Perpendicular disclinations

Fig. 9.8. (a) Distribution of the director around a singularity line or disclination, perpendicular to the plane of the figure, (b) Different types of singularity... 

Figure 10.21 Classes of disclinations in a nematic, with the disclination line perpendicular to the plane of the page. [From Larson 1988 (adapted from Chandrasekhar 1992), with permission from Cambridge University Press.]...

For example. Fig. 2 shows a SchHeren texture, which is typical of nematic distortions of the director field (visible as dark branches usually named brushes). These distortions are induced by the perpendicular anchoring on the microscope slide of topological defects, called disclination lines, which are numbered from 1 to 7 in Fig. 2. These disclination lines can be classified into two groups according to their local topology as the dark brushes seen around these defects can rotate either clockwise or counterclockwise as the crossed polarizers are rotated simultaneously while the sample is kept fixed. This is due to the two different possible defect topologies illustrated in Fig. 2 for cases 1 and 2 [1]. 

As remarked in chapter 1, the nematic state is named for the threads that can be seen within the fluid under a microscope (fig. 1.1.6(a)). In thin films sandwiched between glass plates these threads can be seen end on. A typical example of the texture in a plane film of thickness about 10 /tm between crossed polarizers - the structures a noyaux or schlieren textures - is given in fig. 1.1.6(6). The black brushes originating from the points are due to line singularities perpendicular to the layer. In analogy with dislocations in crystals, Frank proposed the term disinclinations , which has since been modified to disclinations in current usage. 

In this case the singular line is perpendicular to the twist axis. On going round this line, one gains or loses an integral number of half-pitches. The director pattern around the -edge disclination was first worked out by de Gennes who proposed a nematic twist disclination type of solution ... 

The Volterra process for creating these disclinations is the same as for nematic disclinations. For the screw disclination the plane of cut is parallel to the cholesteric twist axis while for the edge disclination it is perpendicular to it. 

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.

It is also possible to have points with 5 = +1/2 joined by line singularities in the nematic phase these 7t disclinations, which are commonly known as threads, pass through the preparation almost perpendicularly with the ends attached to the glass surfaces. Figure 3B shows the topology about s = + 1/2 singularity line the end appears as a point on the... 

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. 

As the incidence angle is made smaller, the irregular shape of the disclination lines changes. At 45° beam incidence (Fig. 5) all disclinations run in the beam direction. Again, turning the cell between crossed polarizers changes the transmission only slightly. It appears that two preferred orientations are established. The director is either in the beam direction or perpendicular to it. The parallel disclinations separate areas of reverse twist. 

The cholesteric texture occurring with perpendicular boundary orientation, on the other hand, is not a uniform texture. Under the microscope the entire field of view is filled with right-and left-handed spirals. This cholesteric texture is known as the scroll texture and appears very much like an end-on view of a bundle of rolled-up scrolls. Capacitance measurements show that the cholesteric helical axis in this texture is still predominantly perpendicular to the plane of the layer. An exact analysis of the structure of this texture, even for the case of equal elastic constants, seems difficult to achieve. Important from the applications point of view is that the scroll texture is adopted without disclinations immediately after a display element is turned off and that this structure is essentially nonscattering. Homeotropic boundary orientation therefore solves the problem of display after-images. 

In order to do this, consider a disclination line viewed from the end and mark the tangents to the director field in the plane perpendicular to the line (see Fig. 9.8a). The schematic corresponds to what is easily observed in thin layers, without special treatment of the substrate, when molecules are confined to the plane of the layer. The resulting texture is called a Schlieren texture. The strength or rank of the line S is defined as the total rotation Q of the director along a closed path around the line, divided by 2tt (i.e., Q = 27tS ). It is attributed a sign -f or — depending on whether the director rotation occurs... 

Nematic phases typically show a schlieren texture between crossed polarizers if the director is oriented perpendicular to the viewing direction. One feature of the schlieren texture is the occurrence of topological point defects. At these point defects either two or four dark brushes meet. The corresponding defects are denoted as 1/2 or 1, respectively. Further characteristic textures of the nematic phase are the thread-like texture, which exhibits n disclinations parallel to the substrate, and the marble texture, in which areas of differing uniform director orientations occur. 

Optical measurements provide valuable information about alignment kinetics, and electron microscopy of aligned samples provides clues about the alignment process. Microtomed slices were taken fi om PS-PMMA block copolymer materials that were aligned in an electric field (far from the edges of the samples) [65]. Alignment was verified by SAXS. Some slice planes were parallel to the electrodes (parallel slices) and others perpendicular to the electrodes (perpendicular slices), as shown in Fig. 27. The slices were stained with ruthenium tetroxide and viewed with a transmission electron microscope. Several classes of defect structures were observed +1/2 disclination lines and defect walls were most prevalent, and... 

FIGURE 28 Transmission electron micrographs of microtome slices of an aligned PS-PMMA block copolymer sample. In (a), the slice plane was perpendicular to the electric field direction, and in (b) and (c) the slice plane contained the electric field direction. Intersection of the slice plane with +1/2 and -1/2 disclination lines and wall defects (denoted with a w ) are indicated in (a). (Reprinted with permission from Ref. 65.)... 

Not only are disclination lines aligned along the field direction, but also wall defects are anisotropically distributed in the aligned sample. This is best understood by first defining a rotation axis for a wall defect. A rotation plus a translation is required to map the lamellar pattern on one side of a wall defect to the other. I refer to this rotation axis as the rotation axis for the wall. If the wall contains its rotation axis, it is a bend wall, and if the axis is perpendicular to the wall, it is of twist character. The wall is of mixed character if the rotation axis is in between. In the field-aligned sample, the rotation axes of the wall defects are aligned predominantly along the direction of the applied field, e.. Thus, walls with normals parallel to S. have primarily twist character, and walls with normals nearly perpendicular to S. have primarily bend character. Examples of bend walls are indicated in Fig. 28a. 

What do these axial disclinations look like in a hqnid crystal The best way to observe them is with the sample between crossed polarisers. As will be discussed at length later, liquid crystals are birefringent, so only light that is polarised parallel or perpendicular to the director is transmitted unchanged. This means that regions of the liquid crystal where the director is parallel or perpendicular to one of the crossed polariser axes are dark. The rest of the liquid crystal is bright. This results in dark bands emanating from a disclination where the director points in either of two perpendicular directions. Thus there... 

There are other dischnations besides axial disclinations that form in nematic liquid crystals. In axial dischnations, the rotation axis of the director in traversing a loop aroimd the disclination is parallel to the disclination. In a twist dischnation, the rotation axis is perpendicular to the disclination. Figure 2.15 shows +1/2 and +1 strength twist dischnations in which the rotation axis for the director is along the y-axis and the dischnation points along the z-axis Due to the fact that the director twists, an entirely new class of dischnations form in chiral nematic liquid crystals. Likewise, the spatial periodicity of both chiral nematic and smectic hquid crystals ahows for defects in the perio(hc stmcture in addition to defects in the director configuration. These additional defects are quite different and resemble dislocations in solids. 

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