Twist disclination

J. J. Gilman, Plastic Relaxation via Twist Disclination Motion in Polymers, Jour. Appl. Phys., 44, 2233 (1973). 

Figure 9. Schematic models for the wedge and twist disclinations of the carbonaceous mesophase.

The configuration of Equation (1.32) is associated with a twist disclination. Both twist and wedge disclinations are shown in Figure 1.24, where the disclination line is normal to this sheet of paper. 

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). 

From the nature of the director patterns it is clear that dark brushes of the schlieren type will not be seen under the polarizing microscope for light propagating normal to the film (see 4.1.1). Twist disclinations may therefore be expected to be less conspicuous than wedge disclinations, and few observations have been reported of their existence in ordinary nematics. They do, however, reveal themselves under favourable circumstances in twisted nematics, often as loops separating regions of different twist. ... 

We now consider a twist disclination loop in a twisted nematic. The nematic is supposed to have a planar structure with the director parallel to the xy plane and an imposed twist of q per unit length about the z axis, and the disclination loop of radius R is supposed to be in the xy plane. The director distortions are planar, = cos = sin = 0. On going once round the disclination line at any point on the loop, the director orientation changes by 2tis, the sign of which may be either the same as that of q or opposite. 

Fig. 3.5.9. Shrinking of twist disclination loops (a) thin thread s = (b) thick...

A stability analysis has shown that twist disclinations are less favourable than wedge disclinations in elastically anisotropic media. This may explain why the former are so rarely seen in ordinary nematics. 

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 cholesteric pitch is altered around the singular line where N is an integer. The pattern for i = j is shown in fig. 4.2.4. Again, the energies and interactions in the one-constant approximation are the same as for nematic twist disclinations. A somewhat more elaborate treatment of this model has been presented by Scheffer and the effect of elastic anisotropy has been investigated by Caroli and Dubois-Violette. ... 

Fig. 5.8.5. Disclinations in the c-director field of smectic C. (a) 5 = 1 wedge disclination with a radial configuration (i) sink, (ii) source and (iii) meridian section of (i). (b)s= 1 wedge disclination with a circular configuration (i) vortex, (ii) antivortex and (iii) meridian section of (i) the nails signifying that the director is tilted with respect to the plane of the paper, (c) (i) = — 1 wedge disclination and (ii) s = 1 twist disclination.

The c-director field can also have twist disclinations, the structures of which are like those shown in fig. 3.5.8, except that the director is polar. The director pattern for s = 1, c = 0 is shown in fig. 5.8.5. 

The symmetry of the columnar phase also permits the occurrence of twist disclinations in the hexagonal lattice and of hybrids consisting of a twist disclination in the hexagonal lattice and a wedge disclination in the director field. According to Bouligand these defects are not likely to exist. 

In addition to the above-discussed discli-nations, which are referred to as wedge dis-clinations, there are twist disclinations. The director is always parallel to the xy plane, but the axis of rotation (z-axis) is normal to the singular line (y-axis). Figure 4 shows the director patterns for (a) 5=1/2, 6q=0 and (b) 5=1, 6[)=0. is a linear function of the angle 0=tan (z/x). 

We have so far assumed Kxx=K22=K =K. Real nematics are of course, elastically anisotropic. From the values of the energies of the disclinations calculated for the case where Ki =K22 K22 it follows that the wedge disclinations are more stable than the twist disclinations if A 22>A =Af i=A 33, and vice versa. Anisimov and Dzyaloshin-skii [38] have shown that lines of half-integral strength may be stable against three-dimensional perturbations if the twist elastic constant (22 i/2(A, j-i-A"3 3). More precisely,... 

Fig. 2.23 Disclinations, among aligned molecules in a chain-folded crystal lamella (a) a twist disclination that can be a part of a dispiration loop (b) a fold-over of two neighboring molecules and (c) a wedge disclination (from Li and Gilman (1970) courtesy of the American Institute of Physics).

According to Li and Gilman (1970) the energies of the twist-disclination and wedge-disclination loops are, respectively,... 

J.L. White and J.E. Zimmer. Twist disclinations in carbonaceous mesophase. Carbon 16,469-475 (1978). 

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.

Hwang, D. K., and A. D. Rey. 2006. Computational studies of optical textures of twist disclination loops in liquid-crystal films by using the finite-difference time-domain method. J. Opt Soc. Am. A. 23(2) 483. 

---