Twisted elastic constant

In SmA and lamellar phases, all twist modes are forbidden due to the relatively large values of twist elastic constant (K22), resulting in a different frequency dependence for 2-dimensional DF. Thus, the spectral density J u>) due to 2-dimensional DF (or layer undulations) is given ( T33 [Pg.102]

Nematic liquid crystals of negative dielectric anisotropy with a low rotational viscosity and a high value of the twist elastic constant k22 are required, see Equations 38-40. Furthermore, a high value for the resistivity and short... 

Table 3. Anisotropy of the magnetic susceptibility and twist elastic constants of some ptdy-...

The viscosity of a typical cholesteric made by doping a nematic with a modest amount of chiral nematic is much lower (around 1 P or so) than that of the typical pure eholesteric. Perhaps this is because the pitch of the doped nematic is higher than that of the typical pure cholesteric, or because the twist elastic constant of the doped nematic is much lower. 

The strain increases the energy of the solid as a stress is applied. The distortion of the director in liquid crystals causes an additional energy in a similar way. The energy is proportional to the square of the deformations and the correspondent coefficients are defined as the splay elastic constant, K, twisted elastic constant K22 and bend elastic constant Kx, i.e., the respective energies are the half of... 

The rigid polymers PBLG in solution is an exception which has been well studied. There have been a few experimental data on the elastic constants, especially on the twist elastic constants. 

PBLG is a para-magnetic material with positive magnetic susceptibility anisotropy ya. It exhibits the cholesteric phase in various solutions with a helical pitch ranging from ten to tens of microns. The unwinding effect is an approach to measure the twist elastic constant K22-... 

The twist elastic constant of PBLG is a function of the concentration in solution, seen from Figure 6.6(a), and of the temperature, shown in Figure 6.6(b). It is demonstrated that K22 is approximately proportional to the concentration in solution as the theory predicts and decreases as temperature increases and thus the order parameter decreases. 

For the CB0n0.fSj2MB series with n - 7 and 9 a blue phase was observed but not for n = 6 and 8 thus, the chiral properties of these materials do indeed exhibit an odd-even effect as expected. This was rationalised in terms of the smaller pitch for the odd relative to the even membered dimers which arises from the smaller twist elastic constant of odd dimers and is related to their lower orientational order. Surprisingly, the helical twisting power of the dimers in a common monomeric nematic solvent appears to depend solely on the nature of the chiral group, the 2-methylbutyl chiral centre, and not on its environment. Thus similar helical twisting powers are observed for both odd and even membered dimers. We will return to the nature of the phases exhibited by some of these chiral dimers in Sect. 4.4. 

Similar expressions are obtained for the splay and twist elastic constants. The temperature dependence of the elastic constants of simple nematics is represented well by (2.3.35). >... 

An important source of error in these calculations is the neglect of short-range order. In particular, the theory fails for the bend and twist elastic constants when smectic-like short-range order is present in the nematic liquid crystal. Under such circumstances these two constants exhibit a critical divergence as the temperature approaches the smectic-nematic point and the light scattering also shows a marked temperature dependence. The present treatment is then inadequate and more elaborate models have been proposed. The phenomenological theory of this aspect of the problem will be discussed in chapter 5. 

Fig. 3.4.4. Twist elastic constant versus temperature for PAA and PAP. Squares, circles and triangles represent independent measurements on different...

We have so far assumed Kxx=K22=K =K. Real nematics are of course, elastically anisotropic. From the values of the energies of the disclinations calculated for the case where Ki =K22 K22 it follows that the wedge disclinations are more stable than the twist disclinations if A 22>A =Af i=A 33, and vice versa. Anisimov and Dzyaloshin-skii [38] have shown that lines of half-integral strength may be stable against three-dimensional perturbations if the twist elastic constant (22 i/2(A, j-i-A"3 3). More precisely,... 

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. 

The three elastic constants of a liquid crystal are important physical parameters which depend on the interaction between the molecules in the liquid crystalline state. While a large number of theoretical and experimental investigations on the elastic constants are contained in the literature for thermotropic liquid crystals, very little is known about them in the case of lyotropic polymer liquid crystals such as those formed by poly-Y-benzyl-L-glutamate (PBLG) in various organic solvents. Some theoretical investigations have been carried out 3 the experimental data is limited largely to measurements of the twist elastic constant and a few recent measurements of the bend and splay constants. ... 

The cell parameters thickness (d), twist (3o)> capacitive threshold voltage (Vc) and the liquid crystal material parameters birefringence (n ), dielectric anisotropy (Ea)> pitch (P), bend to splay elastic constant ratio (K3/KX) and twist elastic constant (K2) were varied one at a time over a wide range of values. Transmission versus voltage curves were calculated at 0 and 40 incidence in the principal viewing plane and values for M0, My,... 

Table 3. Dependence of figures of merit on the twist elastic constant K2.

For most liquid crystals, the twist elastic constant is smaller than the bend elastic constant Therefore it is possible to reduce the total elastie energy by escaping fi om the bend deformation to the twist deformation as shown in Figure 1.21(c). The liquid crystal director is no longer on the r-z plane but twists out of the plane and is given by... 

In Equation (8.5), yi is the rotational viscosity, K22 is the twist elastic constant, Ae is the dielectric anisotropy, E is the electric field strength, and (p is the LC rotation angle. The homogeneous LC layers having cell gap d are along the z axis. 

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