The derivation of the Cole-Davidson and Havriliak-Negami functions and their possible generalizations
Abstract: Using the memory conception developed in the framework of the Mori-Zwanzig formalism, the kinetic equations for relaxation functions that correspond to the previously suggested empirical functions (Cole-Davidson and Havriliak-Negami) are derived. The obtained kinetic equations contain differential operators of non-integer order and have clear physical meaning and interpretation. The derivation of the memory function corresponding to the Havriliak-Negami relaxation law in the frame of Mori-Zwanzig formalism is given. A physical interpretation of the power-law exponents involved in the Havriliak-Negami empirical expression is provided too.
The micro/mesoscopic theory of dielectric relaxation has been developed. Based on the fractional kinetics it gives a possibility to obtain the desired expression for the complex dielectric permittivity (CDP) and describe the asymmetric peaks that are created presumably by the so-called ”excess wing” located in high-frequency region. The well-known empirical Cole-Davidson expression and its generalization for the CDP were obtained from this theory. This theory is based on self-similar phenomenon and multi-channel organization of relaxation process in disordered dielectrics. The relaxation parameters are connected with the structural parameters of the medium considered.
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