Complex permittivity data, analysis

Construction and Analysis of Arrhenius Plots Complex permittivity data, like those shown in Fig. 6.18, are customarily analyzed by a superposition of several Havriliak-Negami functions and a conductivity term, that is... 

Each type of transmission line has different characteristic impedance and propagation constant which are functions of the complex permittivity of the substrate and superstate. The complex permittivity of methanol is extracted in this method for the frequency up to 40 GHz using a hybrid method that combines experimental data with finite element analysis. 

Dielectric relaxation of complex materials over wide frequency and temperature ranges in general may be described in terms of several non-Debye relaxation processes. A quantitative analysis of the dielectric spectra begins with the construction of a fitting function in selected frequency and temperature intervals, which corresponds to the relaxation processes in the spectra. This fitting function is a linear superposition of the model functions (such as HN, Jonscher, dc-conductivity terms see Section II.B.l) that describes the frequency dependence of the isothermal data of the complex dielectric permittivity. The temperature behavior of the fitting parameters reflects the structural and dynamic properties of the material. 

The dielectric spectroscopy study of conductive samples is very complicated because of the need to take into account the effect of dc-conductivity. The dc-conductivity c>o contributes, in the frequency domain, to the imaginary part of the complex dielectric permittivity in the form of additional function a0/(so ). The presence of dc-conductivity makes it difficult to analyze relaxation processes especially when the contribution of the conductivity is much greater than the amplitude of the process. The correct calculation of the dc-conductivity is important in terms of the subsequent analysis of the dielectric data. Its evaluation... 

R. J. Sheppard, B. R Jordan, and E. H. Grant, "Least Squares Analysis of Complex Data with Applications to Permittivity Measurements," Journal of Physics D—Applied Physics, 3 (1970) 1759-1764. 

Conductive-system dispersive response may be associated with a distribution of relaxation times (DRT) at the complex resistivity level, as in the work of Moynihan, Boesch, and Laberge [1973] based on the assumption of stretched-exponential response in the time domain (Eq. (118), Section 2.1.2.7), work that led to the widely used original modulus formalism (OMF) for data fitting and analysis, hi contrast, dielectric dispersive response may be characterized by a distribution of dielectric relaxation times defined at the complex dielectric constant or permittivity level (Macdonald [1995]). Its history, summarized in the monograph of Bbttcher and Bordewijk [1978], began more than a hundred years ago. Until relatively recently, however, these two types of dispersive response were not usually distinguished, and conductive-system dispersive response was often analyzed as if it were of dielectric character, even when this was not the case. In this section, material parameters will be expressed in specific form appropriate to the level concerned. 

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