Director deformations

In smectic A phases where the smectic layers are perpendicular to the molecules, the orientation of the whole structure is, in principle, fixed once the orientation of the molecules is defined by the interface. The surface orientation of achiral smectic A phases is then the same as that of the nematic phase [88, 89]. However, since splay deformations of smectic layers (director bend deformations) are forbidden and layer bend deformations (director splay deformations) require a lot of energy, smectic phases tend to adopt uniform configurations, even between two walls inducing two different orientations. In the latter case, the surface orientation of the smectic phase differs from that of the nematic phase, and depends on the layer configuration in the bulk [90, 91]. 

Another example of the coupling between microscopic and macroscopic properties is the flexo-electric effect in liquid crystals [33] which was first predicted theoretically by Meyer [34] and later observed in MBBA [35], Here orientational deformations of the director give rise to spontaneous polarisation. In nematic materials, the induced polarisation is given by... 

Deformation leading to a change in the director, where the distortion is described by a tensor of third rank... 

Deformation in a direction normal to the initial director, n, characterised by div n Q. 

Fig. 28. Schematic representation of a splay deformation (a) changes in the components of the director n, defining the orientational change (b) splay deformation of an oriented layer of a...

Elastic deformation of the director, induced by a magnetic induction or electric field, in a uniformly aligned, thin sample of a nematic confined between two surfaces. 

Instabilities caused by the anisotropy of conductivity and corresponding to a periodic deformation of the alignment of the director in a nematic monodomain under the action of a direct current or low-frequency alternating current. 

Electric polarization resulting from a splay or bend deformation of the director of a nematic liquid crystal. 

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. 

Fig. 17a-c. Elastic constants for a splay b twist c bend deformations of a nematic phase. The full lines represent the director... 

Fritz Vogtle is Professor and Director at the Kekule-Institute for Organic Chemistry and Biochemistry at the University of Bonn, Germany. His research interests are supramolecular chemistry deformed helical molecules and their chiroptical properties and compounds with appealing architectures such as rotaxanes, catenanes, knots, and dendrimers [37-40],... 

We again stress that this relationship has rigorous physical meaning only if the distribution of local kink orientations has cylindrical symmetry about the director nevertheless, it may provide a semi-quantitative relationship between the REV-8 lineshape and the concentration of chain deformations if the process is at least of a highly random nature. If the ratio p changes with temperature according to a Boltzmann factor, we expect the quantity... 

Sir Frederick Charles Frank (1911-1998) received his Ph.D. in 1937 from Oxford University, followed by a postdoctoral position at the Kaiser Wilhelm Institut fiir Physik in Berlin. During World War II, Frank was involved with the British Chemical Defense Research Establishment, and because of his keen powers of observation and interpretation, he was later transferred to Scientific Intelligence at the British Air Ministry. In 1946, Frank joined the H. H. Wills Physics Laboratory at the University of Bristol under its director, Nevill Mott, who encouraged him to look into problems concerned with crystal growth and the plastic deformation of metallic crystals. A stream of successes followed, establishing his scientific fame, as evidenced by many eponyms the Frank-Read source, the Frank dislocation, Frank s rule, Frank-Kasper phases. His theoretical work has been the foundation of research by innumerable scientists from around the world. Frank was awarded the Order of the British Empire (OBE) Medal in 1946, elected a Fellow of the Royal Society (FRS) in 1954, and was knighted in 1977. 

The three elastic constants are the Frank elastic constants, called after Frank, who introduced them already in 1958. They originate from the deformation of the director field as shown in Fig. 15.52. A continuous small deformation of an oriented material can be distinguished into three basis distortions splay, twist and bend distortions They are required to describe the resistance offered by the nematic phase to orientational distortions. As an example, values for Miesowicz viscosities and Frank elastic constants are presented in Table 15.10. It should be mentioned that those material constants are not known for many LCs and LCPs. Nevertheless, they have to be substituted in specific rheological constitutive equations in order to describe the rheological peculiarities of LCPs. Accordingly, the viscosity and the dynamic moduli will be functions of the Miesowicz viscosities and/or the Frank elastic constants. Several theories have been presented that are more or less able to explain the rheological peculiarities. Well-known are the Leslie-Ericksen theory and the Larson-Doi theory. It is far beyond the scope of this book to go into detail of these theories. The reader is referred to, e.g. Aciemo and Collyer (General References, 1996). 

FIG. 15.52 Elastic responses due to the deformation of the director field Frank elastic constants. Kindly provided by Prof. SJ. Picken (2003). 

Let us now determine the orientation of the anisotropy axis, i.e. of the director of the intramolecular liquid crystal28. It is easy to realize from the symmetry considerations that the field of the orientations of the director is of the type shown in Fig. 8 b. Actually, although such a field of orientations corresponds to the deformed state of the liquid crystal, the deformation energy estimated according to the usual Frank formula28 is of order... 

The spatial and temporal response of a nematic phase to a distorting force, such as an electric (or magnetic) field is determined in part by three elastic constants, kii, k22 and associated with splay, twist and bend deformations, respectively, see Figure 2.9. The elastic constants describe the restoring forces on a molecule within the nematic phase on removal of some external force which had distorted the nematic medium from its equilibrium, i.e. lowest energy conformation. The configuration of the nematic director within an LCD in the absence of an applied field is determined by the interaction of very thin layers of molecules with an orientation layer coating the surface of the substrates above the electrodes. The direction imposed on the director at the surface is then... 

If A < 1, Eq. (10-4) has no solutions in the shearing plane. This means that the director rotates endlessly in the deformation plane. The period of this rotation—that is, the time it takes to rotate through an angle of tt, is... 

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