Linear isotropic dielectrics

When the linear isotropic dielectric medium used in the standard model is replaced with a linear homogeneous medium with Green kernel Ge, and when the charge distribution is entirely supported inside the cavity, the reaction potential inside the cavity still has a simple integral representation ... 

In the continuum solvent distribution models, Vei is evaluated by resorting to the description of the solvent as a dielectric medium. This medium may be modeled in many different ways, being the continuous methods quite flexible. We shall consider the simplest model only, i.e. an infinite linear isotropic dielectric, characterized by a scalar dielectric constant e. The interested reader can refer to a recent review (Tomasi and Persico, 1994) for the literature regarding more detailed and more specialistic models. However, the basic model we are considering here is sufficient to treat almost all chemical reactions occurring in bulk homogeneous solutions. 

The basic outline of the heterogeneous dielectric media method is to divide the total system into two subsystems. The solvated molecule is encapsulated in a cavity C which is given by the surfaces and 2 . The cavity is surrounded by a heterogeneous environment given by two part Sm and St. The two dielectric media are in contact with the cavity through the surfaces Xm and 2,. Each of the two dielectric media is taken to be a linear, homogeneous and isotropic dielectric medium and is characterized by a scalar, optical, inertial or static dielectric constant. As an illustration, we consider two dielectric media, Sm and Sh characterized by the dielectric constants em and eh respectively, with the following spatial positions ... 

In dielectric spectroscopy the polarization response P(t) of a dipolar material is monitored, which is subject to a time-dependent electric field (Maxwell field), E t). For a linear and isotropic dielectric one can write (e.g., Ref. 34) ... 

This chapter is intended as a review of the work done, particularly during the last ten years, in the field of non-linear electric and magnetic i>roperties of isotropic dielectrics. We shall deal with these achievements against the background of earlier results, the majority of which have, by now, become included for good in numerous monographs, handbooks, and review... 

The effect consisting in a change in magnetic pmneability under the influ ice of an electric field still awaits detection, although considered theoretically for paramagnetics by Van Vleck, as wdl as for diamagnetics. Non-linear Electro- and Magneto-optical Effects, Optical saturation in an electric field. When an optically isotropic dielectric is placed in a very... 

Under the influence of a strong fidd, an isotropic dielectric becomes not only non-linear but also anisotropic, with the following dectric permittivi tensor ... 

The non-linearity, induced in a naturally isotropic dielectric by an electric fidd, is defined in terms of the variation in the permittivity tensor, cf. equation (12) ... 

Available theoretical and experimental results on electric field induced non-linearities in isotropic dielectrics prove that we have here an effective method for the study of the dectric structure of molecules, as well as of their mutual interactions in dense states, i.e. of the structure of near ordering in liquids. 

An Outline of Non-linear Effects in Dielectrics. Constitutive Relations in Linear Media. We shall be considering homogeneous and isotropic dielectrics, the electric, magnetic, and optical properties of which, in the absence of external fields, are described by the following three scalar quantities, characteristic of the material of which the medium consists e = electric permittivity /X = magnetic permeability n = refractive index. 

Molar Electric Polarization of Dense Media.— In Kirkwood s semi-macroscopic treatment of the linear proparties of isotropic dielectrics, one has the following relation between the relative electric permittivity Sr and the polarization P( ) induced in the medium ... 

High Electric Field Effects.—Determination of Variations in Electric Permittivity. The electric permittivity e of an isotropic dielectric is usually measured by means of a dowly varying dectric field, of a field strength Eoo so small as to cause only linear polarization of the medium ... 

During 1980-1981 the possibility of the existence of nonlinear surface polaritons of various types was predicted in the literature (18), (19)-(20). In particular, Tomlinson (19) and Maradudin (21) derived s-polarized surface polaritons at a plane interface between two dielectrics, one of which has an isotropic and linear (e1) dielectric constant whereas the dielectric constant of the other is that of a nonlinear uniaxial medium... 

The operator Le has a different form according to the model we are using to describe the system. We report here the expression for three important cases, namely the linear infinite isotropic dielectric, the linear infinite anisotropic dielectric (with homogeneous tensorial permittivity c), and the infinite ionic solutions in the linearized Poisson-Boltzmann formulation ... 

Formal Theory A small neutral particle at equihbrium in a static elecdric field experiences a net force due to DEP that can be written as F = (p V)E, where p is the dipole moment vecdor and E is the external electric field. If the particle is a simple dielectric and is isotropically, linearly, and homogeneously polarizable, then the dipole moment can be written as p = ai E, where a is the (scalar) polarizability, V is the volume of the particle, and E is the external field. The force can then be written as ... 

The isotropic coefficient and the anisotropic coefficients b(m> and c(m) can have both bulk and surface contributions and depend on crystal symmetry. The linear and nonlinear dielectric constants of the material, as well as the appropriate Fresnel factors at co and 2co, are incorporated into the constants a, b m) and c(m). Table 3.1 shows the susceptibilities contained in each of these constants. The models of Tom... 

In much of the above analysis, the relative magnitude of the surface and bulk contribution to the nonlinear response has not been addressed in any detail. As noted in Section 3.1, in addition to the surface dipole terms of Eq. (3.9), there are also nonlocal electric-quadrupole-type nonlinearities arising from the bulk medium. The effective polarization is made of a combination of surface nonlinear polarization, PNS (2co) (Eq. (3.9)), and bulk nonlinear polarization (Eq. (3.8)) which contains bulk terms y and . The bulk term y is isotropic with respect to crystal rotation. Since it appears in linear combination with surface terms (e.g. Eq. (3.5)), its separate determination is not possible under most circumstances [83, 129, 130, 131]. It mimics a surface contribution but its magnitude depends only upon the dielectric properties of the bulk phases. For a nonlinear medium with a high index of refraction, this contribution is expected to be small since the ratio of the surface contribution to that from y is always larger than se2(2co)/y. The magnitude of the contribution from depends upon the orientation of the crystal and can be measured separately under conditions where the anisotropic contribution of vanishes. 

In this chapter, dielectric response of only isotropic medium is considered. However, in a local-order scale, such a medium is actually anisotropic. The anisotropy is characterized by a local axially symmetric potential. Spatial motion of a dipole in such a potential can be represented as a superposition of oscillations (librations) in a symmetry-axis plane and of a dipole s precession about this axis. In our theory this anisotropy is revealed as follows. The spectral function presents a linear combination of the transverse (K ) and the longitudinal (K ) spectral functions, which are found, respectively, for the parallel and the transverse orientations of the potential symmetry axis with... 

Thus the spectral function L(z) of an isotropic medium is represented as a linear combination of two spectral functions determined for an anisotropic medium pertinent to longitudinal ( ) ) and transverse (K ) orientations of the symmetry axis with respect to the a.c. field vector E. It is shown in GT, Section V, that these spectral functions are proportional to the main components of the dielectric-susceptibility tensor. 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

The solvation free energy calculated by considering only the bulk electrostatics is somewhat arbitrary because the boundary between the dielectric medium and the solute is not well defined, and in fact the treatment of the solvent as a homogeneous, isotropic, linear medium right up to a definite boundary is not valid. To obtain an accurate solvation... 

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