β-Relaxation Processes Near Glass Transitions

Abstract

Glass transition singularities as obtained within mode coupling theories can be classified according to underlying topological singularities in a parameter space. The general equations for the β-relaxation process are characterized by a few relevant parameters characteristic for every singularity. The simplest singularity, the Whitney fold, gives a dynamical scaling law with a critical power law decay, and shows features which are in general agreement with those observed near structural liquid-glass transitions. The Whitney cusp and higher order singularities are characterized by two or more parameter scaling laws, where time t enters as ln t and where the scaling times has a Vogel-Fulcher like dependence on control parameters. The critical relaxation follows a 1/lnx(t) law with x = 2/(k − 2), k ⩾ 3. In this case the scaling laws give a relaxation pattern with features which agree with those observed in spin glasses.