Screw disclinations

The properties of disclinations in nematics bear some striking similarities with screw disclinations in crystals and vortex hlaments in superfluids, but at the same time there are important differences that cannot be overlooked while drawing detailed analogies. ... 

Fig. 4.2.2. A pair of like /-screw disclinations forming a stable double helix in a cholesteric (a) a pair of x = disclinations (after Cladis, White and Brinkmann " ), (b) a pair of 5 = I disclinations (after Rault ) see fig. 3.5.24.

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. 

The situation is simpler if the column lattice is helically distorted perpendicular to the column axes blocks of parallel columns are stacked on top of each other with a finite angle between the columns of adjacent blocks (Figure 11.10) [18], The blocks are thus separated by planar tilt grain boundaries, and parallel linear screw disclinations lie within these boundary planes (Figure 11.11). This structure is perfectly analogous to the twist grain boundary phases of chiral smectic liquid crystals. 

Figure 11.11. A single screw disclination in a tilt grain boundary phase.

The dark horizontal line is the screw disclination. (Reprinted with permission from Phys. Rev. E 53, 650 1996, American Physical Society [17].)... 

For f-screw disclinations (see the nematic wedge disclinations discussed earlier) there is a singular line along the z axis (i.e., parallel to the helix axis) and the director... 

As a result of the layered nature of the chiral nematic structure, like the smectic A, it can also exhibit focal-conic textures [79] and both phases exhibit screw and edge dislocations. A dislocation corresponds to a displacement of the layered structure in a plane orthogonal to the layer and may be formed by the pairing of two disclinations of opposite sign. A screw dislocation has a singular line along the screw axis and is equivalent to a f-screw disclination in a chiral nematic. An edge dislocation corre-... 

Another type of interpretation of the textures was proposed by Nas-tishin et al., who suggested that the By phase is a smectic and columnar phase at the same time. The geometry of the helical filaments (ribbons) is that one of the central region of a screw disclination with a giant Burgers vector split into two disclination lines of strength V2/ which boimd the ribbon. 

The helical structure of the c-director in the smectic C phase makes the defects different from those in the smectic C phase. As the Volterra process produces a screw dislocation, for example, along the z axis and the Burger vector b = d, it must be accompanied by a parallel wedge disclination in the c-director, in the form... 

However, an important parameter that has been ignored in this approach is the surface tension at the interface. The interfadal tension T can be taken into account in an elementary way as is generally done for crystal screw dislocations. The total energy of the disclination in the one-constant approximation, including the energy at the core surface, is... 

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... 

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). 

Apart from seamless cones, there are conical structures that are formed by introducing a wedge disclination (Fignre 3.12a) and a screw dislocation (Figure 3.12b) in a graphite sheet, as observed... 

The equivalence just demonstrated for screw dislocations versus wedge x disclinations can be extended to edge dislocations (Figure 5.12) versus twist X disclinations and even further, to mixed dislocations and disclinations, for the simple reason that the two corresponding Volterra processes are the same. 

Figure 5.11. Equivalence in the presentation of / lines (a) wedge /" disclination = screw dislocation (b) /-twist disclination = edge dislocation and (c) splitting of the core of a dislocation into a pair of disclinations.

To identify the antiferroelectric phase, texture observation of the homeotropic cells of racemic compounds is very effective. In the SmC phase, only the schlieren texture with four brushes is observable and that with two brushes is prohibited, because of the head-and-tail inequivalence of the C-director. In the SmCA phase, however, the schlieren texture with two brushes is sometimes seen, as shown in Figure 9.8 [18], [19]. The existence can be explained by taking into account a screw dislocation, as illustrated in Figure 9.9. The discontinuous change (7r-wall) of the C-director is compensated by the screw dislocation. This defect is a combined defect of a disclination and a dislocation, i.e., adispiration [18], [19]. 

Figure 9.9. Model structure of the two-brush defect i.e., dispiration, a combined defect of a wedge disclination and a screw dislocation.

Figure 16. Creation of defects in a smectic A phase, (a, a ) Creation of a right-handed screw dislocation, (b, b ) Creation of an edge dislocation, (c, c ) Creation of a stack of nested conic layers, as observed along focal conics, (d, d, d") Creation of a disclination from a planar cut surface limited by a line L a +jt separation of lips S] and S2 is followed by the addition of matter and relaxation.

Figure 17. The Volterra process applied to cholesteric phases. The core structure is masked by a cylinder along the line L. (a, b) Edge and screw dislocation, (c-e) A section S limited by L, normal to the cholesteric axis, allows one to build either the edge dislocation (a) or a disclination (d), as in smectics (Fig. 16d and d"). (f, g) Construction of the opposite disclination. (Drawing made in collaboration with F. Livo-lant).

Disjunctions into disclination pairs are general in liquid crystals when the Burgers vector is large enough, and this holds for both edge and screw dislocations. This was first considered for edge dislocations in cholesterics [2, 3], but also applies to screw dislocations (see Fig. 24i and j). 

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