Comparison of the Havriliak-Negami and stretched exponential functions

Abstract

Alvarez, Algeria and Colmenero compared the stretched exponential (KWW) and Havriliak-Negami (H N) functions by comparing their distributions of relaxation times. In the case of the KWW function, the distribution of relaxation times was calculated numerically. The numerical results were then represented in terms of the closed form distribution of relaxation times available for the H N function. They found that a specific KWW k parameter corresponds to a specific H N α,β pair. In this paper the time-dependent dielectric constant, calculated from the stretched exponential for various ks and over a time range sufficiently long to define the t = 0 or ∞ limits, was transformed to the complex dielectric constant using the extended Schwarzl method. The complex dielectric constant was fitted directly to the H N function. The results of this procedure are compared with those of Alvarez et al. The two different methods give the same results and the consequences of this agreement are discussed.