Williams-Watts relaxation theory

On the other hand, some phenomenological distributions of relaxation times, such as the well known Williams-Watts distribution (see Table 1, WW) provided a rather good description of dielectric relaxation experiments in polymer melts, but they are not of considerable help in understanding molecular phenomena since they are not associated with a molecular model. In the same way, the glass transition theories account well for macroscopic properties such as viscosity, but they are based on general thermodynamic concepts as the free volume or the configurational entropy and they completely ignore the nature of molecular motions. 

Relaxation functions for fractal random walks are fundamental in the kinetics of complex systems such as liquid crystals, amorphous semiconductors and polymers, glass forming liquids, and so on [73]. Relaxation in these systems may deviate considerably from the exponential (Debye) pattern. An important task in dielectric relaxation of complex systems is to extend [74,75] the Debye theory of relaxation of polar molecules to fractional dynamics, so that empirical decay functions for example, the stretched exponential of Williams and Watts [76] may be justified in terms of continuous-time random walks. 

Analysis of the enthalpy relaxation the enthalpy relaxation time and the activation energy were calculated by KWW in accordance with the previous work (Kawai et al., 2004). The KWW theory was originally proposed in dielectric relaxation study by Williams and Watts (1970), then applied in the form of nonexponential function such as the enthalpy relaxation. In KWW theory, the enthalpy relaxation, AH eiax/ which corresponds to the peak area given from the enthalpy relaxation is expressed by the equation... 

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