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 β 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 β 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.