsible for the SchUeren texture but in their nuclei at the solid substrates limiting a liquid crystal cell. The linear discUna-tions of strength s = 1 may annihilate within the bulk due to some reconstruction of the director field induced, for instance, by temperature or a flow of the material. For example, a bulk discUnation of strength s = +1 shown by the solid vertical line in Fig. 8.18b disappears but its nuclei localized at the surfaces transform into new, surface defects. Fig. 8.18c illustrates the situation at one of the two surfaces. The escaped line leaves behind it a boodjoom. We meet such a situation in thick planar cells where the Schlieren textures with four brushes are observed. 

Textures of the phase in lyotropic liquid crystals have been studied in capillaries. An example of the textures and the corresponding director-field is shown in Figure 6.7. In comparing with Figure 6.4, we note that the center defect line disappears, as a consequence of the biaxiality although nj escapes along the capillary axis (and would be dark in uniaxial system between one of the crossed polarizers set parallel to the capillary axis), n2 will have no extinction there. 

---