Debye type relaxation

Figure 1. Debye-type relaxation spectra for liquid water, adsorbed water, ice, and hydrate. Solid lines correspond to real relative permittivity n and dotted lines represent imaginary permittivity k [3, 5, 11, 10].

Figure 2. Dielectric spectral responses of clay-water mixtures at 298 K. Parameters used in the Debye-type relaxation spectral functions are complied from Ishida et al. (2000).

Here, Eq is the permittivity of free space. For a simple Debye-type relaxation process, Eq. (4), and owing to the incorrect representation of the high-frequency limit inherent in any expression for K (to) consistent with an exponential decay function for the electric moment, one obtains for the high-frequency limit of a(to) from Eqs. (4) and (6) (30) ... 

Since the reduced spectrum x"( ) clearly shows the low-ftequency Raman modes, we introduced a simple model to analyze the spectral profile of x"(.v) for obtaining the quantitative information. The model is composed of two damped harmonic oscillator modes and one Debye type relaxation mode (liquid water) or one Cole-Cole type relaxation mode (aqueous solution). Cole-Cole type relaxation is usually adopted in analyzing the dielectric relaxation. The formula of Cole-Cole type relaxation is represented as ... 

Classically, the experimental curve interpretation is often limited to the definition of a distribution function in which the Debye-type relaxation superposition is accounted for by two parameters a and jS. From this description, we learn nothing about the physical processes involved this is often the relaxation frequency zone which permits connection of the observed evolutions to a particular polarisation phenomenon. Moreover, for materials with large free carrier concentration, the conduction and polarisation effects are separated in an arbitrary way, assuming that the contribution to the conduction phenomena is limited to a term e" conduction = (Tdc/cyto over the whole frequency range. 

The dotted curve shows the semi-circle expected for a single Debye-type relaxation. To plot this do not forget that the effective values of s and oo are the sums of those for the individual relaxations. 

Assuming a Debye-type relaxation process, where all dipoles have a single relaxation time and there are no interactions between dipoles, the instantaneous thermally stimulated current, (/(O) is given by... 

The dielectric loss can be written using the distribution function of relaxation time /(logx) (or fix)) assuming the Debye-type relaxations for simplicity of the kernel ... 

All those modes can be observed via measurements of the perpendicular permittivity component (cj ), so the influence of the l.f. molecular mode is eliminated, whereas the h.f. process can be observed at much higher frequencies than the previous ones. In most cases the collective modes are well described by a simple Debye-type relaxation model however, they usually overlap, which makes the separation of particular components rather difficult. ... 

This result was first published by Peter Debye in 1927, and is called a Debye-type relaxation mechanism. 

The equations described above are valid for Debye type relaxations. In general, real systems... 

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