Relative static permittivity

Here er is the relative -> permittivity (static dielectric constant) of the solution, 0 is the permittivity of free space, e is the unit charge on the electron (- elementary electric charge), 3 is the valence of the ionic species i, Ci is the bulk concentration of the adsorbing species i, k is the Boltzmann constant, T is the absolute temperature, and (V(a)) is the time-averaged value of the electric potential difference across the diffuse layer. The diffuse layer capacitance is (very roughly) of the order of 10 pF cm-2. The thickness of the diffuse layer is essentially the - Debye length Ld,... 

In Fig. 2, the relative permittivities (static dielectric numbers) e of carbon dioxide [23], argon [24], and liquid pentane [25] are plotted against pressure p up to 200 MPa. Even at the highest pressures corresponding to liquid-like densities, e (CO2) is smaller than 1.8, and thus nearly equal to that of a liquid alkane (such as pentane). Since CO2 molecules do not have any permanent electrical dipole moment, the polarization is more or less restricted to the contributions of the electrons and the nuclei. Therefore, typical solvation effects are normally less important, and the intermolecular interactions are predominantly of van-der-Waals type with some higher electrostatic such as quadrupolar interactions. 

Figure 2. Relative permittivities (static dielectric numbers) e of pure carbon dioxide [23], argon [24], and pentane [25] as a function of pressure p (see also [4]).

Many of the different susceptibilities in (18)-(21) correspond to important experiments in linear and non-linear optics. The argument in parentheses again describes the kind of interacting waves. TWo waves interact in a first-order process as described above in (9), three waves in a second-order process, and four in a third-order process. x ° describes a possible zeroth-order (permanent) polarization of the medium t- (0 0) is the first-order static susceptibility which is related to the relative permittivity (dielectric constant) at zero frequency, e,.(0), by (22). 

In the case of a static field, the macroscopic relative permittivity e° has to be used in (82) for the cavity field factor, while the optical relative permittivity extrapolated to infinite wavelength e can be applied to estimate the static polarizability a(0 0) in (84). In this way the Onsager-Lorentz factor for a pure dipolar liquid is obtained (87). 

In some instances evidence favouring ionic conduction is provided by a strong correlation between relative permittivity and conductivity, which is readily explained by the reduction of the Coulombic forces between ions in a high relative permittivity medium. This renders the dissociation energy of an ionic compound inversely proportional to the static relative permittivity es. Consider the dissociation reaction ... 

The dielectric properties of the solvents considered here are summarized in table 4.2. These properties are important in evaluating the solvation of ions in polar solvents under both static and dynamic conditions. The relative permittivity of a solvent at high frequencies, Sop, can be calculated from the refractive index, nop, the relationship being... 

Kita T, Uosaki Y, Moriyoshi T. Static relative permittivity of some compressed fluids. In Taniguchi Y, Senoo M, Hara K, eds. High Pressure Liquids and Solutions. Amsterdam Elsevier, 1994 181-198. 

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