Effective dielectric constant, formulas

The basic formula for capacitance, derived in Ref. [296], shows that the capacitance dependence on the nature of ions is controlled by three integral parameters. These parameters do not depend on the potential or ionic concentrations. They are expressed through the z-dependent profiles of the quantities, varying across the interface (i) the short-range contributions to the free energy of ion transfer for all double layer ions and (ii) the effective dielectric constant of the solvent. These parameters are ... 

A macroscopic model for regular air/solution interfaces has been proposed by Koczorowski et al 1 The model is based on the Helmholtz formula for dipole layers using macroscopic quantities such as dielectric constants and dipole moments. The model quantitatively reproduces Ax values [Eq. (37)], but it needs improvement to account for lateral interaction effects. 

As is obvious from the above relation, the screening effect of the substrate on interactions causes, in the limiting case z —> 0, the change in the surface-normal components by a factor of 2e/( +e) and in the surface-parallel components by a factor of 2/(1 + ), i.e., the renormalization ratio is equal tO . As the substrate dielectric constant increases, the interaction of surface-parallel components monotonically decays to zero, whereas the interaction of surface-normal components is enhanced reaching the maximum, viz. the interaction with a double dipole moment, for a metal (at e -> oo).130 Analogous renormalization factors are also of significance in the treatment of island-like particles on a dielectric substrate.131 With such effects included, formula (3.3.9) can be rewritten as ... 

Ford and Weber included the effect of dispersion by using a Lindhard formula for the dielectric constant, and included also a constant term to account for the bound-electron contribution. They find that the LFE enhancement is <1000 and point out the importance of the coupling to e-h. 

The I U) characteristics exhibit charging effects, which indicates that the ligands are electrical insulators, as desired. They act as tunnel barriers between the cluster and the substrate. The experimentally observed charging energy varies from 50 to 500 meV 140 meV would be expected from the classical formula for Eq of a spherical particle with a dielectric constant Cr = 10 for the surrounding ligands (see... 

Using the effective medium formula of Looyenga [134] it was possible to calculate the dielectric constant for the dispersed PAni as... 

Here, /Xexc is the reduced effective mass of the exciton, in terms of the free electron mass, and e is the dielectric constant. In addition, there are also Frenkel excitons, which are spatially more localized than Mott-Wannier excitons. They cannot be represented by a series formula. Therefore, Frenkel excitons have been assigned to single low-lying absorption bands in the near-edge regime of solid rare gases. 

Application of high pressure changes the position of the electronic conduction level, Vq (see Section 6.9), and it increases the dielectric constant of the liquid. Both effects have an influence on the ionization energy of a solute. The dependence of Vo(p) is complicated and experimental data must be used. The effect of pressure on the dielectric constant is due to the increase in density and it is well described by the Clausius-Mossotti equation (see Section 1.6). In Figure 8a the photoconductivity spectrum of TMPD in neohexane is shown as a function of pressure. The variation of the photoconductivity threshold with pressure is depicted in Figure 8b. Evaluation of the data by means of Bom s formula (Chapter 7, Equation 94) led to the hypothesis that an additional increase of liquid density around the solute molecule due to fluctuations is responsible for the observed shifts (Katoh et al., 1995). 

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