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A dielectric permittivity spectrum over a wide range of frequencies. ε′ and ε″ denote the real and the imaginary part of the permittivity, respectively. Various processes are labeled on the image: ionic and dipolar relaxation, and atomic and electronic resonances at higher energies. [9]
The real and imaginary parts of permittivity are shown, and various processes are depicted: ionic and dipolar relaxation, and atomic and electronic resonances at higher energies. [ 1 ] Dielectric spectroscopy (which falls in a subcategory of the impedance spectroscopy ) measures the dielectric properties of a medium as a function of frequency .
The relative permittivity of a medium is related to its electric susceptibility, χ e, as ε r (ω) = 1 + χ e. In anisotropic media (such as non cubic crystals) the relative permittivity is a second rank tensor. The relative permittivity of a material for a frequency of zero is known as its static relative permittivity.
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The real (blue solid line) and imaginary (orange dashed line) components of relative permittivity are plotted for a single oscillator model with parameters = (12.6 μm), / =, / =, and =. These parameters approximate hexagonal silicon carbide.
All quantities are in Gaussian units except energy and temperature which are in electronvolts.For the sake of simplicity, a single ionic species is assumed. The ion mass is expressed in units of the proton mass, = / and the ion charge in units of the elementary charge, = / (in the case of a fully ionized atom, equals to the respective atomic number).
The Born equation can be used for estimating the electrostatic component of Gibbs free energy of solvation of an ion. It is an electrostatic model that treats the solvent as a continuous dielectric medium (it is thus one member of a class of methods known as continuum solvation methods). It was derived by Max Born. [1] [2]
where z is the electrical charge on the ion, I is the ionic strength, ε and b are interaction coefficients and m and c are concentrations. The summation extends over the other ions present in solution, which includes the ions produced by the background electrolyte. The first term in these expressions comes from Debye–Hückel theory.