Alignment defects disclinations

Fig. 23. Schematic representation of the director alignments at disclinations with different values of s and (J)o,s 72 correspond to two-brush defects and s = 1 to four-brush...

The word nematic comes from the Greek word urjpa, meaning thread, arising from the thread-like textures often seen in nematic samples. These threads correspond to lines of singularity in the director alignment called disclinations. Such defects will be discussed below in Section 3.8 after a more detailed mathematical description of nematic liquid crystals is given in Chapter 2. 

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.)...

Fig. 1. Schematic diagrams of the director field distortions black lines) around particles in an aligned nematic liquid crystal. For a normal anchoring of the liquid crystal molecules at the surface of the particles, there are two possible configurations, a Dipole configuration with a companion point defect (indicated by an arrow) located in the immediate vicinity of the particle, b Quadrupolar Saturn-ring configuration with a disclination ring surrounding the particle at the equator...

Fig. 8.18 Boodjooms. Structure of the director with two boodjooms in a nematic drop with tangential alignment of molecules at the surfaces (a), linear disclination with a point defect at the boundary of a nematic layer (b), and the same point defect (boodjoom) after aimihilation of the linear disclination (c)...

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. 

A very plausible alignment mechanism involves movement of defects. Here, forces on defect structures in an electric field are described. The actual material contains a large number of defects in many configurations, so a full analysis would be prohibitively complex. However, it is instructive to consider instead some simple ca.ses a general wall defect, a +1/2, -1/2 pair of parallel disclination lines, and two compound edge dislocations with opposing Burgers vector. 

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