Isotropic medium dielectric response

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... 

If the angle (3 is much less than 1, then, in accord with Figs. 7 and 9, the most part of the rotators move freely under effect of a constant potential U0, since their trajectories do not intersect the conical cavity. A small part of the rotators moves along a trajectory of the type 1 shown in Fig. 10. However, at d > (3—that is, in the most part of such a trajectory—they are affected by the same constant potential U0- Therefore, for this second group of the particles the law of motion is also rather close to the law of free rotation. For the latter the dielectric response is described by Eq. (77). We shall represent this formula as a particular case of the general expression (51), in which the contributions to the spectral function due to longitudinal A) and transverse KL components are determined, respectively, by the first and second terms under summation sign. Free rotators present a medium isotropic in a local-order scale. Therefore, we set = K . Then the second term... 

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],... 

An applied electric field can be the electric held component of an electromagnetic wave, in which case electronic excitations or other optical responses may ensue. These are the topic of the next chapter. Here, the concern is with electrostatics, specihcally, the dielectric, or insulative, properties of materials. In an electrical conductor, an applied electric held, E, produces an electric current - ions, in the case of an ionic conductor, or electrons, in the case of an electronic conductor. Electrical conductivity has already been examined in earlier chapters. In insulating solids, the topic of the current discussion, the response to an applied electric held is a static spatial displacement of the bound ions or electrons, resulting in an electrical polarization, P, or net dipole moment (charge separahon) per unit volume, which is a vector quantity. In a homogeneous linear and isotropic medium, the polarization and electric held are aligned. In an anisotropic medium, this need not be so. The fth component of the polarization is related to the jth component of the electric held by ... 

Having obtained expressions for the dielectric susceptibility and the dielectric response functions in terms of microscopic variables, we may proceed to express other observables in microscopic terms. Consider an electromagnetic mode whose electric component is described by a plane wave propagating in the x direction in an isotropic medium, and assume that the field is weak enough to make linear response theory valid. The field is given by... 

The non-local dielectric effect can be a more serious concern. Fuchs and Claro investigated the multipolar response of small metallic spheres and derived an approximation for the non-local dielectric function. In Eqs. (27) and (28) the index n has the interpretation of being the angular momentum in units of h. Note that the sums extend m one to infinity. They argue that there should be a cutoff in the angular momentum. Electrons in a solid sphere (treated as an isotropic medium) have a maximum angular momentum np determined by the Fermi level. For a ffee-electron... 

An essential part of the electro-optic effect in PSFLCs depends on the dielectric response of the medium. Assuming the composite medium to be subjected to a constant isotropic dielectric constant, we have... 

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. 

A dielectric medium is said to be linear if the vector held P r, t) is linearly related to the vector held E r, t). This approximation is always used in the held of linear optics but fails in the case of nonlinear optics as will be discussed in more details in Sect. 3. A medium is said to be nondispersive if its response is instantaneous, meaning that the polarization at time t depends only on the electric held at that same time t and not on prior values of E. In most dielectrics the response time is very short (femtosecond or picosecond response times), but the fact that it is nonzero has huge consequences as will be discussed later. A medium is said to be homogeneous if the response of the material to an electric held is independent of r. A medium is said to be isotropic if the relation between E and P is independent of the direction of the held vector E. In the simplest case, when the medium satishes all these conditions, the vectors P and E at any position and at any time are parallel and proportional and related to each other by... 

One of the simplest responses a dielectric medium can make to the impressed field is via electronic polarization (displacement of bound charges). The traditional vector used to describe the response is the displacement vector, 5(r, t). Under most experimental conditions B is linearly related to E, i.e., B = sE, where 8 is real and is also a scalar if the medium is isotropic. In this case, B and E are in phase. 

Originally, continuum models of solvent were formulated as dielectric models for electrostatic effects. In a dielectric model the solvent is modeled as a continuous medium, usually assumed homogeneous and isotropic, characterized by a scalar, static dielectric constant e. This model of the solvent, that can be referred to the original work by Bom, Onsager and Kirkwood 60-80 years ago, assumes linear response of the solvent to a perturbing electric field due to the presence of the molecular solute. 

Dielectric properties describe the polarization, P, of a material as its response to an applied electric field E (bold symbols indicate vectors) [1—3], In the field of solution chemistry, the discussion of dielectric behavior is often reduced to the equilibrium polarization, Pq = So(s — V) Eq (eq is the electric field constant), of the isotropic and nonconducting solvent in a static field, Eq. Characteristic quantity here is the static relative permittivity (colloquially dielectric constant ), , which is a measure for the efficiency of the solvent to screen Coulomb interactions between charges (i.e., ions) embedded in the medium. As such, enters into classical electrolyte theories, like Debye-Hiickel theory or the Bom model for solvation free energy [4, 5] and is used... 

Since this section is intended to investigate the optical properties of conducting polymers, it is relevant to review some basic optical properties of simple solids. Therefore, this section starts with a rather elementary treatment of the optical constants. The optical constants of solids provide information on their electronic and vibronic structure since the electromagnetic field of the light wave interacts with all fixed and mobile charges [1171,1172]. For a simple solid (a homogeneous, isotropic, and linear medium that is local in its response), the response of the system to the field is characterized by a complex dielectric function, e(o)), given as... 

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