H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems

被引：120

作者：

Hilfer, R. ^{[1
,2
]}

机构：

[1] ICA-1, Universität Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany

[2] Institut Für Physik, Universität Mainz, 55099 Mainz, Germany

来源：

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | 2002年 / 65卷 / 06期

关键词：

Approximation theory - Functions - Glass transition - Integral equations - Laplace transforms - Mathematical models;

D O I：

10.1103/PhysRevE.65.061510

中图分类号：

学科分类号：

摘要：

Analytical expressions in the time and frequency domains are derived for non-Debye relaxation processes. The complex frequency-dependent susceptibility function for the stretched exponential relaxation function is given for general values of the stretching exponent in terms of H-functions. The relaxation functions corresponding to the complex frequency-dependent Cole-Cole, Cole-Davidson, and Havriliak-Negami susceptibilities are given in the time domain in terms of H-functions. It is found that a commonly used correspondence between the stretching exponent of Kohlrausch functions and the stretching parameters of Havriliak-Negami susceptibilities are not generally valid. ©2002 The American Physical Society.

引用

页码：1 / 061510