Edge disclinations

Fig. 4.2.4. The director pattern for -edge disclination in a cholesteric. Dots signify that the director is normal to the plane of the diagram, dashes that it is parallel to and nails that it is tilted.

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. 

Xj < 2A0Z3 and attractive for x > 2AoZ,. Thus, as in the case of smectic A (see fig. S.4.7), there can result a clustering of like edge disclinations to form a grain boundary . Such clustering is often observed in fingerprint textures (fig. 4.2.7). 

As for achiral disclinations, the Volterra process may be used to create screw or edge disclinations by cutting parallel or perpendicular, respectively, to the chiral nematic twist axis. 

Figure 15. Schematic representations of the pairing of A and t disclinations of opposite signs in achiral nematic. The schematic diagrams show edge disclinations comprised of (a) A and A, (b) T and r, (c) r and A, ...

E phases, calamities 12 edge disclinations, chiral nematics 354 Ehrlich magic bullet, chromonics 984 elastic constants 63, 79 ff... 

It is named the wedge dispiration, designated as (b,—b/p). Similarly, an edge dislocation of the Burger vector b must be accompanied by a partial twist disclination, designated as the twist dispiration (b,b/p). 

Fig. 3.5.4. Brushes connecting a pair of disclinations of equal and opposite strengths, s = 1 and — 1, in nematic MBBA. Crossed polarizers rotated clockwise by 22.5° in each successive photograph. In (d) the directions of extinction are parallel to the edges of the picture. (Nehring and Saupe. )...

Ideal graphite does not exist and the ideal crystal forms invariably contain defects, such as vacancies due to a missing atom, stacking faults and disclination as depicted in Figure 2.18. Other defects include screw and edge dislocations (Figure 2.19). Edge defects find some... 

Fig. 8.28 Illustration of the difference between a 7t-disclination and an edge dislocation in the smectic A...

The defects that can occur in BCP nanopatterns can take several forms and it is beyond the scope of this chapter to detail these in full, however, it is worth providing a general overview. They take the form of many structural defects in other systems and can be broadly described as dislocations and disclinations and a good review is provided elsewhere (Krohner and Antony, 1975). In the simplest explanation, a dislocation is a defect that affects the positional order of atoms in a lattice and the displacement of atoms from their ideal positions is a symmetry of the medium Screw and edge dislocations representing insertion of planes or lines of atoms are typical of dislocations. For a discUnation the defects (lines, planes or 3D shapes) the rotational symmetry is altered through displacements that do not comply with the symmetry of the environment. Kleman and Friedel give an excellent review of the application of these topics to modern materials science (Kleman and Friedel, 2008). 

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... 

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. 

Disclination lines must either form complete loops or end at the edge of the sample or, more likely, at a wall defect (Fig. 35b). For the defect wall to translate, the total length of lines will change. For this reason also, the wall energy loses translation invariance. 

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