Disclination strength

An important conclusion obtained from Equation (1.33) is that the deformation energy is proportional to the square of the disclination strength to. The equation is derived for a special case but the above conclusion is universal, with only the coefficient being different. It is expected that a to = 2 disclination is likely to divide into two to = 1 disclinations or so, in order to achieve a more stable configuration. 

Many liquid crystalline polymers exhibit Schlieren textures, which display dark brushes. These correspond to extinction positions of the mesophase. At certain points, two or more dark brushes meet at points called disclinations see Figure 7.11 (27). The disclination strength is calculated from the number of dark brushes meeting at one point ... 

Liquid crystals may have line defects called disclinations. The name comes from discontinuity and inclination. The director rotates about a line normal to the disclination. The strength of a disclination, S, is defined by... 

Figure 8. Wedge disclinations, with rotational strength -it, in a cubic crystal and in a liquid crystal. Note that the molecular scale of the liquid crystal is much larger than the atomic scale of the cubic crystal.

Figure 4. Isolated topological defects in a triangular lattice, (a) Isolated -1 and +1 disclinations. A vector aligned along a local lattice direction is rotated by 60° upon parallel transport around a unit strength disclination. (6) An isolated dislocation. The heavy line represents a Burgers circuit around the dislocation, and the Burgers vector of the dislocation is the amount by which the circuit fails to close. The core of the dislocation is a tightly bound pair of +1 and -1 disclinations (Reproduced from [78] by permission of Oxford University Press.)...

The local translational and orientational order of atoms or molecules in a sample may be destroyed by singular points, lines or walls. The discontinuities associated with the translational order are the dislocations while the defects associated with the orientational order are the disclinations. Another kind of defect, dispirations, are related to the singularities of the chiral symmetry of a medium. The dislocations were observed long after the research on them began. The dislocations in crystals have been extensively studied because of the requirement in industry for high strength materials. On the contrary, the first disclination in liquid crystals was observed as early as when the liquid crystal was discovered in 1888, but the theoretical treatment on disclinations was quite a recent endeavor. 

Figure 1.21(a), and rotate the two opposite slips of the cut A1 and A2 by 7T. 7r is a symmetry element. Insert a new sample piece of liquid crystals and arrange their director to fit the directors on the A1 and A2 slips, as shown Figure 1.21(b). The liquid crystals then relax themselves to the configuration shown in Figure 1.21(c). A disclination with the strength of —1/2... 

Figure 1.23. The director configurations of disclinations with various strengths.

The disclination line of m = 1/2 and disclination point of m = 1 are frequently observed in liquid crystals. In some cases high strength discli-nations may be observed, such as in a thin layer of small molecular mass liquid crystals, polymer liquid crystals, lyotropic liquid crystals, binary thermotropic liquid crystals, etc. 

In a nematic phase, the strength of disclination may have values that are half-numbered or whole-numbered. However because the disclination energy is proportional to s2 (Nehring and Saupe, 1972), it is rare to observe singularities with s > 1. In studies of a series of nematic polymers with two-dimensional mesogenic units Zhou and coworkers (1993) have been... 

Figure C2.2.8. The director field in a nematic around disclinations of various strengths, s. The director fields are given by equation (C2.2.2).

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