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Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays

D. C. Johnston
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Abstract

Stretched exponential relaxation of a quantity n versus time t according to n = n_0 exp[-(lambda* t)^beta] is ubiquitous in many research fields, where lambda* is a characteristic relaxation rate and the stretching exponent beta is in the range 0 < beta < 1. Here we consider systems in which the stretched exponential relaxation arises from the global relaxation of a system containing independently exponentially relaxing species with a probability distribution P(lambda/lambda*,beta) of relaxation rates lambda. We study the properties of P(lambda/lambda*,beta) and their dependence on beta. Physical interpretations of lambda* and beta, derived from consideration of P(lambda/lambda*,beta) and its moments, are discussed.

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BibTeXRIS

D. C. Johnston. 2006-11-01. Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays. https://doi.org/10.1103/physrevb.74.184430

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