Dynamics of supercooled melts treated in terms of the random-walk concept

The concept of random walk of an excitation within a Gaussian density of states (DOS) is applied to treat diffusion and viscous motion of glass-forming elements controlled by the random potential established upon supercooling a melt. It relates the super-Arrhenius-type temperature dependence observed for viscosity and related properties at T>T_g (the glass transition temperature) to the energetic relaxation of the glass elements within the DOS. The resulting relaxation pattern implies that the system must become non-ergodic at the temperature where the time required to relax to dynamic equilibrium exceeds the experimental time-scale. The model is able to explain quantitatively (i) eta (T) data in the temperature range T_c>T>or=T _g (T_c being a critical temperature above which collective effects, tractable within the mode-coupling concept, become important), (ii) the dependence of T_g on cooling rate and (iii) the Arrhenius-type T dependence of molecular motion below T_g, and qualitatively (iv) the occurrence of physical aging and (v) non-exponential relaxation patterns.