Director tilted

One of the key experimental results leading to the elucidation of this overall structural puzzle involved depolarized reflected light microscopy (DRLM) studies on NOBOW freely suspended films in the high-temperature SmCP phase.48 In the freely suspended films it appears that only one phase is observed, which is assumed to be the phase forming the majority domains in the EO cells. The DRLM experiment provides two key results. First, thin films of any layer number have a uniformly tilted optic axis, suggesting all of the layer interfaces are synclinic. Second, films of even-layer number are nonpolar, while films of odd-layer number are polar, with the polar axis oriented normal to the plane of the director tilt (lateral polarization). 

As can be easily seen by inspection of these illustrations of the SuiCsPa and ShiCsPf phases, while the director tilt in the tilt plane is synclinic for both, the layer interfaces have a different character when observed in projection in the bow plane. The antiferroelectric diastereomer has synclinic character at the layer interfaces, while the ferroelectric diastereomer is anticlinic in the bow plane. This suggests a very simple reason for the tendency toward antiferroelectric bananas, this being basically the same as the tendency toward ferroelectric calamitic smectics preference for synclinic layer interfaces. 

This equation indicates that the average anisotropic part of A along the magnetic field is now scaled by a reduction factor P2(cos ft). As a consequence of the director tilt, the total Hamiltonian becomes... 

Hexatic smectic mesophase the structure of which may be regarded as a C-centered monoclinic cell with a hexagonal packing of the molecules with the director tilted, with respect to the layer normals, towards the sides of the hexagons. 

The existence of the layers and director tilt in the achiral smectic C liquid crystal phase are experimental facts. Given these, the maximum possible symmetry of the phase would be Ci, with a C2 axis normal to the tilt plane, and a a plane congruent with the tilt plane. In fact, there is no fundamental reason why a given C phase must possess either of these symmetry elements. But, breaking of either of the symmetry elements would afford polar symmetry, and no C phase has ever been shown to possess any property associated with polar symmetry (e.g. pyroelectricity). Therefore, we can say that all known C phases indeed possess the maximum possible symmetry consistent with the layers and tilt. 

Fig. 3 Above a certain threshold the effective dilatation due to the director tilt will lead to buckling of the layers. Note the difference in directions the director is tilted in the flow direction, whereas the wave vector points along the y-axis. This configuration cancels the direct coupling between the flow and the buckling...

Equation (39) shows that nematic degrees of freedom couple to simple shear, but not the smectic degrees of freedom the modulus of the nematic order parameter has a non-vanishing spatially homogeneous correction (see (39)), whereas the smectic order parameter stays unchanged. The reason for this difference lies in the fact that J3 and /3 include h and p, respectively, which coupled differently to the flow field (see (22) and (23)). Equation (38) gives a well defined relation between the shear rate y and the director tilt angle 9o, which we will use to eliminate y from our further calculations. To lowest order 0O depends linearly on y ... 

In contrast to the director tilt the lowest order correction to the nematic order parameter is quadratic in the shear rate (tilt angle) ... 

Fig. 16 Time evolution of the director tilt after a step-like start of the shear for two different final shear rates (0.008 and 0.010 in Lennard-Jones units). The lines show the fit to the data using the solution of the averaged linearized form of (27). Fig. 5.12 of [54]...

Fig. 18 Ground state flow alignment director tilt in the Z direction at r = 0.1SR as a function of the polar angle 0. The tilt is zero at 0 = 0 and

Fig. 3.4.9. Computed values of the tilt angle in the midplane of the sample versus voltage for various twist angles for a standard TN mixture. Cell thickness/pitch = /2n in all cases and the director tilt at the surface 0 = 1°.

Such walls are associated with the Freedericksz deformation. With the homeotropic geometry of Fig. 3.4.1 (c), the possible distortions for H> are illustrated in fig. 3.S. 16. Since the director tilt has a degeneracy in sign with respect to H, there can arise twist walls parallel to the field (fig. 3.5.16(6)) or splay walls perpendicular to the field (fig. 3.5.16(c)). Similarly with the homogeneous geometry, there can arise bend walls. 

Fig. 13.13 Geometry for discussion of the anchoring energies for the c-diiector. a and P are the angtes the director n forms with the easy axis z coinciding with the normal to smectic layers 9 is the director tilt angle and AC is the c-director forming angle (p with y-axis...

Fig. 6. Computed director tilt angle at midplane (O ) and at surface (0 j), and transmittance for 90° twisted cholesteric cell with surface energy function Ug. Surface tilt at zero field Is 86°. (Listed kg and risO...

If there is a pretilt, i.e., the director tilt angle at the walls is nonzero, the changes near Vq are gradual. We then define as the intersection of the extrapolated linear portion of the capacitance/voltage curve with the horizontal C=C(V 0) curve (see Fig. 1). We assume the surface coupling to be strong, so that the tilt angle at the surface is constant. 

Consider a 90 twist cell with S3rmmetric surface director tilt between crossed polars after application of a relatively high AC field. Then 61=62 and Eq. (6) reduces to zero. Light intensity transmitted through this system is essentially zero for all values of 0. Figure 4 shows the experimental verification of this situation. The cell was known to have a twist of 90. ... 

It was fabricated using SiO alignment layers evaporated at a high angle of Incidence thus producing equal to surface director tilts... 

In contrast, consider a 90 twist cell of unsymmetric surface director tilts. Such dissymmetry can be introduced by depositing SiO at different angles of Incidence on the two plates. Under this circumstance 61 62. Light intensity falls to zero only when 0=0 , i.e., when the front surface director lies in the incident plane of polarization. Light intensity increases with the absolute value of 0. Figure 5 shows the behavior of such a cell. 

There are three possible deformation modes of the liquid erystal director as shown in Figure 1.9. Choose the cylindrical coordinate such that the z axis is parallel to the director at the origin of the coordinate it (0) = f. Consider the variation of the director at an infinite small distance away from the origin. When moving along the radial direction, there are two possible modes of variation (1) the director tilts toward the radial direetion p, as shown in Figure 1.9(a), and (2) the director tilts toward the azimuthal direction as shown in Figure 1.9(b). The first mode is called splay, where the director at (Sp, (f>, z = 0) is... 

The second possibility to avoid the singularity at the center of the cylinder is to escape from the splay deformation to the bend deformation, as shown in Figure 1.21(b) [30-32]. The liquid crystal director tilts to the z direction and is given by... 

Lyotropic liquid crystals tend to form layered strucmres, which are called lamellar phases. Yet, the mesogens are usually parallel to the layer normal k (c/ lamellar L phase. Sect. 3.2.2) and not tilted with respect to it, as is the case in the thermotropic SmC phase. A very plausible explanation is commonly accepted for this behavior. In lyotropic liquid crystals the lamellas are composed of alternating bilayers of surfactant and solvent molecules as shown in Fig. 1.5a. The individual layers of surfactant molecules are therefore separated from each other by layers of solvent molecules, which only possess short range order as in common liquids. Thus, the disordered layers of solvent molecules prevent any correlation of the director tilt between adjacent surfactant layers. In consequence, a long-range correlation of the director tilt, as depicted in Fig. 1.5b, or moreover of chirality, which would be necessary for the formation of a lyotropic analog of the SmC phase, does not seem to be possible in lyotropic liquid crystals. StiU, there are very rare examples in... 

---