Models of Kohlrausch Relaxations

Abstract
The contributions of R. and F. Kohlrausch to the description of mechanical and dielectric relaxation in complex systems are briefly cited as background for a discussion of models of relaxation. Models that have as predictions both the Kohlrausch time-dependent relaxation rate expressed in the form Wo(wct)-n, O<n<1, and the Kohlrausch fractional exponential exp[-t/τ*)1-n] relaxation function are presented. In addition, these models lead to a third prediction concerning the crossover between relaxation phenomena dominated respectively by a linear exponential or a fractional exponential functional behavior. These three predictions are expressed in terms of three coupled relations that are susceptible to experimental verification. The successful verifications and applications in many apparently diverse fields such as conductivity and polarization phenomena pertinent to electrets, viscoelasticity, rheology, etc. are discussed. Also discussed are other models of relaxation which are rejected on the basis that they are primarily satisfied to obtain the fractional exponential form without the appropriate connection to the other two experimentally verified coupled relations.