Homogeneous dielectric

Consider next a homogeneous dielectric exposed to a non-uniform field. The above considerations may be applied to any element of volume dv. Since the polarization is the moment per unit volume, the... 

Let us next consider a non-uniform field, where the intensity X is a function of position. The expression (7) applies to unit volume if then (7) is multiplied by dv, the expression will give the amount of free energy lost in an clement of volume dv, where the field has an intensity X. The total loss of free energy will be obtained by integrating over the whole volume of the homogeneous dielectric ... 

For all common substances the temperature coefficient of t is negative that is to say, the temperature coefficient of 1/e is positive hence (11) represents a loss of entropy on subjecting the homogeneous dielectric to the field. 

The Born equation thus derived is based on very simple assumptions that the ion is a sphere and that the solvents are homogeneous dielectrics. In practice, however, ions have certain chemical characters, and solvents consist of molecules of given sizes, which show various chemical properties. In the simple Born model, such chemical properties of ions as well as solvents are not taken into account. Such defects of the simple Born model have been well known for at least 60 years and some attempts have been made to modify this model. On the other hand, there has been another approach that focuses on short-range interactions of an ion with solvent molecules. 

E-A. Numerical or analytic solution of the classical electrostatic problem (e.g., Poisson equation) with homogeneous dielectric constant for solvent. 

A homogenous dielectric environment with the didctric constant of water was modded using SCRF calculations (see Wong, M. W. Frisch, M. J. Wiberg, K. B. Solvent Effects. 1. The Mediation of Electrostatic Effects by Solvents J. Am. Chon. Soc 1991,113,4776-4782). 

The theory proposed by Debye and Huckel dominated the study of aqueous electrolytes from around 1920 to near the end of the 1950 s. The Debye-Huckel theory was based on a model of electrolyte solutions in which the ions were treated as point charges (later as charged spheres), and the solvent was considered to be a homogeneous dielectric. Deviations from ideal behaviors were assumed to be due only to the long range electrostatic forces between ions. Refinements to include ion-ion pairing and ion... 

If one is interested in changes of the solute molecule, or if the structure of the surrounding solvent can be neglected, it may be sufficient to regard the solvent as a homogeneous dielectric medium, as was done in the older continuum theories, and to perform a quantum mechanical calculation on the molecule with a modified Hamiltonian which accounts for the influence of the solvent as has been done by Hylton et al. 18 5>. Similarly Yamabe et al. 186> substituted dipole-moment operators for the solvent in their perturbational treatment of solvent effects on the activation energy in the NH3 + HF reaction. 

In studying systems in an electrostatic field, we must consider two systems because of the dependence of the field on matter within the field. One system is a parallel-plate condenser in empty space. The area of the plates is designated by A, and the distance between the plates by /. The other is an identical condenser immersed in an isotropic, homogenous, dielectric medium. The conductivity of the medium is zero, so no free charges are present in the medium. Edge effects are neglected and rational units are used throughout. 

The propagation of light in a nonlinear medium is governed by the wave equation, which was derived from Maxwell s equations for an arbitrary homogeneous dielectric medium,... 

The OWB model describes the solute as a classical polarizable point dipole located in a spherical or ellipsoidal cavity in an isotropic and homogeneous dielectric medium representing the solvent. In the presence of a macroscopic Maxwell field E, the solute experiences an internal (or local) field E given by a superposition of a cavity field Ec and a reaction field ER. In terms of Fourier components E -n, Ec,n, ER,n of the fields we have... 

Homogeneous Dielectric Medium Response for Two-photon Absorption... 

The required modifications of the response equations follow closely those that occur for the homogeneous dielectric medium and heterogeneous dielectric media methods [10— 14,82-84,91], The different methods differ only by the representation of the effective operators. Furthermore, the mathematical structure of the WQM/CM-induced modifications to the response equations is similar to those for response equations for the molecule in vacuum [90], For the actual implementation of the contributions to the response equations due to the interactions between the molecular subsystem and the structured environment, it is easily observed that one needs to define, formulate and calculate the effective QM/CM operators and to insert these into an existing response program. 

The potential energy of interaction between two electronic charges qx and q2 separated by a distance r in a medium of homogeneous dielectric constant (e) is given by Coulomb s law and can be written in arbitrary units as... 

In contrast to dielectric losses permittivity is not, in general, sensitive to small amounts of impurities and for homogeneous dielectrics values can be calculated as described in Section 2.7.1, and the various mixture rules allow good estimates to be made for multiphase dielectrics. For Ba- and Sr-based dielectrics having the perovskite structure the variation of permittivity with temperature, which determines rf (see Eq. (5.37)), can be correlated with the tolerance factor t (see Section 2.7.3) [13] providing guidance for tailoring ceramics to have xf = 0. 

The model proposed in the present paper for the polarization is based on a simple idea. In a real medium, the interactions between remote dipoles are screened by the intervening solvent molecules and hence are decreased by a factor equal to the inverse ofthe dielectric constant of the medium. On the other hand, the interactions between adjacent dipoles are muchless screened andhence are more important. In a medium with homogeneous dielectric properties, a planar layer of dipoles produces a vanishing average electric field above it. However, because the medium is not homogeneous at the molecular level, the field of a nearby dipole is screened less and an electric field is generated above the plane. 

One of the models for the hydration force, the polarization model,5 assumes that the hydration force is generated by the local correlations between neighboring dipoles present on the surface and in water. The macroscopic continuum theory, in which water is assumed to be a homogeneous dielectric, predicts that there is no electric field above or below a neutral surface carrying a uniform dipolar density. However, at microscopic level the water is hardly homogeneous, and the electric interactions... 

For a homogeneous dielectric medium, in the absence of interface effects (see Sect. 3.2), the experimental quantities sx and e" are equal to the bulk properties e and e", and the experimental loss tangent becomes... 

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