Dielectric effective field

Experimental and theoretical results are presented for four nonlinear electrooptic and dielectric effects, as they pertain to flexible polymers. They are the Kerr effect, electric field induced light scattering, dielectric saturation and electric field induced second harmonic generation. We show the relationship between the dipole moment, polarizability, hyperpolarizability, the conformation of the polymer and these electrooptic and dielectric effects. We find that these effects are very sensitive to the details of polymer structure such as the rotational isomeric states, tacticity, and in the case of a copolymer, the comonomer composition. 

When a strong static electric field is applied across a medium, its dielectric and optical properties become anisotropic. When a low frequency analyzing electric field is used to probe the anisotropy, it is called the nonlinear dielectric effect (NLDE) or dielectric saturation (17). It is the low frequency analogue of the Kerr effect. The interactions which cause the NLDE are similar to those of EFLS. For a single flexible polar molecule, the external field will influence the molecule in two ways firstly, it will interact with the total dipole moment and orient it, secondly, it will perturb the equilibrium conformation of the molecule to favor the conformations with the larger dipole moment. Thus, the orientation by the field will cause a decrease while the polarization of the molecule will cause an... 

Since the absorption process is 7r/2 out of phase with the electromagnetic field its effect on the index of refraction will also lag in the same way behind the simple dielectric effect. The total index of refraction is therefore formulated as 77 = n + ik, where k is the absorptive contribution. 

A through-space electrostatic effect (field effect) due to the charge on X. This model was developed by Kirkwood and Westheimer who applied classical electrostatics to the problem. They showed that this model, the classical field effect (CFE), depended on the distance d between X and Y, the cosine of the angle 6 between d and the X—G bond, the effective dielectric constant and the bond moment of X. 

The relative permittivity of a solvent depends also on the electric field E, but ordinary fields employed in the laboratory are rarely strong enough to cause an appreciable change of s. The phenomenon is called the non-linear dielectric effect. A relevant expression (Grahame 1953) is ... 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

The dielectric effect on the interactions among inner region atoms is represented through a reaction field term,... 

In the general case, electrostriction is not isotropic even in isotropic dielectrics a field-induced anisotropy of electrostriction appears and is perceptible also in measurements of the static" and optical" Kerr effects. This anisotropy of electrostriction is particularly apparent if the field acting on the dielectric is strong, such as the intense electromagnetic field of a light wave, in which case the time-dynamics of the electrostrictive effect have to be studied s arately." ... 

Another model of experimental interest concerns the case of a highly conductive shell around practically non-conductive material. It may be applied to macromolecules or colloidal particles in electrolyte solution which usually have counterion atmospheres so that the field may displace freely movable ionic charges on their surfaces. The resulting dielectric effect turns out to be equivalent to a simple Maxwell-Wagner dispersion of particles having an apparent bulk conductivity of... 

The field penetration effect is much smaller than structural and nonlocal solvent dielectric effects. Particularly, the increase of Er with increasing electrode-molecule distance is retained, although attenuated. Attenuation can be appreciated as an image delocalization compared to the localized image charge contribution in eqn. (8-8). ... 

In applying this relationship to dipolar molecules in dense gases and liquids the field E is understood to be the local or effective field E. In order to estimate E one must solve the statistical mechanical problem which relates the local quantity to the macroscopic applied field E. The problem is solved by estimating the local field in a spherical cavity within the dielectric (fig. 4.1). The cavity is assumed to have molecular dimensions with diameter a. The material within the sphere is considered in terms of individual molecules, whereas that outside the sphere is... 

Insulating material Dielectric constant Field-effect mobility (cm V- s )... 

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