Splay elastic properties

In the smectic A phase the director is always perpendicular to the plane of the smectic layers. Thus, only the splay distortion leaves the interlayer distance unchanged [7], and only the elastic modulus K i is finite while K22 and Kzz diverge when approaching the smectic A phase from the nematic phase. On the other hand, the compressibility of the layered structure and the corresponding elastic modulus B is taken into account when discussing the elastic properties of smectic phases. The free energy density for the smectic A phase, subjected to the action of an external electric field, is... 

It is clear that the two polar vectors respect the apolar nature of n. There is also an obvious analogy of the above mechanism with the orientation polarization of a liquid dielectric, which was used by Helfrich to relate the two flexocoefficients with molecular properties. The intrinsic splay or bend can be related to an appropriate angle and molecular dimensions. The relevant component of the electric dipole moment and the curvature elastic constant, viz., and the splay constant Ki or /ux and the bend constant It s figure in the estimation of the flexocoefficients. Nematic liquid crystals made of banana-shaped molecules have been studied only recently, and a comparison of the experimental measurements with the Helfrich formula leads to interesting inferences, as will be mentioned later in this chapter, and covered more thoroughly in the companion Chapter 3 by Jakli et al. ... 

The principal elastic constants for a nematic liquid crystal have already been defined in Sec. 5.1 as splay (A , j), twist(/ 22) and bend(fc33). In this section we shall outline the statistical theory of elastic constants, and show how they depend on molecular properties. The approach follows that of the generalised van der Waals theory developed by Gelbart and Ben-Shaul [40], which itself embraces a number of earlier models for the elasticity of nematic liquid crystals. Corresponding theories for smectic, columnar and biaxial phases have yet to be developed. 

Soft membranes attracted the attention of physicists in recent years because of novel properties related to their nonplanarity. Typically, thermal energies are sufficent to produce marked deviations from the planar state. In the case of fluid membranes, these fluctuations depend primarily on their bending elasticity. The energy of bending per unit area, g, is usually expressed by a quadratic form in the principal curvatures, C and C2 which are splays in the language of liquid crystals ... 

Until 1982 Schadt and coworkers successfully developed experimental techniques for reliably determining all relevant liquid crystal material parameters, i.e., optical An = (nil and dielectric anisotropy Ae = (fn — l), splay (A h), twist ( 22) and bend ( 33) elastic constants, viscosity constants (//, y,), etc. This provided the basis for searching for correlations between molecular structural elements, LC material properties, and display performance [12, 16,17]. Figure 1.2 illustrates an example... 

Fig. 1.3 (a) Dependence of the splay/bend elastic constant ratio iaa/Ai i of different nematic liquid crystals on molecular structural elements versus normalized (reduced) temperature TfTc. (b) Odd-even dependence of the material properties of a homologous stales of Odi CPS alkenyl liquid crystals on side-chain double-bond position d (i = 3,4,5,7)... 

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