Defects 7, 117 twist disclinations

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. 

Experiments demonstrate that at even higher Er, the rolls become unstable and irregular. Ultimately, defect lines called disclinations form in the flow direction. As the linear analysis concerns the behavior of infinitesimal disturbances, the growth of the instability and further bifurcations are inaccessible to such analyses. This motivated Feng, Tao, and Leal to carry out a direct numerical simulation of a sheared nematic. Using the LE theory, with the one-constant approximation, they predicted a cascade of instabilities illustrated in Fig. 3. Steady state rolls first appear at Er = 2368. The director twists toward the flow (z) direction at the center of the cells. With increasing Er, the secondary flow and the director twisting intensify. 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

Effects that do not involve rotational isomers, but gradual twists, compressions or expansions of the chain have also been proposed earlier. Successive small rotations about the backbone bonds and bond angle ddbrmations are involved in such defects. A 360° rotation about the chain axis leads to proper register with the neighboring chains in the crystal above and below the defect. Defects of this type are called disclinations. 

In 3-D space, the defects formed between the double-twist cylinders are line defects and are called disclinations. The organization of the disclinations in the 3-D space has the same symmetry as the structure of the packed the double-twist cylinders. The disclinations in the simple cubic packing and body-centered cubic packing are shown in Figure 13.9(b) and (c), respectively. 

As the temperature increases, up to three types of blue phases BPI, BPII, and BPIII may exist [14]. BPIII is believed to possess amorphous stmcture. BPI (Figure 14.2(a)) and BPII (Figure 14.2(c)) are composed of double-twist cylinders arranged in cubic lattices. Inside each cylinder, the LC director rotates spatially about any radius of the cylinder. These double-twist cylinders are then fitted into a three-dimensional stmcture. However, they cannot fill the full space without defects. Therefore, blue phase is a coexistence of double-twist cylinders and disclinations. Defects occur at the points where the cylinders are in contact (Figures. 14.2(b) and 14.2(d)). BPI is known to have body-center cubic stmcture and BPII simple cubic stmcture. 

Not only are disclination lines aligned along the field direction, but also wall defects are anisotropically distributed in the aligned sample. This is best understood by first defining a rotation axis for a wall defect. A rotation plus a translation is required to map the lamellar pattern on one side of a wall defect to the other. I refer to this rotation axis as the rotation axis for the wall. If the wall contains its rotation axis, it is a bend wall, and if the axis is perpendicular to the wall, it is of twist character. The wall is of mixed character if the rotation axis is in between. In the field-aligned sample, the rotation axes of the wall defects are aligned predominantly along the direction of the applied field, e.. Thus, walls with normals parallel to S. have primarily twist character, and walls with normals nearly perpendicular to S. have primarily bend character. Examples of bend walls are indicated in Fig. 28a. 

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. 

Neel walls, twist- and tilt-reverses are the three major disclinations in actual LCDs. A Neel wall disclination may be caused by weak azimuthal anchoring. A twist-reverse is a defect in which the twist direction is opposite to the chirality of the added chiral agent. A tilt-reverse is a defect in which the inclination direction induced by applying a voltage is the opposite of the intended direction. These tilt-reverse defects may be caused by the lateral electric field generated by the fringe field of the pixel electrodes. 

When L/p I, the cholesteric does not differ much from the nematic phase. No wonder therefore that optical observations for weakly twisted cholesterics reveal thick (nonsingular) and thin (singular) line defects —disclinations similar to that in the nematic phase. Moreover, in droplets of the so-called compensated cholesteric mixtures with extremely small Ljp one can observe point defects [6] which, from the topological point of view, are allowed only in a nematic phase. 

One can think of the blue phase as a lattice of double-twist tubes (which necessitates a lattice of disclinations) or a lattice of disclinations (which necessitates a lattice of double-twist tubes) [20]. Thus, a theory involving a lattice of double-twist tubes becomes implicitly a theory for a lattice of defects. 

This simple treatment of liquid crystalline defects is only applicable to nematics, and the detailed appearance of disclination lines will differ from the simple structures described above because of differences between the elastic constants for splay, twist and bend. In smectic phases, defects associated with positional disorder of layers will also be important, and some smectic phase defects such as edge dislocations have topologies similar to those described for crystals. The defect structures of liquid crystals contribute to the characteristic optical tex-... 

The characteristic feature by which cholesterics differ from the nematics is the spontaneous formation of twisted structures, reflecting the existence of a preferred screw sense. For this reason, the defect lines no longer merge and cancel each other as in nematics instead, complicated stable networks of disclination lines may form. The "streaks" in planar cholesteric films that often form a crackle consist of bimdles of thin individual lines (Figure 6.18). A single line itself may show a number of complicated features. ... 

A TN cell without having reverse twist defect (disclination) will be fabricated by giving the twist angle of less than 90° [16] or by adding a chiral agent [17]. 

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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