Deformations nematics

It has been shown that changing the length of the flexible spacer, m, by one unit can change the optical properties of a deformed nematic LCE qualitatively [15]. While for... 

S. T. Wu and C. S. Wu, Small angle relaxation of highly deformed nematic liqitid crystals, Appl. Phys. Lett. 53, 1794 (1988). 

MBBA SiO, oblique evaporation Direct measurement of the mechanical torques in a deformed nematic 10 (in the vicinity of Tni) [73]... 

The elastic continuum theory is based on the assumption that at each point within the liquid crystal a preferential direction for the molecular orientation is given which is described by a unit vector L, and which varies continuously from place to place — except for a few singular lines or points. Any distortion of the undisturbed state requires a certain amount of energy since elastic torques attempt to maintain the original configuration. The elastic energy density of a deformed nematic liquid crystal is given by... 

Figure 15. Molecular distributions in a deformed nematic liquid crystal.

For finite wavelengths, the collective dynamics of bulk nematics can be described within the hydrodynamic equations of motion introduced by Ericksen [4-8] and Leslie [9-11]. A number of alternate formulations of hydrodynamics [12-18] leads essentially to the equivalent results [19]. The spectrum of the eigenmodes is composed of one branch of propagating acoustic waves and of two pairs of overdamped, nonpropagating modes. These can be further separated into a low- and high-frequency branches. The branch of slow modes corresponds to slow collective orientational relaxations of elastically deformed nematic structure, whereas the fast modes correspond to overdamped shear waves, which are similar to the shear wave modes in ordinary liquids. 

Note that for A < 1, there is no angle where the hydrodynamic torque would be zero, and a strongly deformed nematic structure forms. Such situation is called "tumbling." ... 

To characterize the diffraction properties of the LC grating, we estimated the director distribution in the cell based on the elastic continuum theory of nematic LCs. The elastic energy density of a deformed nematic LC, u, is given by... 

Fig. 6. The three basic curvature deformations of a nematic Hquid crystal bend, twist, and splay. The force constants opposing each of these strains are...

Fig. 16. Gibbs energy-temperature diagram if FCC and ECC are present in the system. Ai-isotropic (undeformed) melt, A2-deformed melt (nematic phase) points 1 and 4 - melting temperatures of FCC and ECC under unconstrained conditions (transition into isotropic melt) points V and 2 -melting temperatures of FCC and ECC under isometric conditions (transition into nematic phase), point 3 - melting temperature of nematic phase (transition into isotropic melt but not completely randomized)...

First of all the term stress-induced crystallization includes crystallization occuring at any extensions or deformations both large and small (in the latter case, ECC are not formed and an ordinary oriented sample is obtained). In contrast, orientational crystallization is a crystallization that occurs at melt extensions corresponding to fi > when chains are considerably extended prior to crystallization and the formation of an intermediate oriented phase is followed by crystallization from the preoriented state. Hence, orientational crystallization proceeds in two steps the first step is the transition of the isotropic melt into the nematic phase (first-order transition of the order-disorder type) and the second involves crystallization with the formation of ECC from the nematic phase (second- or higher-order transition not related to the change in the symmetry elements of the system). 

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... 

Navard and Zachariades (125) examined the optical properties of shear deformed trifluoroacetox3q)ropyl cellulose and observed band phenomena identical to that for thermotropic nematic copolyesters. Steinmeier and Zugenmaier (107) demonstrated that the phenylacetate... 

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.

Note 1 In the equation for g, the term go is usually equal to zero because the undistorted state of nematics is the state of uniform alignment. However, for chiral nematics, a nonzero value of go allows for the intrinsic twist in the structure. In order to describe g for smectic phases, an additional term must be added, due to the partially solid-like character of the smectic state and arising from positional molecular deformations. 

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. 

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. 

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. 

Rusakov 107 108) recently proposed a simple model of a nematic network in which the chains between crosslinks are approximated by persistent threads. Orientional intermolecular interactions are taken into account using the mean field approximation and the deformation behaviour of the network is described in terms of the Gaussian statistical theory of rubber elasticity. Making use of the methods of statistical physics, the stress-strain equations of the network with its macroscopic orientation are obtained. The theory predicts a number of effects which should accompany deformation of nematic networks such as the temperature-induced orientational phase transitions. The transition is affected by the intermolecular interaction, the rigidity of macromolecules and the degree of crosslinking of the network. The transition into the liquid crystalline state is accompanied by appearence of internal stresses at constant strain or spontaneous elongation at constant force. 

It has been shown 65,68) that the threshold voltage is a function of the dielectric anisotropy Ae and the elastic constants of splay (ku), twist (k22) and bend (k33) deformation of the nematic phase (Fig. 17) ... 

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

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 ... 

Examples of these formulations are systems based on a difunctional LC epoxy monomer (diglycidyl ether of 4-4 -dihydroxy-Q -methylstilbene), cured with methylene dianiline (Ortiz et al., 1997). The generation of liquid-crystalline microdomains (smectic or nematic) in the final material required their phase-separation before polymerization or at low conversions. This could be controlled through the initial cure temperature. Values of GIc, (kJm-2) were 0.68 (isotropic), 0.75 (nematic), and 1.62 (smectic). The large improvement produced by the smectic microdomains was attributed to an extensive plastic deformation. 

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