Dielectric anisotropy, theory

As an example of an application of the mean field method we shall consider the theory of the dielectric anisotropy of the nematic phase. The low frequency dielectric anisotropy of a molecule is determined by two factors (i) the polarizability anisotropy which for the elongated molecules of nematogenic compounds always makes a positive contribution (i.e., a... 

In contrast to diamagnetism where the magnetic interactions between molecules can be neglected, the polarization field in the medium becomes important when discussing dielectric anisotropy (see, e.g., Bottcher< >). Maier and Meier > took this into account by applying the Onsager theory.The effective induced dipole moments per molecule along and... 

FIGURE 5.7. Experimental dependences of the threshold voltage for Ka-pustin-Williams domains with a planar initial orientation (a) on the anisotropy of the electrical conductivity and (b) on the dielectric anisotropy for doped MBBA (circles) and for mixture A of azoxy compoimds (crosses). Calculation is according to a two-dimensional theory (curve 1) and a one-dimensional theory (curve 2). The threshold of the Prederiks effect for doped MBBA is shown in curve 3, which represents the theory, while the squares represent the experimental measurements [31]. 

Results of experiments performed by Durand et al. [5] are presented in Figure 2.15. They show excellent agreement with the theory. These authors have also verified that the critical field varies as the inverse of the pitch p. The helical unwinding can also be observed when an electric field is applied to a cholesteric liquid crystal with a positive dielectric anisotropy [6],... 

Equation (27) presents a simple anisotropic attraction potential that favors nematic ordering. This potential has been used in the original Maier-Saupe theory [11, 12]. We note that the interaction energy (Eq. 27) is proportional to the anisotropy of the molecular polarizability Aa. Thus, this anisotropic interaction is expected to be very weak for molecules with low dielectric anisotropy. Such molecules, therefore, are not supposed to form the nematic phase. This conclusion, however, is in conflict with experimental results. Indeed, there exist a number of materials (for example, cyclo-... 

A full theory of the frequency dependence of the electric permittivity of liquid crystals cannot yet be given. It is a formidable problem since it requires proper account to be taken of the influence of orientational order on molecular motion, as well as the effects of macroscopic dielectric anisotropy. The dielectric response of a rigid dipolar molecule rotating in an isotropic fluid can be described in terms of a single relaxation time or rotational diffusion constant. In a liquid crystal phase, the rotational motion is no... 

Electroclinic Effect Near the Smectic A—Smectic C Phase Transition. The electric field may induce a tilt of the director in the orthogonal smectic A phase near the smectic A-smectic C phase transition (electroclinic effect [189, 191]). The electroclinic effect may be understood within framework of the Landau phase transition theory [7]. If the dielectric anisotropy is negligible, the free energy density of the smectic A phase may be expanded over the field-induced tilt angle 6 ... 

The dielectric anisotropy Ae of LC-materi-als is defined by Ae= j -ex, where and ej. are the dielectric constants parallel and perpendicular to the director. From the Maier and Meier theory it can be seen that both the polarizability anisotropy Aa and the permanent dipole movement /i of the LC molecule determine the dielectric anisotropy... 

Helfrich [49] was first to propose electro-hydrodynamic instability in cholesterics with negative dielectric anisotropy. Harault [56], combining Helfrich theory with time-dependent formalism, calculated a voltage frequency relationship similar to that observed for Williams domains. The existence of conduction and dielectric regimes was experimentally verified. The domain periodicity is proportional to wherepo... 

In all of the present theories about the excitation of nematic or cholesteric liquids by an electric field, the mesomorphic material is treated as a continuous elastic anisotropic medium. The Oseen -Frank elastic theory is used to describe the interaction between the applied field and the fluid. The application of an electric field causes the liquid crystal to deform. For a material with a positive dielectric anisotropy, Ae = > 0, the director aligns in the direction of... 

Lin Y, Boker A, Sill K, Xiang H, Abetz C, Li X, Wang J, Emrick T, Balazs AC, Russell TP (2005) Self-directed self-assembly of nanoparticle/copolymer mixtures. Nature 434(1 ) 55-59 Lopatina LM, Selinger JM (2011) Maier-Saupe-type theory of ferroelectric nanoparticles in nematic liquid crystals. Phys. Rev E 84 041703/1-041703/7 Lorenz A, Zimmermann N, Kumar S, Evans DR, Cook G, Martinez ME, Kitzerow H-S (2013) X-ray scattering of nematic liquid crystal nanodispersion with negative dielectric anisotropy. Appl Opt 52(22) E1-E5... 

The anisotropy of the a and P relaxations for drawn poly(ethylene terephthalate) has been studied by several workers.Davies and Ward showed that the a process exhibited little anisotropy but the p process a pronounced anisotropy when measurements were made on sections cut from an oriented rod (extrusion ratio = 3.3 1). In a study of the p relaxation in oriented poly(ethylene terephthalate), Hsu et attempted to modify the Kirkwood equation (equation (42) above) for application to systems of oriented dipoles. They found that the change in the dielectric properties on orientation of a sample could not be explained in terms of the alignment of chains alone, but the effect of conformational changes on dielectric anisotropy needed to be considered. In a further paper these authors showed that satisfactory agreement was obtained between the observed dielectric anisotropy and a theory in which the director order parameter (c/ Section 18.3.4) and the angle between the dipole moment vector of a repeat unit and the chain axis were adjustable parameters. 

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