Surface disclination line

Note A nucleus can indicate either the end of a disclination line terminating at the surface of a sample or an isolated defect. 

Thick, thread-like disclination line anchored along its length to the upper or the lower of the surfaces between which a sample is placed. 

Disclination lines are energetically disfavored because they produce gradients in the director profile and Frank stresses. So if the sample is left alone, the disclination lines and loops spontaneously shrink in length and annihilate one another (see Fig. 10-22) until no disclinations are left—except for any that are pinned by any impurities in the fluid or by wall irregularities, and those trapped because of incompatibilities in anchoring conditions at surfaces (Chuang et al. 1991 Nagaya et al. 1992). 

Parabolic focal conics are a special case of generic focal conic defects, which are composed of layers curved to form toroidal surfaces called Dupin cyclides (see Fig. 10-31). Each such structure contains a pair of disclination lines—one an ellipse and the other... 

The threaded texture is also often observed for nematics especially when a thicker film is examined. In this texture disclination lines show up as dark lines swimming in the sample with thermal motion. The lines are observable without polars (Figure 4.17) but the thread contrast will be higher when crossed polars are used. Because of the stopless molecular reorientation with thermal motion in the sample the old dark lines may disappear and new ones may form. In cases when the two ends are anchored on the surfaces the ends will stay where they have been but the thread may swing about. 

The Volterra process for creating a loop, i.e., a closed disclination line, in a nematic is as follows. Let S be the surface enclosed by the loop L. Call the two sides of the surface and S . Rotate the molecules in contact with... 

Fig. 7.19. Left The 180° slips in the grating structure ensure stability of the selected states as they pin the disclination lines. Right Scanning electron microscopy image of a surface grating showing the slips. The image also shows regions with different pitch gratings allowing for greyscale. Prom Jones,reproduced with kind permission of the Society for Information Display.

At the disclination the main orientation of the director is perpendicular to the surface the lines are black at crossed polarizers but white for parallel polarizers. 

In this section we consider the interaction between a particle and a wall. We first present the results from the theory. Figure 1.2.2 shows the director profile and scalar order parameter maps for a particle of radius R = 0.36 located at the surface of a wall. Comparing these maps with those for a particle further away, (Fig. 1.2.2 ), we observe that the disclination line is no longer at the equatorial plane, but is shifted towards the wall. Similar deviations of the position of the ring are observed in the Monte Carlo simulations. 

As mentioned earlier, most studies of field interactions with liquid crystals are done using thin films with a well-defined initial state, usually a monodomain or a thin film with a simple distortion induced by incommensurate surface anchoring. These conditions simplify observation and theoretical analysis. However, most liquid crystal materials that are not specially prepared contain topological defects that are very important to their response to external fields. One class of defect commonly observed in nematics is the disclinalion line. At a disclination line the director field is ill defined. The director field turns around the disclination line a multiple of half-integer times. Several disclination lines are shown in Fig. 8. 

Defects can also be trapped by an object submerged within the liquid crystal. For example, Terentjev [29] gave a theoretical description of a -1/2 disclination line bound just outside the surface of a colloidal particle in a nematic fluid, as illustrated in Fig. 11. Here, also, one can imagine an applied field changing the equilibrium loop size. The response depends not only on viscosity but also on the elastic constants and the defect core energy. 

Figure 5.4. Blue phases are composed of regions with double twist three such regions, with a singularity that relieves frustration between them, are shown in the figure. Two cylinders with double twist match at the contact point if the director tilt at their surfaces is h/4 however, the region where all three cylinders meet is singular. In current models, such singularities form a network of disclination lines. The circle marks the core of the disclination the insert shows the director lines around the core.

It is instructive to examine boundary disclination lines at a nematic surface or interface by introducing some additional modelling and approximations that incorporate surface tension and the effect due to gravity. Many of these aspects introduced here in this Section are common throughout the literature on liquid crystals and will also form a basis for the discussion on point defects at a free surface of nematic discussed in the next Section. The results presented below are based on those derived by de Gennes [107] and have been further elucidated in physical terms by de Gennes and Prost [110]. 

In some preparations, the disclination lines do not lie perpendicularly, but more or less horizontally, their ends being attached to the glass surfaces and the other parts floating freely in the LC. The term threads is usually used to describe these disclination lines and the corresponding texture is the threaded texture. 

Fig. 22. (a) Identification of the angles and 6 used to describe a disclination. (b) Director arrangement of an 5 = I/2 singularity line. The end of the line attached to the sample surface appears as the point s = + V2 (points P). The director alignment or field does not change along the z direction. The director field has been drawn in the upper and the lower surfaces only. 

Texture with n-line disclinations which lie essentially parallel to the surfaces between which a sample is placed, with the ends of the lines attached to the surfaces and the other parts of the lines moving freely in the liquid crystal, appearing as thin thread-like lines. 

---