arXiv subjects

Christos Tsonos

Publications and source records attributed to Christos Tsonos.

3 recordsLinked to original sources

arXiv2019

Comments on frequency dependent ac conductivity in polymeric materials at low frequency regime

The AC conductivity response in a broad frequency range of disordered materials is of great interest not only for technological applications, but also from a theoretical point of view. The Jonscher power exponent value, and its temperature dependence, is a very important parameter in dielectric data analysis as well as the physical interpretation of conduction mechanisms in disordered materials. In some cases the power exponent of AC conductivity has been reported to be greater than 1 at the low frequency regime. This fact seems to contradict the universal dynamic response. The present work focuses on the analysis of dielectric spectroscopy measurements in polymeric materials, below 100 MHz. The apparent power exponent n gets values in the range (0,1) and is directly related to the characteristics of mobile charges at shorter time scales, in the case of the occurrence of DC conduction and the slowest polarization mechanism that is due to the charge motions within sort length scales, in log(epsilon'')-log(frequenvy) plot. The emergence of apparent n values in the range [1,2], for a relatively narrow frequency range, may be attributed to an additional molecular dipolar relaxation contribution at higher frequencies, in log(epsilon'')-log(frequency) plot. The appearance of apparent n values in the range (1,2], can be assigned to the existence of a well defined minimum between DC conductivity contribution and a molecular dipolar dispersion or between two well separated dielectric loss mechanisms, in log(epsilon'')-log(frequency) plots, above the crossover frequency. In these latter cases, the apparent power exponent n is merely related to the Havriliak-Negami equation shape parameters of the higher frequencies molecular dipolar relaxations.

cond-mat.mtrl-sci↗

arXiv2012

A new closed formula for the Hermite interpolating polynomial with applications on the spectral decomposition of a matrix

We present a new closed form for the interpolating polynomial of the general univariate Hermite interpolation that requires only calculation of polynomial derivatives, instead of derivatives of rational functions. This result is used to obtain a new simultaneous polynomial division by a common divisor over a perfect field. The above findings are utilized to obtain a closed formula for the semi--simple part of the Jordan decomposition of a matrix. Finally, a number of new identities involving polynomial derivatives are obtained, based on the proposed simultaneous polynomial division. The proposed explicit formula for the semi--simple part has been implemented using the Matlab programming environment.

math.RA↗

arXiv2012

AC and DC conductivity correlation: The coefficient of Barton--Nakajima--Namikawa relation

It has been some time since an empirical relation, which correlates DC with AC conductivity and contains a loosely defined coefficient thought to be of order one, was introduced by Barton, Nakajima and Namikawa. In this work, we derived this relation assuming that the conductive response consists of a superposition of DC conductivity and an AC conductivity term which materialized through a Havriliak--Negami dielectric function. The coefficient was found to depend on the Havriliak--Negami shape parameters as well as on the ratio of two characteristic time scales of ions motion which are related to ionic polarization mechanism and the onset of AC conductivity. The results are discussed in relation to other relevant publications and they also applied to a polymeric material. Both, theoretical predictions and experimental evaluations of the BNN coefficient are in an excellent agreement, while this coefficient shows a gradual reduction as the temperature increases.

cond-mat.mtrl-sci↗