The impact of hierarchically constrained dynamics with a finite mean of cluster sizes on relaxation properties Original Research Article

In this paper, a stochastic scenario of relaxation underlying the generalization (Kahlau et al., 2010)  of the Cole–Davidson (CD) and Kohlrausch–Williams–Watts (KWW) functions is proposed. As it has been shown (Kahlau et al., 2010) , the new three-parameter time-domain fitting function provides a very flexible description of the dielectric spectroscopy data for viscous glass-forming liquids. In relation to that result we discuss a hierarchically-constrained model yielding the proposed relaxation fitting function. Within the “exponentially decaying relaxation contributions” framework we show origins of the high-frequency (short-time, respectively) fractional power law, i.e., the characteristic feature of the new, as well as, of both CD and KWW response functions. We also bring into light a reason for which their common behavior in the opposite frequency limit is linear on external field frequency. Finally, we relate the new relaxation pattern (Kahlau et al., 2010)  with the Generalized Gamma (GG) survival probability of an imposed, non-equilibrium initial state in a relaxing system.