α-relaxation near the glass transition

The general mode-coupling equations with activated processes included are analysed in the α-relaxation region. This region is intimately connected with the β-relaxation region, where dynamics is completely ruled by generic properties of various bifurcation singularities inherent in the nonlinear equations of motion. In particular the von Schweidler relaxation, which describes the overlap region between the α- and β-processes, plays a central role for the properties of the α-relaxation function. This satisfies the time-temperature superposition principle with a master function which is well described by a Kohlrausch law. The α-relaxation scale is proportional to the macroscopic viscosity, and for the temperature dependence one finds an algebraic increase above a critical temperature T_c, i.e. η∝(T-T_c)^-γ. For lower temperatures, there is eventually a crossover to an Arrhenius law η∝ exp(E/k_BT).