Dielectric loss spectra model

Fig. 4.3. The Jonscher representation of the Dissado-Hills dielectric loss spectrum. So is the static permittivity copH is the principal relaxation rate n and m are the Dissado-Hill parameters. Arrows indicate variations of the loss curve on increasing values of the model parameters.

In addition to dielectric property determinations, one also can measure valence electron densities from the low-loss spectrum. Using the simple free electron model one can show that the bulk plasmon energy E is governed by the equation ... 

An ESR spectrometer (Varian model E-3) was used to observe and quantify Mn2+ species at a field strength of 3155 50 G and a frequency of 9.5 GHz. A flat fused silica ribbon cell (Wilmad Glass No. WG-812) was used at very low concentrations to optimize the signal-to-noise ratio by minimizing dielectric losses. Microwave power was set routinely to 4 mW, but was occasionally raised to optimize sensitivity at very low concentrations. Quantitation was based on the height of the lowest-field peak in the first derivative of the absorption spectrum. As reported by others (63), this technique is characterized by precision and accuracy of about 1% relative standard deviation over a linear range from CIO"6 to If)"4 M (<0.05-5 mg/L). 

In the low-frequency range (with x spectral function L(z) depends weakly on frequency x. Then Eq. (32) comes to the Debye-relaxation spectrum given by Eq. (33). Its main characteristics, such as the dielectric-loss maximum Xd and its frequency xD, are given by Eq. (34). A connection between these quantities and the model parameters becomes clear in an example of a very small collision frequency y. In this case, relations (34) come to... 

The second model of Debye or the Debye-Frohlich model may also be generalized to fractional diffusion [8,25] (including inertial effects [26]). Moreover, it has been shown [25] that the Cole-Cole equation arises naturally from the solution of a fractional Fokker-Planck equation in the configuration space of orientations derived from the diffusion limit of a CTRW. The broadening of the dielectric loss curve characteristic of the Cole-Cole spectrum may then be easily explained on a microscopic level by means of the relation [8,24]... 

A Cole—Cole plot is permittivity plotted in a Wessel diagram. If the permittivity is according to the Cole—Cole equation, the locus will be a circular arc. The permittivity used in the Cole—Cole equations implies that the model is changed from regarding tissue as a conductor (2R-1C model) to regarding tissue as a dielectric (1R-2C model) with only bound charges and dielectric losses. A 2R-1C model cannot have the same spectrum as a 1R-2C model with a fixed set of component values, so an arc locus in one model will not result in an arc locus in the other model. In living tissue, there is a substantial DC conductance. Such... 

The hat-curved model also gives a satisfactory description of the wideband dielectric/FIR spectra of a nonassociated polar fluid (CH3F) (Fig. 25). It is worthwhile mentioning that only a poor description of the low-frequency (Debye) spectrum could be accomplished, if the rectangular potential were used for such a calculation [32] see also Section IV.G.3. Unlike Fig. 25b, the estimated peak-loss frequency does not coincide38 in this case with the experimental frequency vD. 

---