Surprising conductive- and dielectric-system dispersion differences and similarities for two Kohlrausch-related relaxation-time distributions

• Published in: Journal of physics. Condensed matter 2006-01, Vol.18 (2), p.629-644
• Main Author: Ross Macdonald, J
• Format: Article
• Language: English
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Dielectric loss and relaxation; Dielectric properties of solids and liquids; Dielectrics, piezoelectrics, and ferroelectrics and their properties; Exact sciences and technology; Physics
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/0953-8984/18/2/019

General distributions of relaxation times are discussed and then specialized to two types associated with Kohlrausch stretched-exponential temporal response, the K0 and K1 models. For the important choice of 1/3 for their beta shape parameters, their specific distributions and different temporal responses are first compared. Then the 16 real and imaginary parts of their dielectric- and conductive-system frequency responses are presented in normalized form. Only eight of these are distinct, however, because of pairing of identical dielectric and conductive responses. There are five different peaked imaginary-part pairs, two of which differ only in scale: the important conductive-system M''(omega) response and the dielectric-system epsilon''(omega) one. Their near equality explains how the widely used but inappropriate original modulus formalism (OMF) of Moynihan and associates, proposed in 1973, could be implicitly derived from pure dielectric considerations and yet fortuitously yield conductive-system response. The crucial effects of the endemic dielectric quantity on K0- and K1-model responses are illustrated, and they explain why conductive-system shape parameter values derived from data fitting with the OMF model have been misleadingly found to depend on temperature and charge-carrier concentration. Instead, the K1 model fits data for a wide variety of homogenous materials with a value of 1/3 independent of the values of these variables. Finally, different fits of a historic experimental data set are compared to illustrate the present findings.