Deforming Liquid Crystals

The molecular orientation (i.e., the director) in liquid crystal materials can be deformed under the influence of mechanical shear or the action of an external electric or magnetic field. Deformations to the director can be classified in three different ways as there are only three ways in which the nematic ordering can be deformed. These are known as splay, twist, and bend. (Note that in this section, we consider only the nematic phase for simplicity.) 

After the deformation force is removed from the liquid crystal material, it will relax back to the equilibrium state. This behavior is analogous to the elastic properties of continuous solids. Therefore, it has been possible to describe the deformation of liquid crystals in terms of a continuum elastic theory. When we consider the elastic properties of a solid, we think of Hookes law  

This continuum elastic theory was extended successfully to the liquid crystal medium by Frank in 1958. The following expression represents the general form in which the free energy F of a deformed liquid crystal medium is usually expressed  

This expression, while appearing highly complex, can be simply broken down into three parts, each representing a different mode of deformation, or curvature of the director field n. 

FIGURE 2.21 The three different modes of liquid crystal deformation (a) bend, (b) splay, and (c) twist. 

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We may therefore expand the free energy per unit volume of a deformed liquid crystal relative to that in the state of uniform orientation as... 

In this book the flexoelectric effect is mainly considered from the phenomenological point of view. At the same time it is very interesting and important to reveal the molecular origin of flexoelectricity and, in particular, to consider different types of intermolecular interactions that may be responsible for the dipolar ordering in a deformed liquid crystal, and to study the effects of intermolecular correlations and the molecular structure. This problem can only be solved using a molecular-statistical theory, which eventually allows us to express the flexoelectric coefficients in terms of molecular model parameters using various approximations. 

Deformed liquid crystal layer d distance of electrodes... 

In order to compensate for the distortions in the wavefront due to the atmosphere we must introduce a phase correction device into the optical beam. These phase correction devices operate by producing an optical path difference in the beam by varying either the refractive index of the phase corrector (refractive devices) or by introducing a variable geometrical path difference (reflective devices, i.e. deformable mirrors). Almost all AO systems use deformable mirrors, although there has been considerable research about liquid crystal devices in which the refractive index is electrically controlled. 

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... 

Fig. 29. Schematic representation of a bend deformation (a) changes in the components of the director, n defining the orientation change (b) bend deformation of an oriented layer of a nematic liquid crystal.

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

Note 4 The flexo-electric effect is the analogue of the piezo-electric effect in solids, where the polarization is induced by a strain that produces a translational deformation of the crystal. The flexo-electric effect in a liquid crystal is caused by a purely orientational deformation. 

Fig. 32. Schematic representation of the flexo-electric effect, (a) The structure of an undeformed nematic liquid crystal with pear- and banana-shaped molecules (b) the same liquid crystal subjected to splay and bend deformations, respectively.

Domain corresponding to a periodic deformation caused by the inverse flexo-electric effect in a nematic liquid crystal. 

Techniques and procedures of such thermoeleastic measurements under unidirectional or uniform (hydrostatic) deformation of solid and rubberlike polymers are described in 1 64 66). Similar methods have been used more often for recording the temperature changes resulting from the plastic deformation of solid polymers. Besides thermocouples, fluorescent substances, liquid crystals and IR-bolometers are used for such measurements. 

In this review we are mainly concerned with thermotropic materials, i.e. with liquid crystals and LC-glasses which do not contain a solvent. The transitions of the macro-molecular, thermotropic liquid crystals are governed then by temperature, pressure and deformation. In lyotropic liquid crystals and LC-glasses a solvent or dispersing agent is present in addition. The transitions then also become concentration dependent. 

The theory of nematic liquid crystal deformation, forced by an electric field is well developed and permits to establish the relationship between the threshold voltage U, causing sample orientation, with Ae and elasticity constants of a liquid crystal (Kn). For the main S and B types of deformation the equation is the following27 ... 

Liquid crystals are widely believed to be closely related to membranes of living cells and have been used as model systems in studies to understand membrane behavior. Among dynamic processes of interest here are transport of various species across membranes and various motions and deformations of membranes. 

Interest in thermotropic liquid crystals has focussed mainly on macroscopic properties studies relating these properties to the microscopic molecular order are new. Lyotropic liquid crystals, e.g. lipid-water systems, however, are better known from a microscopic point of view. We detail the descriptions of chain flexibility that were obtained from recent DMR experiments on deuterated soap molecules. Models were developed, and most chain deformations appear to result from intramolecular isomeric rotations that are compatible with intermodular steric hindrance. The characteristic times of chain motions can be estimated from earlier proton resonance experiments. There is a possibility of collective motions in the bilayer. The biological relevance of these findings is considered briefly. Recent similar DMR studies of thermotropic liquid crystals also suggest some molecular flexibility. 

So far we have discussed 2D density modulated phases that are formed by deformation or breaking of the layers. However, there are also 2D phases with more subtle electron density modulations. In some cases additional peaks observed in the XRD pattern (Fig. 10) are related to a double layer periodicity in the structure. As double layer periodicity was observed in the bent-core liquid crystals formed by the asymmetric as well as symmetric molecules [22-25] it should be assumed that the mechanism leading to bilayers must be different from that of the pairing of longitudinal dipole moments of molecules from the neighboring layers, which is valid for smectic antiphases made by asymmetric rod-like molecules. 

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