Smectic liquid crystals edge dislocations

Figure 10.7. Edge dislocations in a smectic liquid crystal. The value of the path integral of n - ds along a closed loop is always an integer which corresponds to the number of inserted layers. According to de Gennes (14), this is the liquid crystal analog of the magnetic flux quantization in superconductors.

In addition to focal conic singularities, smectic liquid crystals exhibit edge dislocations in the layer spacing, i.e., a layer can be added that does not extend throughout the entire material (Figure 6.11). Such edge dislocations are difficult to observe, because the layers are typically 3 nm in thickness. The introduction of edge dislocations allows some bend in a texture if the boundary conditions require it. 

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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