Logarithmic moments of relaxation time distributions

In this paper a novel way to quantify nonexponential relaxations is described. So far, this has been done in two ways: (1) by fitting empirical functions with a small number of parameters, (2) by calculation of the underlying distribution function g(ln tau) of (exponential) relaxations using regularization methods. The method described here is intermediate, it does not assume a specific functional form but also does not aim at the complete distribution g(ln tau) but only its logarithmic moments <(ln tau)(k)>. It is shown that these exist (in contrast to the linear moments) and can be calculated analytically for all currently used empirical descriptions of nonexponential relaxations. Therefore, the logarithmic moments represent a common basis for comparing literature data from authors which prefer different empirical formulas (e.g., those of Kohlrausch and Havriliak-Negami). The logarithmic moments are also shown to be related in a simple way to the (linear) moments of an underlying distribution of activation energies giving them a physical significance. (C) 2002 American Institute of Physics.