General susceptibility functions for relaxations in disordered systems

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Abstract
A general equation for the susceptibility of disordered systems is proposed. It is based on the experimental observation of power laws at frequencies far from the peak frequency of the imaginary part of the frequency dependent relaxation function, the susceptibility. The obtained general expression contains the equations of other proposed relaxation functions as special cases and, thus, it might be considered as a generalization of these. From this general equation we derive an equation specially adapted for the α relaxation in glass-forming materials. This equation contains only three fit parameters and it is thus very suitable for fitting real experimental data. It is shown that this equation is a good frequency domain representation of the time domain Kohlrausch–Williams–Watts stretched exponential. From the general equation we also derive a four-parameter “universal” equation that describes most types of responses and even inverted response data, i.e., response peaks more stretched on the low frequency side than on the (as is normal) high frequency side. The physical significance of the different parameters is qualitatively discussed and the proposed functions are shown to satisfactorily describe typical experimental data.

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