Optical dielectric constants

The excess polarizability a is related to the (optical) dielectric constants o and of the solvent and of the solution, respectively, in the following manner ... 

Optical dielectric constant of the medium, of the solvent, and their difference (Chap. VII). 

Interestingly, the contributions from the gradient of the electromagnetic field across the interface, Tfg xx and Tfg zzz, which scale with the mismatch in the optical dielectric constants of the media forming the interface [37], only appear in the susceptibility tensor components nd xl zzz- Therefore, these contributions may be rejected with a... 

The solvent medium is characterized by its static and optical dielectric constants, e and <, respectively, and its polarization is assumed to be the sum of two components... 

These expressions appear more applieable to nonpolar solvents or mixtures than to polar solvents. The nature of the solvation process (and the radii and so forth of the solvated reactants) may stay approximately constant in the first situation but almost certainly will not in the seeond. The function (E>op A ) features in the reorganisation term Xq which is used for estimating rate constants for redox reactions (Eqn. 5.23). is the optical dielectric constant and Dj the static dielectric constant (= refractive index ). 

The physical significance of these variables is apparent when they are evaluated in the Onsager cavity description of solvation, which treats the solute as a sphere (which we will assume here is unpolarizable) of radius a. The solvent is modeled as a uniform dielectric medium with a static dielectric constant s and an optical dielectric constant op. The following relationships apply in the Onsager cavity description... 

In Equation (I). i2 ikT is the average component in the direction of the field of the permanent dipole moment of the molecule. In order that this average contribution should exist, the molecules must be able to rotate into equilibrium with the field. When the frequency of the alternating electric field used in the measurement is so high that dipolar molecules cannot respond to it, the second term on the right of the above equation decreases to zero, and we have what may he termed the optical dielectric constant f,.t defined by the expression... 

Thcse equations require that the dielectric constant decrease from the static to the optical dielectric constant with increasing frequency, while the dielectric loss changes from zero to a maximum value f" and back to zero. These changes are the phenomenon of anomalous dielectric dispersion. From the above equations, it follows that... 

The unique properties of dilute metal-ammonia solutions depend not upon the nature of the metal species, but upon the solvated electron common to all these solutions. Thus, the electron-in-a-cavity model (17, 19, 21) seems best suited to describe the species present in these solutions since the model is independent of the type of cation present. Jortner and his associates (15, 16) have extended this model by assuming that the cavity arises from polarization of the medium by the electron. The energy levels of the bound electrons are obtained by using a potential function containing the static and optical dielectric constants of the bulk medium as parameters. Using one-parameter hydrogen-like wave functions for the first two bound states of the electron, the total energy of the ith state is expressed as... 

This longitudinal relaxation time differs from the usual Debye relaxation time by a factor which depends on the static and optical dielectric constants of the solvent this is based on the fact that the first solvent shell is subjected to the unscreened electric field of the ionic or dipolar solute molecule, whereas in a macroscopic measurement the external field is reduced by the screening effect of the dielectric [73]. 

By expanding / so1 as a function of the dipole of the isolated molecule and the polarizability a of the molecule, it is possible to obtain an expression for ffJJP /dQ as a function of e, the solute refractive index n, the solution refractive index ns and a [17,18]. Note that the Buckingham approach accounts for nonequilibrium solvent effects (see below), described in terms of the optical dielectric constant eopt. A comparison between PCM calculated IR intensities and classical equations is reported in ref. [8],... 

When the dielectric medium is not homogeneous, one approach in the DC framework is to divide the medium into component homogeneous DC zones, each governed by its respective static and optical dielectric constants, e0k and ,, k, k = 1 -N, where N is the number of zones [23], The Poisson equation can be solved for such a system, taking due account of boundary conditions at zone interfaces, leading to a generalized expression for As [23],... 

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