Restriction on the Form of Relaxation-Time Distribution Functions for a Thermally Activated Process

Abstract

When a distribution of relaxation times is associated with thermally activated processes in a material and arises solely from a distribution of activation energies, the form of the relaxation-time distribution may be restricted. In this case, the temperature dependence of some of the parameters which enter into the distribution function will be uniquely determined. The Wagner relaxation-time distribution function may be made entirely consistent with a distribution of activation energies by taking its shape parameter temperature dependent, but the Cole-Cole, Fuoss-Kirkwood, and Davidson-Cole distribution functions can only be made approximately consistent in the separate limits of very wide and narrow distributions of relaxation times. The temperature dependences of their parameters found experimentally for thermally activated processes is compared where possible with that required for the distribution of activation energies situation. A new relaxation-time distribution is proposed which is completely consistent with a distribution of activation energies in an activated process and which can describe a variety of experimental data.