Splay alignment

To fix the twist direction of the twisted nematic (TN) display mode, several methods are used. One is to add a small amount of a chiral agent. A typical chiral pitch for the 5 pm gap TN mode is 100 pm. The other method involves the rubbing direction. The rubbing direction determines the inclination direction of the LC, and it is selected so as to avoid a splay alignment as shown in Fig. 2.32. If the pretilt... 

For a nematic LC, the preferred orientation is one in which the director is parallel everywhere. Other orientations have a free-energy distribution that depends on the elastic constants, K /. The orientational elastic constants K, K22 and K33 determine respectively splay, twist and bend deformations. Values of elastic constants in LCs are around 10 N so that free-energy difference between different orientations is of the order of 5 x 10 J m the same order of magnitude as surface energy. A thin layer of LC sandwiched between two aligned surfaces therefore adopts an orientation determined by the surfaces. This fact forms the basis of most electrooptical effects in LCs. Display devices based on LCs are discussed in Chapter 7. 

The model predicts that for the typical elastic parameters the polarization splay is small, just a few degrees. This was also confirmed experimentally as only a small change of birefringence under the electric field is detected for the Blrev phase. The electric field eliminates the spontaneous splay by aligning the dipole moments along the electric field direction. 

When the duplicated centrosomes have become aligned, formation of the spindle proceeds, driven by simultaneous events at centrosomes and chromosomes. As just discussed, the centrosome facilitates spindle formation by nucleating the assembly of the spindle microtubules. In addition, the (—) ends of microtubules are gathered and stabilized at the pole by dynein-dynactin working with the nuclear/mitotic apparatus protein. The role of dynein in spindle pole formation has been demonstrated by reconstitution studies in which bipolar spindles form in Xenopus egg extracts in the presence of centrosomes, microtubules, and sperm nuclei. The addition of antibodies against cytosolic dynein to this in vitro system releases and splays the spindle microtubules but leaves the cen-trosomal astral microtubules in position (Figure 20-35). 

PLATE IV Figure 31 The crystal lattice of (Cu2(7)2l(C104)2, showing the interleaved splayed chelates parallel to the view direction. The chelate ligands which are mutually parallel in each molecule are all aligned perpendicular to the view direction... 

Fig. 3.13.3. A hybrid aligned cell for the determination of the anisotropy of the flexoelectric coefficients. In this geometry, the director has a splay-bend distortion which gives rise to a flexoelectric polarization P. On applying an electric field E, the director is twisted by an angle (j> cc — which can be measured optically.

Figure 3.12. LCE films with a (a) splayed or (b) twisted molecular alignment, ao and e indicate perpendicular and parallel coefficients of thermal expansion. Source Mol et al., 2005.

Fig. 4.8. Relaxation time r for the fundamental splay fluctuation mode as a function of sample thickness (circles) and best fit of the theoretically predicted relation for weak anchoring (solid line). The aligning layer was UV illuminated photoactive poly-(vinyl-cinnamate), the liquid crystal was 5CB in the nematic phase (T = 32°C) [59].

This chapter is concerned with experimental measurements of flexo-electric coefficients. After a brief introduction to flexoelectricity in nematic liquid crystaJs, some applications exploiting the flexoelectric effect and the influence of this effect on electrohydrodynamic instabilities are pointed out. Flexoelectricity axises in samples with a splay-bend distortion in the director field and as such its measurement is not as direct as for dielectric constants. The theoretical background needed to analyse electro-optic experiments and extract the flexocoefficients is outlined in Section 2.2. Various experimental techniques that have been developed are described in Section 2.3. These involve cells in which the alignment of the nematic director is homeotropic, or planar or hybrid. In the first case, the interdigitated electrode technique is particularly noteworthy, as it has been used to establish several features of flexoelectricity (1) the effect can arise purely from the quadrupolar nature of the medium, and (2) the dipolar contribution relaxes at a relatively low frequency. 

Fig. 2.2. Schematic diagram of a hybrid-aligned nematic cell. The field-free director (shown by the continuous curved line) has a splay-bend curvature distortion in the xz plane. A DC field applied along the y axis rotates the polarization and the director (shown by the curved dashed line) acquires a 4>(z) profile. (Reproduced from Dozov et al. with the permission of EDP Sciences, http //publications.edpsciences.org.)...

Preedericksz transition in planar geometry is uniform in the plane of the layer and varies only in the z direction. However, in some exceptional cases, when the splay elastic constant Ki is much larger than the twist elastic constant K2 (e.g., in liquid crystal polymers), a spatially periodic out-of-plane director distortion becomes energetically favourable. The resulting splay-twist (ST) Freedericksz state is manifested in experiments in the form of a longitudinal stripe pattern running parallel to the initial director alignment no x. 

Fig. 7.1. The field-induced twist in a hybrid-aligned device, based on the torque between E and the fiexoelectric polarization P permanently induced in the splay-bend due to the hybrid alignment. The arrows indicate the crossed polarizers.

When switching from the homeotropic to the planar state the first part of the bipolar pulse is negative. The nematic has a positive Ae and aligns with the applied field during this stage squeezing the splay and bend deformations towards the surface. This means that the homeotropic state is... 

Unoriented poly (p-hydroxybenzoic acid-co-2,6-hydroxynaphthoic acid) exhibited smoothly wandering director fields in three dimensions. Alignment with a 1.1 T magnetic field for 30 min at 300 C transformed this structure to domains with an anisotropic shape within which the polymer was highly oriented, and the global order parameter amounted to 0.85 [110]. Boundaries were of the splay-bend type and involved a 180 director rotation. At lower field strengths, the domains were less... 

Consider elementary distortions of a nematic. The undistorted director n = (0,0,1) is aligned along the z-axis. Fig. 8.5a. For instance, at a distance 8x from the origin of the Cartesian frame O the director has been turned through some angle in the zOx plane like in Fig. 8.5b. The relative distortion is then described by the ratio of hn, an absolute change of the x-component of the director, to distance 8x, over which the distortion occurs. In the same sketch, but in the zOy plane we see similar fan-shape or splay distortion 8/iy. Thus for the two elementary splay distortions we write ... 

Fig. 8.6 Splay, bend and twist distortions in nematics confined between two glasses that align liquid crystal at the surfaces either homogeneously (for splay and twist) or homeotropically (for bend)...

Fig. 8.25 Distortion of a honieotropically aligned SmA liquid crystal by a corrugated surface of solid boundary plate with the dotted line pictured an exponential decay of the distortion (a) and the wave-like splay distortions in a thin layer with the arrows indicating the direction of the induced local pressure (b)...

The director at one of the boundaries of a hybrid cell is aligned homeotropically, at the opposite boundary homogeneously as was shown earlier in Fig. 10.11. Therefore, a hybrid cell has intrinsic bend-splay distortion and must have a projection of the macroscopic polarization along the cell normal. We can clearly see in Figs. 10.11 and 11.25 how the quadrupolar polarization emerges. The molecules may have positive (eo > 0) quadrupoles shown in Fig. 11.25 or negative ones (fio < 0) seen in Inset to Fig. 11.26b. 

As has been shown, the splay and bend distortions of a nematic create electric polarization. There is also a converse effect the external electric field causes a distortion due to the flexoelectric mechanism. For example, if the banana-shape molecules with transverse dipoles are placed in the electric field, the dipoles are partially aligned along the field and their banana shape induces some bend. This effect takes place even in nematics with zero dielectric anisotropy. 

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