Anchoring external fields

In the absence of further limit conditions which may hold in the case of the electron (see later), we can now think of an electron spin and a nuclear spin anchored at points A and B, both aligned along the external magnetic field Bo, as shown in Fig. 1.5. Since the two magnetic moments are forced to be parallel by the strong external field, the energy of the interaction between them, given by Eq. (1.1), simplifies to... 

The radial configuration occurs when the liquid crystal molecules are anchored with their long axes perpendicular to the droplet wall (Figure 3B). The radial droplet is not birefringent. Application of an external field switches the radial droplet to an axial configuration. As with the bipolar case the films switch from scattering to transparent upon application of an electric field if np=n0. 

The liquid crystals can be deformed by applying external fields. Even a small electric or magnetic field, shear force, surface anchoring, etc., is able to make significant distortion or deformation to liquid crystals. Thus, n is actually a function of position r. According to the symmetry of liquid crystals there exist three kinds of deformations in liquid crystals splay, twist and bend deformations, shown in Figure 1.17. The short bars in the figure represent the projections of the local directors. 

Let us now apply a magnetic field H (or an electric field E) perpendicular to the director n of a nematic monocrystal (see Fig. 9.6). If the magnetic (electric) susceptibility of the compound is such that molecules seek to align themselves with the field, it is easy to see that the nematic structure will distort under the antagonistic constraints of anchoring and external field. 

When a nematic liquid crystal is confined, such as when sandwiched between two parallel substrates with alignment layers, in the absence of external fields, the orientation of the liquid crystal director is determined by the anchoring condition. When an external electric field is applied to the liquid crystal, it will reorient because of the dielectric interaction between the liquid crystal and the applied field. If the dielectric anisotropy is positive (Ae > 0), the hquid crystal... 

Figure 5. Switching in a regular fiber array examples of director fields for different 77 a T = 1.0, R = 5a, and w = 1 yz-cioss sections through the fiber center). From left to right homogeneous (h), deformed (d), and saturated (s) structure. Anchoring easy axis is planar and z, while the external field E is directed along y. Note that the d-structure is twisted along the x-axis, while there is no twist in a simple nematic slab. This, however, does not affect the qualitative analogy of the two systems.

Most studies of nematics in fields are performed on thin films where the initial director field is dictated by surface anchoring. The thin film permits easy observation, and a well-defined initial state simplifies analysis. It should be noted, however, that a typical bulk liquid crystal transformed from the isotropic state contains many topological defects. These defects are likely to play a central role in the response of liquid crystalline materials to external fields,... 

As mentioned earlier, most studies of field interactions with liquid crystals are done using thin films with a well-defined initial state, usually a monodomain or a thin film with a simple distortion induced by incommensurate surface anchoring. These conditions simplify observation and theoretical analysis. However, most liquid crystal materials that are not specially prepared contain topological defects that are very important to their response to external fields. One class of defect commonly observed in nematics is the disclinalion line. At a disclination line the director field is ill defined. The director field turns around the disclination line a multiple of half-integer times. Several disclination lines are shown in Fig. 8. 

Before outlining the effect of fields on the orientation of the director, it must be emphasized that surface interactions and boundary conditions are usually of importance. The models applied here assume that there is a well-defined director distribution in the absence of any external field, and in practice this can only be provided by suitable treatment of boundary surfaces. The strength of surface interactions must also be considered as this will influence the equilibrium director configuration in the presence of a field. For the simplest description of field effects in liquid crystals it is usual to assume an infinite anchoring energy for... 

The dynamics of the splay and bend distortions inevitably involve the flow processes coupled with the director rotation. Such a backflow effect usually renormalizes the viscosity coefficients. Only a pure twist distortion is not accompanied by the flow. In the latter case, and for the infinite anchoring energy, the equation of motion of the director (angle variation) expresses the balance between the torques due to the elastic and viscous forces and the external field (and... 

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-... 

This reduction in the anchoring forces results in reduction of the voltage required for device operation and in faster transitions from off- to on-states, when a given external field is applied (seconds to milliseconds). The stability of the devices upon prolonged operation was tested by switching the samples more than 1000 times between on- and off-states without any loss in their electro-optical properties. 

Figure 3.2. A homeotropic nematic liquid crystal with strong surface anchoring (a) external field off (b) external field on — only the bulk director axis is deformed.

D MEASUREMENT TECHNIQUES OF THE SURFACE ANCHORING ENERGY D1 External Field OffMethod... 

Anchoring energies for nematics D2 External Field On Method... 

Hydrodynamic effects on phase separations and morphologies are also important [144, 152, 153], Sulaiman et al. [153] have presented a lattice Boltzmann algorithm that includes hydrodynamics to describe the deformations of a drop of isotropic fluid immersed in a nematic Uquid crystal solvent, both in the absence and in the presence of an external field. The equilibrium shape of the drop is affected by the elastic constant K of a liquid crystal, the radius Rof a droplet, and the anchoring strength W of the director at the surface of a droplet, and the surface tension o. As W/a, or Io/Ro increases, the anchoring energy dominates over the surface tension and the droplet distorts to more easily allow homeotropic anchoring at its surface. 

---