Defects in the presence of an external field

The thickness of the Helfrich wail is of the order of 2, where is the magnetic coherence length defined as H k/Xs) (see 3.4.1), and the wall energy per unit length 

Such walls are associated with the Freedericksz deformation. With the homeotropic geometry of Fig. 3.4.1 (c), the possible distortions for H are illustrated in fig. 3.S. 16. Since the director tilt has a degeneracy in sign with respect to H, there can arise twist walls parallel to the field (fig. 3.5.16(6)) or splay walls perpendicular to the field (fig. 3.5.16(c)). Similarly with the homogeneous geometry, there can arise bend walls. 

Consider a nematic film of negative dielectric anisotropy (e 0) aligned homeotropically between glass plates. If an electric field is applied along the director axis (z axis) a distortion will set in when the field exceeds the critical Freedericksz value given by 

Two possible types of distortions are depicted in fig. 3.5.17. In the distorted state we have a ncomponent which is degenerate in the plane. Therefore, there can be defects in the field, and because of the synunetry in the xy plane, only defects of integral strength can occur. Such defects have been observed (fig. 3.5.18) and are called umbUics. They are somewhat similar to the 5 = 1 of the schlieren texture but differ in detail. Over a distance 

Other interesting cases have been investigated by Sunil Kumar and Ranganath.  

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