Parallel disclinations

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. 

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. 

Disclinations in tire nematic phase produce tire characteristic Schlieren texture, observed under tire microscope using crossed polars for samples between glass plates when tire director takes nonunifonn orientations parallel to tire plates. In thicker films of nematics, textures of dark flexible filaments are observed, whetlier in polarized light or not. This texture, in fact, gave rise to tire tenn nematic (from tire Greek for tliread ) [40]. The director fields... 

Disclinations can be expected when shear occurs between two parallel polymer chains (Gilman, 1973). This has been postulated to account for anelas-tic relaxation in some polymers at low temperatures. A general discussion of disclinations in polymers has been given by Li and Gilman (1970). 

Texture with n-line disclinations which lie essentially parallel to the surfaces between which a sample is placed, with the ends of the lines attached to the surfaces and the other parts of the lines moving freely in the liquid crystal, appearing as thin thread-like lines. 

The textures in homeotropic lamellar phases of lecithin are studied in lecithin-water phases by polarizing microscopy and in dried phases by electron microscopy. In the former, we observe the La phase (the chains are liquid, the polar heads disordered)—the texture displays classical FriedeVs oily streaks, which we interpret as clusters of parallel dislocations whose core is split in two disclinations of opposite sign, with a transversal instability of the confocal domain type. In the latter case, the nature of the lamellar phase is less understood. However, the elementary defects (negative staining) are quenched from the La phase they are dislocations or Grandjean terraces, where the same transversal instability can occur. We also observed dislocations with an extended core these defects seem typical of the phase in the electron microscope. 

Several examples of disclinations viewed parallel to the line of the disclination. 

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.)...

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... 

In terms of the Volterra process one can visualize the topological features of these disclinations in the following way. Cut the material by a plane that is parallel to the director. The limit of this cut is a line L called... 

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. )...

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. 

Such disclinations are closely analogous to nematic wedge disclinations ( 3.5.1). The singular line is along the z axis (parallel to the twist axis) and the director pattern is given by... 

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.

---