Director fields, surface alignment

Liquid crystal displays depend upon the reorientation of the director , the defining alignment vector of a population of liquid crystalline molecules, by a localised applied electric field between two glass plates, which changes the way in which incident light is reflected directional rubbing of the glass surface imparts a... 

Fig. 22. (a) Identification of the angles and 6 used to describe a disclination. (b) Director arrangement of an 5 = I/2 singularity line. The end of the line attached to the sample surface appears as the point s = + V2 (points P). The director alignment or field does not change along the z direction. The director field has been drawn in the upper and the lower surfaces only. 

Fig. 1. Schematic diagrams of the director field distortions black lines) around particles in an aligned nematic liquid crystal. For a normal anchoring of the liquid crystal molecules at the surface of the particles, there are two possible configurations, a Dipole configuration with a companion point defect (indicated by an arrow) located in the immediate vicinity of the particle, b Quadrupolar Saturn-ring configuration with a disclination ring surrounding the particle at the equator...

The equilibrium configuration in a liquid crystal sample is strongly influenced by the sample boundaries. The confining surfaces can induce order, disorder, or can align liquid crystal molecules in a given direction. Surface interactions not only have influence on the static properties of a confined liquid crystal, but can also have a strong effect on the director dynamics. By studying temporal fluctuations of the director field in confined samples, information about the surface-liquid crystal interaction can be obtained. 

When a nematic is put in contact with a crystalline substrate, tbe surface of wbicb possesses the A-fold rotational symmetry (e.g., IV = 6 for mica, A7 = 4 for NaCl), the director is free to choose any of those N easy axes. In experiments, the orientation depends on the pre-history of the sample. A director field n(r) in a nematic drop put on the surface of a crystal acquires the same N-fold symmetry. In a sandwich cell, when crystalline axes of the opposite interfaces coincide, different domains are observed, with uniform structure or twisted through an angle 2k/N [20]. Using a properly oriented external in-plane field one can switch domains from one of the possible N orientations to another. Thus we have multistable alignment. When the crystalline axes of the opposite interfaces do not coincide, many domains with different twist angles are possible. 

The Freedericksz transition is also the basis of operation for most liquid crystal displays. In a twisted-nematic display cell, the surface anchoring at the two substrates is incommensurate, inducing a twist to the director field that rotates light polarization. Application of an electric field sufficiently strong to align the director... 

The director field of the TGBa phase is very similar to the director field of a cholesteric phase (Chapter 2). Thus, a TGBa phase with parallel surface alignment of the director shows selective reflection of circularly polarized... 

Except for the short discussion at the end of the last section, a uniform director alignment has been assumed up to now. Surface alignment and inhomogeneous fields can lead to an inhomogeneous alignment and the occurrence of elastic torques. For a complete description of hydrodynamics of nematic liquid crystals these elastic torques have to be included. 

If the direction of the surface alignment and the magnetic field H differ, the alignment of the director within a surface layer of thickness... 

In the geometry to be considered, the chiral nematic is contained between cell walls in the x, y plane with the uniform surface alignment layers designed to align the helix axis along x with the electric field applied along z (see Fig. 35). In such a sandwich like cell [29, 173-175], the director spirals along the x direction in the z, y plane and is therefore described by... 

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