Disclinations biaxial nematics

Figure 11. The three possible half integer disclination lines in the biaxial nematic phase of Vectra B 950 . (a) Rotation around the X axis, (b) rotation about the Y axis and (c) rotation around the Z axis [53], It is worth noting that the Ey line is perpendicular to the main director Y.

One of the most spectacular consequences of noncommutativity of the group Q is the possibility of a topological entanglement of the disclinations. Originally, the problem was considered by Toulouse for biaxial nematics [42], but it apphes to any medium with a non-Abelian fundamental group [50]-[52. ... 

The uniaxial nematic (Ny) phase usually exhibits a schlieren texture with two and four point singularities (two and four brushes). However, the texture exhibited by complex 2, shown in Fig. 4, often consists of [S] = l/2 (two-brush) disclinations similar to that exhibited by a smectic C phase. Also, this complex showed zig-zag disclinations [24] occasionally, and since this type of disclination has been observed in N phases [25] it cannot be regarded as conclusive evidence for biaxiality. It is also possible that an entanglement of disclination lines may lead to topological rigidity, as discussed by Toulouse [26] and others [27-29]. These possibilities have not been examined experimentally. Hence optical textures that... 

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