Nematic liquid crystal topological defects

Very large GB systems (over 80,000 molecules) have also been recoitly studied to investigate some of the most distinctive features of liquid crystals topological defects [27,28], until now simulated only with lattice models [29]. In particular, the twist grain boundary phase in smectics [27] and the formation of a variety of defects in nematics by rapid quenching [28] have been examined. 

The singularities in the liquid crystals cause the deformation of the director field of liquid crystals and thus affect the symmetry of liquid crystals. This idea provides an approach to analyze the characteristics of the defects. The order vectors (or scalars, or tensors) of various liquid crystals are not the same. The director n is the order vector of the nematic liquid crystals, but the order for the cholesteric liquid crystals is a symmetric matrix, i.e., a tensor. Because the order vector space is thus a topological one, any configuration of the director field of liquid crystals is thus represented by a point in the order vector space. The order vector space (designated by M) is associated with the symmetry of liquid crystals. The topologically equivalent defects in liquid crystals constitutes the homotopy class. The complete set of homotopy classes constitutes a homotopy group, denoted Hr(M). r is the dimension of the sub-space surrounding a defect, which is related to the dimension of the defect (point, line or wall) d, and the dimension of the liquid crystal sample d by... 

Keywords. Liquid crystal. Emulsion, Nematic, Topological defect, Silicone oU... 

Polymer-dispersed liquid crystals (PDLC) [7] are materials that consist of microscopic nematic droplets, with typical radii from a few hundred Angstrom to more than a micron, embedded in a polymer matrix (see Fig. 1). These systems are interesting both for technical applications and for an understanding of the behavior of mesophases in a confined environment. PDLC droplets also represent practical realizations of systems exhibiting topological defects of interest in many fields... 

Most studies of nematics in fields are performed on thin films where the initial director field is dictated by surface anchoring. The thin film permits easy observation, and a well-defined initial state simplifies analysis. It should be noted, however, that a typical bulk liquid crystal transformed from the isotropic state contains many topological defects. These defects are likely to play a central role in the response of liquid crystalline materials to external fields,... 

As mentioned earlier, most studies of field interactions with liquid crystals are done using thin films with a well-defined initial state, usually a monodomain or a thin film with a simple distortion induced by incommensurate surface anchoring. These conditions simplify observation and theoretical analysis. However, most liquid crystal materials that are not specially prepared contain topological defects that are very important to their response to external fields. One class of defect commonly observed in nematics is the disclinalion line. At a disclination line the director field is ill defined. The director field turns around the disclination line a multiple of half-integer times. Several disclination lines are shown in Fig. 8. 

This simple treatment of liquid crystalline defects is only applicable to nematics, and the detailed appearance of disclination lines will differ from the simple structures described above because of differences between the elastic constants for splay, twist and bend. In smectic phases, defects associated with positional disorder of layers will also be important, and some smectic phase defects such as edge dislocations have topologies similar to those described for crystals. The defect structures of liquid crystals contribute to the characteristic optical tex-... 

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