Kohlrausch-Williams-Watts function, structural

A model having predictions that are consistent with the aforementioned experimental facts is the Coupling Model (CM) [21-26]. Complex many-body relaxation is necessitated by intermolecular interactions and constraints. The effects of the latter on structural relaxation are the main thrust of the model. The dispersion of structural relaxation times is a consequence of this cooperative dynamics, a conclusion that follows from the presence of fast and slow molecules (or chain segments) interchanging their roles at times on the order of the structural relaxation time Ta [27-29]. The dispersion of the structural relaxation can usually be described by the Kohlrausch-William-Watts (KWW) [30,31] stretched exponential function,... 

A basic feature of the response of fragile liquids to various perturbations is the pronounced nonexponential relaxation behavior. The relaxation function typically exhibits a two-step feature. The fast relaxation at short times is generally associated with vibrational degrees of freedom. The long-time decay of the relaxation function 4>(t), which is governed by the structural relaxation, can often be described by the stretched exponential or the Kohlrausch-Williams-Watts (KWW) function... 

Moynihan s formulation [5] of the Tool-Narayanaswamy [7] model is used in tins woilc. In Moynihan s equations, the Active temperature, Tf, originally d ned by Tod [78], is used as a measure of the structure of the glass. The evdution of Active temperature is represented by the generalized stretched exponential Kohlrausch-William-Watts(KWW) function [76,77] ... 

Here tq is the relaxation time at equilibrium (Tf = T) at high temperatures, x is a structural parameter and measure of nonlinearity, with values 0 < x < 1, and AE is the activation energy for the relaxation processes and has an Arrhenius temperature dependence. The models also use the stretched exponential function of Kohlrausch, Williams, and Watts [1970] (KWW) to describe the distribution of relaxation times as... 

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