Nematic Texture and Volterra Process

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

Generally, microscopic observations reveal different types of defects, which may be 0-dimensional (points), one-dimensional (lines) and two-dimensional (walls). Typical nematic texmres are 

The thread texture usually observed in thick layers 

In Fig. 8.11 an example is given of a Schlieren texture in the nematic phase observed under a polarisation microscope. The polariser and analyser are always crossed and their positions with respect to photos (a) and (b) differ by 45° as shown by small crosses. On both photos characteristic brushes (threads) are seen originated and terminated at some points. The points are linear singularities (disinclinations or just disclinations) to be discussed below. Note the difference between a number of brushes originated or terminated in different points only two brushes in points 1 and 5 and four brushes in points 2, 3 and 4. It is evident that the pictures discussed are related to the local orientation of the director, i.e. to the structure of 

The major part of the arrows directed to the right in Fig. 8.12a correspond to the initial orientation of the director no in the planar nematic slab. However, the part of the slab shown by arrows directed to the left is virtually taken from the sample by some mysterious force , turned about axis Q through angle n and put back into the slab. After this operation called Volterra process, the director is everywhere again parallel to no due to the no = —no symmetry and such a structure in each of the two parts (initial and turned) is topologically stable. However, in the close proximity of the plane 2 , on the scale of molecular size, the director changes its orientation by 

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