Director patterning

Figure 10.19 Velocity field (a) and director pattern (b) in roll cells that form in a tumbling nematic initially oriented in the vorticity direction of a shearing flow. (From Larson 1993, with permission from the Journal of Rheology.)...

From the nature of the director patterns it is clear that dark brushes of the schlieren type will not be seen under the polarizing microscope for light propagating normal to the film (see 4.1.1). Twist disclinations may therefore be expected to be less conspicuous than wedge disclinations, and few observations have been reported of their existence in ordinary nematics. They do, however, reveal themselves under favourable circumstances in twisted nematics, often as loops separating regions of different twist. ... 

From the superposition principle (3.5.6) we know that the director pattern around a pair of like disclinations located at jc = d and — d is given by... 

The radial force of interaction between disclination will, of course, be modified because of anisotropy. In addition there will now be an angular component of the force. The physical basis for the angular force can be understood by referring to fig. 3.5.23, which shows the director patterns for two pairs of unlike defects, (+, — ) and ( +1, — 1), each in two different situations. It is seen that there are significant differences in the... 

Fig. 3.5.23. The director patterns for (, — ) and (1,-1) defect pairs in two situations, c = 0 and c = ti/2. The double-headed arrow at the centre indicates the director orientation far away from the defect pairs. (After reference 98.)...

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.

In this case the singular line is perpendicular to the twist axis. On going round this line, one gains or loses an integral number of half-pitches. The director pattern around the -edge disclination was first worked out by de Gennes who proposed a nematic twist disclination type of solution ... 

The c-director field can also have twist disclinations, the structures of which are like those shown in fig. 3.5.8, except that the director is polar. The director pattern for s = 1, c = 0 is shown in fig. 5.8.5. 

In addition to the above-discussed discli-nations, which are referred to as wedge dis-clinations, there are twist disclinations. The director is always parallel to the xy plane, but the axis of rotation (z-axis) is normal to the singular line (y-axis). Figure 4 shows the director patterns for (a) 5=1/2, 6q=0 and (b) 5=1, 6[)=0. is a linear function of the angle 0=tan (z/x). 

The development of novel instabilities of the director pattern was also observed as the... 

Several mechanisms of photoalignment reactions have been reported in the literature and hence a variety of photoalignment materials are available for director patterning. For the manufacturing of a patterned retarder applied in a transflective display (Sect. 9.4.2), we have tested two commercially avail-... 

Fig. 9.20. A schematic of the molecular order of the reactive LC molecules after director patterning. The order is forced to be planar in two domains by a dual domain photoalignment layer. The domains exhibit identical dAn values, but the effective retardation depends on the angle between the main optical axis and the transmissive axis of the polariser.

A director patterned retarder can be used in a transflective LCD to boost the optical performance and to lower the power consumption. A transflective display is the combination between a reflective and a transmissive display. 

Let both the helical axis and the electric field are parallel to the normal z of a cholesteric liquid crystal layer of thickness d and >0. In the case of a very weak field the elastic forces tend to preserve the original stack-like arrangement of the cholesteric quasi-layers as shown in Fig. 12.15a. On the contrary, in a very strong field, the dielectric torque causes the local directors to be parallel to the cell normal, as shown in Fig. 12.15c. At intermediate fields, due to competition of the elastic and electric forces an undulation pattern appears pictured in Fig. 12.15b. Such a structure has two wavevectors, one along the z-axis (nld) and the other along the arbitrary direction x within the xy-plane. The periodicity of the director pattern results in periodicity in the distribution of the refractive index. Hence, a diffraction grating forms. Let us find a threshold field for this instability. 

H. A. van Sprang and P. Breddels, Numerical calculations of director patterns in highly twisted nematic configurations with nonzero pretilt angles, J. Appl. Phys., 60, 968 (1986). 

Despite their highly successful record, MD or MC simulations are still hardly extended to the direct interpretation of complex set-ups, typical of most rheological experiments. In such cases it is preferable to employ mean-field or continuum descriptions, based of the numerical solution of the constitutive equations describing hydrodynamic properties. Such techniques were for instance applied to the prediction of transient director patterns of liquid crystalline nematic samples [11-14]. Hydrodynamic treatments are algebraically complex and computationally intensive, and their implementation is limited mostly to nematic phases. 

LC-elastomers (see Fig. 4a) have been investigated in detail (4-8). Although the liquid crystalline phase transitions are nearly unaffected by the network, the network retains the memory of the phase and director pattern during cross-linking... 

For materials with > 0 the interaction free-energy minimum corresponds to a parallel alignment of the director with respect to the field. In nematic cells -such as the ones shown in Fig. 2.- a competition takes place between the orienting action of the substrates and that of the external field (unless the initial alignment of the director coincides with the direction of the applied field). As a result the initial director pattern becomes distorted. 

Additionally, it is important to realize that deformations at an N1 phase transition occur locally, on the level of a small volume of the material in the micrometer range. To observe the unique properties of LCEs on a macroscopic scale, the mesogens have to be aligned uniformly over the whole sample, yielding an LC monodomain or, at least, a sample with a well-defined overall director pattern (see Chap. 1). Thus, the use of LCEs as actuators always requires a step to orient the sample prior to final crosslinking [184]. Consequently, we will discuss first the influence of different preparation strategies on the orientation step, focusing on materials for actuator applications (Sect. 1.1). This sectimi will be followed by a discussion of properties needed for application. We will examine temperature-driven actuators (Sect. 2) and electrically driven systems (Sect. 3). 

Figure 5.12. Confocal-microscope image of a dislocation b = p n the fingerprint cholesteric texture. The confoeal microseope technique allows one to obtain the image of the director pattern not only (a) in the plane of the sample but (b), (c) in the vertieal cross-section as well (photo D. Voloschenko).

In the fibers produced from lyotropic spinning dopes, there still appear to be limitations on the ultimate physical properties due to higher-order morphological defects (the periodic director-orientation distortions alluded to earlier) [115]. In this context, much experimental and theoretical work remains to be done to delineate those parameters that control disclination textures and director patterns created by complex shear fields encountered in processing LCPs. As is typically the case, there are natural systems wherein these difficulties appear to have been optimally minimized spiders spin nearly defect-free fibers from a mesomorphic form of silk [116]. Consequently, efforts to analyze the spinning process - the spinner draw-down geometry and its associated shear field - used by arachnids are under way. 

NMR line shapes resulting from the convective director pattern formed after 2 h are shown in Fig. 10b and c. 

The one-dimensional deformations in Freedericksz cells and their optical characteristics are now well understood. A comprehensive theoretical treatment of the one-dimensional director patterns in electro-magnetically driven cells can be found in publications by Thurston [25], who has also considered the stability of configurations in pretilted cells. Ong [26] has calculated the optical properties when the splay/... 

Several types of spontaneous periodic director pattern yield information about elastic coefficients. Static stripe textures, as described by Lonberg and Meyer [45], appear in polymer nematics if the twist/splay ratio below the critical value of 0.303. Calculations of director fields and the influence of elastic constants and external fields on the appearance of these periodic patterns have been performed by several authors (e.g. [49-51]). In nematic cells with different anchoring conditions at the upper and lower cell plates (hybrid cells), other types of striped texture appear these are similar in nature, but involve different director deformations and elastic coefficients. For a description of various types of static periodic texture and their relationship to elastic coefficients see, for example, Lavren-tovich and Pergamenshchik [52]. In thin hybrid aligned films, a critical thickness is observed below which the director align-... 

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