Abstract
Experimental data collected to provide us with information on the course of dielectric relaxation phenomena are obtained according to two distinct schemes: one can measure either the time decay of depolarization current or use methods of the broadband dielectric spectroscopy. Both sets of data are usually fitted by time or frequency dependent functions which, in turn, may be analytically transformed among themselves using the Laplace transform. This leads to the question on comparability of results obtained using just mentioned experimental procedures. If we would like to do that in the time domain we have to go beyond widely accepted Kohlrausch–Williams–Watts approximation and become acquainted with description using the Mittag–Leffler functions. To convince the reader that the latter is not difficult to understand we propose to look at the problem from the point of view of objects which appear in the stochastic processes approach to relaxation. These are the characteristic exponents which are read out from the standard non-Debye frequency dependent patterns. Characteristic functions appear to be expressed in terms of elementary functions whose asymptotics is simple. This opens new possibility to compare behavior of functions used to describe non-Debye relaxations. It turnes out that the use of Mittag-Leffler function proves very convenient for such a comparison.
Highlights
A description of physical phenomena whose kinetics is influenced by complexity, disorder, or randomness often requires a radical departure from theoretical methods established for analogous, but simpler, phenomena discussed in textbooks of general physics
It is much better is to use the CC model. This model breaks down in many physically interesting cases: this was the reason of introducing the HN and JWS models as phenomenological schemes fit the data in the frequency domain
If transformed to the time domain, both these models lead to the time decay laws given in terms of multiparameter Mittag–Leffler functions, until recently unfamiliar to the physicists’ community
Summary
A description of physical phenomena whose kinetics is influenced by complexity, disorder, or randomness often requires a radical departure from theoretical methods established for analogous, but simpler, phenomena discussed in textbooks of general physics. They are governed by infinitely divisible probability distributions and they are uniquely characterized by functions called the characteristic (either Laplace or Lévy) exponents, which carry all information concerning distributions under consideration This formalism adopted for studies of the relaxation phenomena leads to an unexpected result which merges basic, mathematical theory and pure phenomenology-characteristic exponents may be uniquely reconstructed from the knowledge of spectral function, i.e., experimentally obtained relaxation patterns. This provides us with a new tool to compare various schemes describing relaxation processes-as we mentioned a few lines earlier our goal is to study similarities and/or dissimilarities of the relaxation descriptions based on the KWW and Mittag–Leffler functions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
