Disclinations chiral nematics

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

Usually the Cano method [8] is used for chiral nematic liquid crystals. It can also be applied to SmC phases, but then the demands on the orientation of the liquid crystal are more extensive as a nearly perfect orientation of the layer normal k as well as of the c-director are required. The presented method utilizes the different thicknesses which occur in a sample if a lens is placed on top of it. A sketch of this is shown in Fig. 4.6a. Due to the anchoring conditions, only helical structures with integer multiples N of the pitch p are allowed and regions with different values of N are separated by disclination lines [14]. Thus, a picture similar to the one shown in Fig. 4.6b occurs [15]. If the radius of curvature Rc of the lens is known, the value of the pitch p can be calculated according to [9]... 

There are other dischnations besides axial disclinations that form in nematic liquid crystals. In axial dischnations, the rotation axis of the director in traversing a loop aroimd the disclination is parallel to the disclination. In a twist dischnation, the rotation axis is perpendicular to the disclination. Figure 2.15 shows +1/2 and +1 strength twist dischnations in which the rotation axis for the director is along the y-axis and the dischnation points along the z-axis Due to the fact that the director twists, an entirely new class of dischnations form in chiral nematic liquid crystals. Likewise, the spatial periodicity of both chiral nematic and smectic hquid crystals ahows for defects in the perio(hc stmcture in addition to defects in the director configuration. These additional defects are quite different and resemble dislocations in solids. 

J. Bezic and S. Zumer, Chiral nematic liquid crystals in cylindrical cavities A classification of planar structures and models of nonsingular disclination lines, Liq. Cryst. 14, 1695 (1993). 

Figure 9. Typical Cano-wedge textures for a chiral nematic. The Grandjean-Cano disclination lines occur at the blue-yellow interface. The slightly curved distortion shows how sensitive the technique is to undulations in the glass of the wedge cell used here.

Figure 13. The director pattern for s= A%-tdge disclinations in a chiral nematic. The filled in dots signify that the director is orthogonal to the plane of the figure, the dumbbells that it is in the plane, and the pins that it is tilted in a spiraling structure.

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. 

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-... 

Figure 14. The director configurations around defects leading to (a) A, (b) A, (c) r, and (d) r disclinations in a chiral nematic. The dumbbells, pins, and dots have the same significance as in Fig. 13 and the black star circles L represent the disclination lines.

Figure 8.14a, c shows double twist cylinders, and the bold black lines in Fig. 8.14b, d show disclinations (defect Unes). In each double twist cylinder, the molecules are radially twisted towards each other through 90°. The molecules are parallel to the cylinder axis at the cylinder center and are tilted by 45° at the outer radial periphery. In other words, the molecules twist from —45° to -t45° through the cylinder, which corresponds to a quarter pitch. The diameter of a double twist cylinder is typically about 100 nm, and a simple calculation shows that approximately 200 molecules with a diameter of 0.5 nm mildly twist against each other. The lattice constant for blue phase I corresponds to a one helical pitch, and the lattice constant for blue phase II corresponds to one half helical pitch. We generally see a very small mismatch in pitch length with that of the lower-temperature chiral nematic phase. Peculiar to soft matter, a complex hierarchical structure is formed in... 

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