Kohlrausch-Williams-Watts expression

The considered model of a straight line of M nanoparticles illustrates only general features of dielectric losses caused by an M nanoparticle cluster in polymer matrix. Actually such cluster is a complex fractal system. Analysis of dielectric relaxation parameters of this process allowed the determination of fractal properties of the percolation cluster [104], The dielectric response for this process in the time domain can be described by the Kohlrausch-Williams-Watts (KWW) expression... 

If the first scenario were real, the slower secondary relaxation should express its presence as an excess wing on high frequency side of the a- relaxation peak. To check this we superimposed dielectric loss spectra of octa-O-acetyl-lactose measured above and below Tg to that obtained at T=353 K. Next we fitted a master curve constructed in this way to the Kohlrausch-Williams-Watts function... 

The molecular domains in amorphous structure behave like an ensemble of autonomous substates, each following unique relaxation kinetics during annealing (Kawakami and Pikal 2005). This relaxation distribution is often expressed using an empirical Kohlrausch-Williams-Watts (KWW) equation (Eq. 14.3) ... 

The relaxation function, can also be expressed in terms of a senuempirical function introduced originally by Kohlrausch (1897) and revived by Williams and Watts (1970), abbreviated as the KWW equation ... 

This function, originally introduced by Kohlrausch in 1854 to describe creep in silk and glass threads used as supports in magnetometers, is a very slow function of time and hence gives broad dispersion and loss curves when used in conjunction with equation (10). The integration cannot be expressed generally in closed form. For the special case jS=0.5 Williams and Watts showed that equations (10) and (25) give... 

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