TEMPERATURE-DEPENDENCE OF VISCOSITY NEAR THE GLASS-TRANSITION

Real glass transitions, where activated processes are included, are analysed near Whitney fold and cusp singularities. In particular the temperature dependence of the viscosity η is studied. For sufficiently strongly coupled systems there is close to a fold singularity located at T=Tc, a crossover from an algebraic divergence η∝(T-Tc)-γ for T>Tc, to an Arrhenius dependence η∝exp(E/kBT) for T<Tc. If a parameter vector specifying the system also passes close to a cusp singularity, at T0<Tc, there may be a temperature region where the viscosity also shows Fogel-Fulcher like dependence. The results for the viscosity are intimately connected with the dynamics for the so-called β-relaxation process, where relaxation occurs via a fractal time process in the delevant time region. © 1990 Springer-Verlag.