Optical permittivity

From McManis, G.E., Golovin, M.N., Weaver, M.J. J. Phys. Chem. 1986, 90, 6563 Galus, Z. in Advances in Electrochemical Science and Engineering, (Eds H. Gerischer, C.W. Tobias), VCH, Weinheim, Vol 4, p. 222. s static permittivity op optical permittivity ecrj infinite frequency permittivity ... 

The expression for the vibration susceptibility is analogous to Eq. (281a) but we should cancel the optical permittivity n2, since it was included into the term Xor-Hence,... 

The second (ionic) term in Eq. (387) is assumed to vanish in the limit co —> oo, just as does the term As (v) in Eq. (278) stipulated by oscillating charges of a nonrigid dipole. The first term in Eq. (387) will be calculated below in terms of the hybrid model, which was briefly described in Section IV.E. For the limit co —> oo we set this term to be equal to optical permittivity n2, the same as in pure water. 

The quantity eoo represents the optical permittivity, which is determined by the electronic polarizability. The second term represents the ionic crystal lattice as a sum of N classical harmonic oscillators with eigenfrequencies ujj, damping constants Tj and oscillators strengths Sj. In order to fit Equation (5.7) to the observed far infrared spectra, these parameters are used... 

If vdielectric permittivity in vacuum will then be equal to 80. This is the so-called static permittivity. The permittivity of the vaccum is 0.855x 10 C m. The static dielectric permittivity near the ion or the surface of the charged electrodes, however, will exhibit smaller values. For instance, in the case of water at the electrode surface is assumed to approach 6. When applying the Marcus theory [8] both static and optical permittivities are used in calculations. These parameters therefore are listed in Table 1. In other calculations and correlations of the rate constants of electrode reactions and the dynamic relaxation properties of the solvents, the relaxation time of the solvents is used (Thble 1). 

From the fundamental relation (189), we derive for changes in optical permittivity in two mutually perpendicular directions ... 

The dielectric constant is a natural choice of order parameter to study freezing of dipolar liquids, because of the large change in the orientational polarizability between the liquid and solid phases. The dielectric relaxation time was calculated by fitting the dispersion spectrum of the complex permittivity near resonance to the Debye model of orientational relaxation. In the Debye dispersion relation (equation (3)), ij is the frequency of the applied potential and t is the orientational (rotational) relaxation time of a dipolar molecule. The subscript s refers to static permittivity (low frequency limit, when the dipoles have sufficient time to be in phase with the applied field). The subscript oo refers to the optical permittivity (high frequency limit) and is a measure of the induced component of the permittivity. 

According to the Debye model there are three parameters associated with dielectric relaxation in a simple solvent, namely, the static permittivity s, the Debye relaxation time td, and the high-frequency permittivity Eoq. The static permittivity has already been discussed in detail in sections 4.3 and 4.4. In this section attention is especially focused on the Debye relaxation time td and the related quantity, the longitudinal relaxation time Tl. The significance of these parameters for solvents with multiple relaxation processes is considered. The high-frequency permittivity and its relationship to the optical permittivity Eop is also discussed. 

In order to extend the above treatment to the metal solution interface, one must consider the effect of the solvent molecules adsorbed on the metal on the electronic overspill. Because the solvent molecules are polarizable, an induced dipole moment is established in the solvent monolayer, which acts to reduce the extent of overspill. As a result, the dipolar potential due to the metal is reduced by a factor corresponding to the optical permittivity of the monolayer, Sop. Recalling that this dipole potential is designated as one has at the PZC... 

Libration amplitude of a dipole in the hat well Complex susceptibility Optical permittivity in the case of ice Variable part of H-bond length (see Fig. 1)... 

Note, the optical permittivity n is included in the first term eor(v), so... 

In view of Eq. (28), the key aspect of our two-fraction model is reveals division of the total complex permittivity s into the part or(v), including contribution of librations performed in the hat well, and the part Ag(v), including contribution of vibrating H-bonded molecules. These parts are arranged in such a way that when v tends to infinity, or(v) tends to optic permittivity n and As(v) vanishes. In another limit, at zero frequency, eor(0) almost coincides with the static permittivity s, while A (0) is much less ... 

The representation (6.69) of e s indicates that this quantity includes contributions from all the resonance frequencies (C0 =P ) of the frequency dependent permittivity (6.68). Moreover it also is determined by some dissipative properties of the material reflected in the spectral function (,(p)) and also in the optical permittivity =n p,), [6.6, 6.29]. 

Instead we want to emphasize that simple electric network models of LPS may include three different elemental systems capacitors, resistances, and inductances [6.12]. The basic physical relations, admittance functions, elements of the representation theorem (6.55) and corresponding static and optical permittivity are collected in Table 6.1 below. These elements can be combined by series or parallel connections in may different ways. For the admittance functions of the electric network generated in this way, the simple rules hold that... 

Here we have introduced the static permittivity (Er) and the optical permittivity (Eto) by the relations, cp. (6.66)... 

The results from recent decades allow us to describe a picture of thermal motion of long macromolecules in a system of entangled macromolecules. The basic picture is, of coarse, a picture of thermal rotational movement of the interacting rigid segments connected in chains - Kuhn - Kramers chains. One can refer to this model as to a microscopic model. In the simplest case (linear macromolecules, see Sect. 3.3), the tensor of the mean orientation (e,ej) of all (independently of the position in the chain) segments can be introduced, so that the stress tensor and the relative optical permittivity tensor can be expressed through mean orientation as... 

---