Director twisted

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. 

UP2 regimes turn out to be p2 = 1-75 and ps = 2.4 instead of p 2 = 1.45 and P3 = 1.75 when the backflow is neglected [39, 40]. In [9], it was also shown that the precession frequency /o for UPl states actually increases when the backflow is included (as expected because 71 effectively decreases). An unanticipated spatial oscillations of the backflow in the UP2 regime were also found which results from spatial oscillations of the director twist dz. They are a consequence of oscillations in the torque resulting from interference phenomena between ordinary and extraordinary light. The backflow behaves very differently for the three types of the director motion and thus can act as a sensitive diagnostic to distinguish them. 

Another example is a twist nematic cell with a planar orientation of the director at both boundaries 9 = ti/2 differing by their azimuth, cp = 0 and Jt/2. In such cells, the areas with the director twist in the bulk by angle -rjt/2 and —Jt/2 have the same... 

Projection of the TN-LCD geometry on its substrate plane showing the total director twist. 

We showed in last section that in a uniform anisotropic medium, for each propagation direction, there are two eigenmodes which are linearly polarized. The polarization state of the eigenmodes is invariant in space. In this section, we discuss the propagation of light in a special case of a non-uniform anisotropic medium a cholesteric liquid crystal which locally is optically uniaxial, but the optic axis twists uniformly in space [6,7]. Choose the z axis of the lab frame to be parallel to the helical axis of the cholesteric liquid crystal. The pitch P of the liquid crystal is the distance over which the liquid crystal director twists In. The components of the liquid crystal director of a right-handed cholesteric liquid crystal q > 0) are given by... 

In electro-optical devices, it is usually required that the liquid crystal director is unidirectionally oriented. In the smectic-C phase, however, the liquid crystal director twists from layer to layer. 

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. 

In this structure, the director twists in moving perpendicular ftom the z-axis along any radius. Thus at the centre the director points along the z-axis, but has rotated by 45° at all pomts in the xy plane located a distance equal to one-eighth the pitch away from the origin. If the stmcture does not vary in the z-direction, then this defines a double twist cylinder. 

FIGURE 4.20. The geometry of the SEE display, (a) An SEE cell with the directors twisted at an angle of 270 L and L2 show the projection of the directors on the two substrates) is placed between (P) polarizer and (A) analyzer oriented at angles and 7 with respect to Li and L2, respectively, (b) Distribution of the director angles inside the supertwist cell in the off and on states, 0 is the director pretilt angle and ( m is the maximum rotation angle. 

The transmitted light intensity was calculated by the Berreman 4x4 matrix method [22]. The director tensor is determined by the director tilt angle 7 and the director twist angle (f), which are expressed as... 

In Fig. 5.1.25, the director twist angle 4> is plotted as a function of the cell thickness direction Y at various surface pretilt angles, where represents the director twist angle at the chevron interface and is expressed as... 

It is shown that memory angle 0m is approximately equal to half of the total director twist angle in the cell and determined by the following equation,... 

Pig. 5.1.21 Coordinate systems used for simulations. Y and Z represent the cell thickness direction and the smectic layer normal, respectively, and z is the perpendicular line of the cone, (a) Chevron layer system, (b) Cone system, (c) Director tilt angle 7 and director twist angle . (d) Definition of the smface... 

Figure 5.3. Double-twisted nematic droplets suspended in an isotropic matrix. The central part of the droplet is bright when the polarizers are crossed and one of them is aligned along the droplets axes (a) the central part can be made dark by changing the angle between the polarizer and analyzer. This behavior indicates the optical activity of the droplets caused by the director twist. The insert shows the director configuration at the droplet s surface. Nematic -butoxyphenyl ester of nonylhydro-benzoic acid dispersed in glycerin [17].

The structure of liquid crystals can broadly be classified as nematic, cholesteric and smectic, see Fig. 1. None of them have full three-dimensional (3-D) positional order, but some degree of orientational order. Most often the constituent molecules are elongated, as indicated in Fig. 1, but distinctly flat molecules make up the socalled discotic liquid crystals. The nematic phase has only orientational ordering of the molecules. The collection of molecules have one symmetry axis called the director n. The cholesteric phase has only orientational order, formed by the constituent chiral molecules. The director twists with a pitch comparable to the wavelength of light. 

---