Generalization of the Cole-Davidson and Kohlrausch functions to describe the primary response of glass-forming systems.

We introduce a three-parameter step-response function which is based on a generalization of the Cole-Davidson (CD) and Kohlrausch (K) functions, and which provides a highly flexible susceptibility description for viscous liquids. A second parameter α characterizing the overall width, in addition to a parameter ß determining the high-frequency behavior of the susceptibility, allows for a continuous change of the spectral shape from the CD-type to the K-type. We prove that the function fulfills mathematical conditions required for a step-response function. When applying the function to interpolate dielectric spectra of neat (pure) glass formers, it is possible to keep the high-frequency parameter ß temperature-independent while varying the parameter α to account for the change of the overall width. This analysis might suggest that the failure of frequency-temperature superposition in glass formers is reflected by a broadening in the low-frequency region instead of in the high-frequency one.

Anomaly of the nonergodicity parameter and crossover to white noise in the fast relaxation spectrum of a simple glass former.

We present quasielastic light scattering and dielectric spectra of the glass former alpha-picoline. At high temperatures the evolution of the susceptibility minimum is well described by the mode coupling theory (MCT). Below the critical temperature T(c) the simple scaling laws of MCT fail due to the appearance of the excess wing of the alpha process, which shows a universal evolution as a function of log(10)tau(alpha). Taking this into account, however, we observe the predicted cusplike anomaly of the nonergodicity parameter as well as a crossover to "white noise."