The generalized Jonscher's relationship for conductivity and its confirmation for porous structures

Identification of relaxation processes in pure polyethylene oxide (PEO) films by the dielectric permittivity and electric modulus formalisms

“…Various ways are often used to display measured data of dynamic relaxation response of a sample in the frequency domain such as the Argand diagrams (complex‐plane plots) and Bode‐like plots, each of which has its own merits and limits in interpreting the ac‐data . The directly measured electrical quantities of a material sample, at temperature T , in common ac‐measurements are the macroscopic complex impedance and/or complex admittance , where ω (=2π f ) is the angular frequency of the ac‐signal applied to the sample and .…”

“…Argand diagrams depict the imaginary part against real part of a complex electric quantity over a range of frequencies, from which one may infer a plausible electrical circuit model that describes relaxation mechanisms operative in the sample; yet, such electric representation is not much inspiring and is difficult to appraise visually complex circuit network of nonideal electrical elements, as different circuit combinations yield same effective impedance of the sample, or real heterogeneous systems, where diverse conduction and relaxation processes dominate in different frequency ranges. A Bode‐like plot displays the real or imaginary part of a complex electric quantity against frequency, which often provides more prospectus for reliable interpretation of the frequency‐domain spectral shape arising from diverse conduction and polarization mechanisms …”

“…One had to achieve a global solution of the problem when utilizing traditional curve‐fitting of loss data measured over a wide frequency range to a combination of multi‐constant permittivity dispersion functions. In practice, however, it is rather difficult to isolate the real dielectric dispersion spectra of a sample from low‐frequency relaxation processes arising from interfacial/electrode polarization and dc conduction . The as‐measured loss spectrum is then less inspired and the numerical curve‐fitting analysis of loss data becomes remarkably complicated, and it is not easy or always reliable to detach the effect of dc conductivity, specially when its contribution is much larger than the amplitude of the real dielectric relaxation and/or when a low‐frequency relaxation of similar power‐law frequency dependence (eg, Jonscher's term) is present, a procedure that is crucial for interpretation and subsequent reliable analysis of experimental dielectric data …”

“…A methodology that is widely adopted, despite of some criticism and no consensus among the dielectrics community, for analyzing the as‐measured ac‐impedance of a semiconductive/dielectric sample is the electric modulus formalism, via which the low‐frequency permittivity contributions could be split apart or minimized from the coexisting low‐frequency relaxations of dielectric origin (dipolar reorientations or molecular motions) . Modeling of the as‐measured data of ac‐impedance of a dielectric sample in terms of frequency‐domain electric modulus may provide complementary insights into the problem of understanding its electric responses on equal footing with representations based on electric permittivity or impedance/admittance (resistivity/conductivity) formalisms …”

“…More information about relaxation and conduction processes giving rise to observed dielectric/loss behavior of a material sample can be realized by performing numerical curve‐fitting of as‐measured data to a theoretical permittivity model, which is an ill‐posed problem and yet far beyond attainable in a closed form that is valid over a wide range of frequencies. A variety of empirical expressions were developed to describe the complex relative permittivity of a dielectric sample, at a fixed temperature, like Cole‐Cole (CC), Cole‐Davidson (CD), and Havriliak‐Negami (HN) relations, which are modifications to Debye dispersion relation and map departures from ideal Debye responses . Other empirical formulas were proposed to describe only ε ′′( ω ) such as the Jonscher loss function and the alike Fuoss‐Kirkwood loss equation for Mott and Davis, Jonscher, Macdonald, Kremer and Schönhals, and Riande and Diaz‐Calleja .…”