Comments on the alpha -peak shapes for relaxation in supercooled liquids

The alpha -peak master functions as obtained within the mode coupling theory for the supercooled liquid dynamics near the glass transition singularity are discussed. Double peak phenomena are found as a generic feature of the theory related to the self crossing of the transition hypersurface. They lead to two scenarios for liquid to glass transitions characterized by alpha '- alpha -peak pairs and by alpha -resonances accompanied by gamma -peaks. An efficient numerical procedure is developed for the solution of the nonlinear scaling equations for the master functions. A schematic three component model is used to fit quantitatively the dielectric loss spectra of polyvinylacetate, ortho-terphenyl, CaKNO₃ and poly propylene glycol, which all deviate strongly from the Kohlrausch decay pattern. The model yields also triple resonances of alpha - gamma - delta -peaks.