Static solvent permittivity

However, the latter formula is not more applicable, if xlaa is rather long and/ or Cm is rather high, so that the zero-frequency ionic contribution Aefon(0) to permittivity is noticeable in comparison with the static permittivity es of the solution. We note that the Kirkwood correlation factor g is used for calculation of the component p in Eq. (387). Thus, even in our additivity approximation the solvent permittivity )jip is determined in this case by concentrations of both solution components. This complication leads to a new self-consistent calculation scheme. 

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). 

Solvent Static dielectric permittivity, Outer Helmholtz plane potential, zero charge vs. potential of the Foe /Foe electrode (V)... 

The static permittivities of mixtures of organic liquids with water may be interpreted in terms of polarization theory. We shall see that water can be used as a solvent for the determination of dipole moments of highly polar molecules, but for less polar molecules the Kirkwood-Frohlich equation has been used as a method of demonstrating molecular interactions between water and solute. 

One of the purposes for which static permittivities of aqueous nonelectrolyte solutions have been determined, by Franks and his coUeagues, is for calculation of the dipole moments of molecules. There are molecules for whidi no studies can be made in the vapour phase or in solution in non-polar solvents however, sufficiently good comparisons of determinations of dipole moments in aqueous solution with other determinations can sometimes be made to allow an estimate of the limitations of the method. 

The above examples illustrate that continuum models such as the Kirkwood model are reasonably successful in describing the static permittivity, provided one has an independent means of estimating the correlation parameter Unfortunately, these estimates are available for only a few polar solvents, so that gK must be considered an independent parameter. The version of Kirkwood s theory presented here only considers orientational polarization. When distortional polarization, that is, the effect of molecular polarizability, is included, interpretation of experimental results is less clear. Since the approach taken here involves continuum concepts, it is necessarily limited. In the following section, a simple model based on a molecular description of a polar liquid is presented. 

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. 

Concerning the nature of interaction between a delocalized electron and polar solvents and the dependence of this interaction on the structure and properties of the solvent only a tentative conclusion can be made at present. Vg does not show correlation either with the dimensions of the solvent molecule or with its characteristics such as acceptor and donor numbers, optical and static permittivity, and the molecule s dipole moment. It is obvious that the electron-medium electrostatic interaction alone cannot explain the results obtained. 

From the preceding relation, it is apparent that 1/k is inversely proportional to the valence Z of the ions in the solution phase and to the square root of their concentrations. It is also directly proportional to the square roots of the absolute temperature and the relative static permittivity (or dielectric constant) of the medium. It is therefore to be expected that in a solvent of high dielectric constant, such as water, electrical effects extend much further into the solution phase than in a solvent of low dielectric constant, such as a hydrocarbon. Also, in the presence of an electrolyte, electrical effects have shorter ranges than in its absence—that is, the electrical double layer is compressed. 

Calculation of the dielectric permittivity of an isotropic polar material involves the problem of the permanent dipole contribution to polarizability and the problem of calculation of the local field acting at the molecular level in terms of the macroscopic field applied. Debye s model for static permittivity considers the local field equal to the external field. This assumption is valid only for gases at low density or dilute solutions of polar molecules in nonpolar solvents. Several workers... 

In the first equality, is the static permittivity of the solvent, its infinite frequency permittivity, is the ratio of the dynamic coupling and the Kirkwood dipole... 

Liquid acetic acid is a hydrophilic (polar) protic solvent, similar to ethanol and water. With a moderate relative static permittivity (dielectric constant) of 6.2, it can dissolve not only polar compounds such as inorganic salts and sugars, but also non-polar compounds such as oils and elements such as sulfur and iodine. It readily mixes with other polar and non-polar solvents such as water, chloroform, and hexane. With higher alkanes (starting with octane) acetic acid is not completely miscible anymore, and its miscibility continues to decline with longer n-alkanes. This dissolving property and miscibility of acetic acid makes it a widely used industrial chemical. 

The comparison becomes more solid when the data for Fc /Fc and relative redox pairs in different solvents are considered in parallel [e.g., for bis biphenyl)chro-mium (1/0) (BCr /BCr) or for cobaltoceniumicobaltocene (CcVCc)]. A relative redox probe containing the anion (carborane compound, bis-o-dicarbollyl-nickel) was studied for comparison [12], A consideration of the potential differences in various solvents, rather than relative redox potential values, ehminates the UP. The tabulated values for differences between the formal potentials of BCr /BCr and Fc /Fc couples in 22 solvents with significantly different static permittivity values are equal within the accuracy of few mV [7]. Similarly, the differences of the formal potentials of Fc /Fc and CcVCc in five aprotic solvents and three aqueous-organic mixtures remain practically constant within the limits of experimental error [12], when the difference in water is somewhat larger, ca 40 mV. The comparison with aqueous systems is slightly risky, as the reactants tmder study are not so stable in water. 

Static solution permittivity, e(c), and static solvent permittivity, es(c), for solutions of various electrolytes at various concentrations (c) have been obtained by dielectric relaxation spectroscopy [44]. Ion-pairs contribute to permittivity if their lifetime is longer than their relaxation time. However free ions do not contribute to permittivity. Thus,... 

The origin of the effect here represented by x0) can be derived from modelistic considerations. Solvent molecules are mobile entities and their contribution to the dielectric response is a combination of different effects in particular the orientation of the molecule under the influence of the field, changes in its internal geometry and its vibrational response, and electronic polarization. With static fields of moderate intensity all the cited effects contribute to give a linear response, summarized by the constant value e of the permittivity. This molecular description of the dielectric response of a liquid is... 

The case of DNA in the double helix form is of especial interest because dipoles along the oppositely directed helical strands cancel to leave little or no resultant dipole moment. The observed dielectric increments, i.e., excess of permittivity over that of solvent water,are very large, however, and reach a static value only at audio or subaudio frequencies, showing the necessity of some mechanism of considerable charge displacements which develop slowly. 

Dynamic solvent effect — is a phenomenon typical for adiabatic -> electron transfer and -> proton transfer reactions. This effect is responsible for a dependence of the reaction rate on solvent relaxation parameters. The initial search for a dynamic solvent effect (conventionally assumed to be a feature of reaction adiabatic-ity) consisted in checking the viscosity effect. However, this approach can lead to controversial conclusions because the viscosity cannot be varied without changing the -> permittivity, i.e. a dynamic solvent effect cannot be unambiguously separated from a -> static solvent effect [i]. Typically a slower solvent relaxation goes along with a higher permittivity, and the interplay of the two solvents effects can easily look as if either of them is weaker. The problems of theoretical treatment of the dynamic solvent effect of solvents having several relaxation times are considered in refs, [ii-iii]. 

Static solvent effect — is widely understood as the dependence of -> reaction rate on solvent -> permittivity. The most systematic studies of this effect were stimulated by the early version of -> Marcus theory and mostly consisted in experimental verification of Mar-... 

---