Frequency-dependent permittivity, time-domain

Since the frequency-dependent permittivity is related to a relaxation function in the time domain (see equation 10), another way of introducing an empirical modification to the SRT function is to modify the relaxation function itself. A general procedure used for many years in relaxation theory is to express 0(f) as a discrete set of exponential decay functions or as an integral over a continuous distribution of such decay functions so that... 

As mentioned above, the frequency dependence of the complex dielectric permittivity (e ) of the main relaxation process of glycerol [17,186] can be described by the Cole-Davidson (CD) empirical function [see (21) with a = 1, 0 < Pcd < 1], Now Tcd is the relaxation time which has non-Arrhenius type temperature dependence for glycerol (see Fig. 23). Another well-known possibility is to fit the BDS spectra of glycerol in time domain using the KWW relaxation function (23) < )(t) (see Fig. 24) ... 

The dielectric relaxation at percolation was analyzed in the time domain since the theoretical relaxation model described above is formulated for the dipole correlation function T(f). For this purpose the complex dielectric permittivity data were expressed in terms of the DCF using (14) and (25). Figure 28 shows typical examples of the DCF, obtained from the frequency dependence of the complex permittivity at the percolation temperature, corresponding to several porous glasses studied recently [153-156]. 

The polarizability of the individnal molecules is also frequency dependent, but the characteristic values are of the order of lO Vs and lO Vs for the rotational and electronic polarization, respectively. " Therefore, in the typical frequency domain for investigation of dispersions (1/s < co < 10 /s) the polarizability, e, of the material building up the particles is frequency independent. On the other hand, the disperse medium (which is usually an electrolyte solution) has a dielectric permittivity, Ej, for which the freqnency dependence can be described by the Debye-Falkenhagen theory. Besides, the characteristic relaxation time of the bulk electrolyte solutions is also given by Eqnation 5.385. ... 

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