Susceptibility functions for slow relaxation processes in supercooled liquids and the search for universal relaxation patterns

In order to describe the slow response of a glass former, we discuss some distributions of correlation times, e.g., a generalized gamma distribution (GG) and an extension thereof (GGE), the latter allowing us to reproduce a simple peak susceptibility such as of the Cole–Davidson type as well as a susceptibility exhibiting an additional high-frequency power law contribution (excess wing). Applying the GGE distribution to the dielectric spectra of glass formers exhibiting no β process peak (glycerol, propylene carbonate, and picoline) we are able to reproduce the salient features of the slow response (10−6–109 Hz). A line shape analysis is carried out either in the time or frequency domain and in both cases an excess wing can be identified. The latter evolves in a universal way while cooling and shows up for correlation times τα>10−8 s. It appears that its first emergence marks the breakdown of the high-temperature scenario of mode coupling theory. In order to describe a glass former exhibiting a β process peak we have introduced a distribution function which is compatible with assuming a thermally activated process in contrast to some commonly used fit functions. Together with the GGE distribution this function allows in the frame of the Williams–Watts approach to completely interpolate the spectra, e.g., of fluoro aniline (10−6 Hz–109 Hz). The parameters obtained indicate an emergence of both the excess wing and the β process again at τα>10−8 s.