Liquid crystal edge dislocations

Fig. 6. Isolated edge dislocation. System composition liquid crystal, 98.4%wt silicone oil...

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.

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-... 

Disjunctions into disclination pairs are general in liquid crystals when the Burgers vector is large enough, and this holds for both edge and screw dislocations. This was first considered for edge dislocations in cholesterics [2, 3], but also applies to screw dislocations (see Fig. 24i and j). 

Figure 41. Creation of defects in a lamellar liquid crystal, (a) Edge dislocation due to a layer rupture, (b) Deformation of an edge dislocation into the helical structure of a screw dislocation, (c) Differentiation of an elementary pinch, (d) A pair of elementary pinches transforming into a pair of edge dislocations.

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. 

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