Energy landscape, minimum points, and non-Arrhenius behavior of supercooled liquids

The present paper gives a theoretical explanation of the non-Arrhenius behavior that can be observed in supercooled liquids at sufficiently low temperatures. The starting point of the investigation is the determination of the density of minimum points of the energy landscape. This density allows the determination of characteristic length scales in the $3N$-dimensional configuration space and finally the transition rate between neighbored minimum points. From this point of view it is possible to analyze the dynamics of the glass transition. The characteristic relaxation time and the viscosity, respectively, can be expressed as a nonlinear function of the reduced inverse temperature ${x=T}_g/T$. This relation contains no free parameters with the exception of the gauge point $\{T_g,{\eta }_g\}$, in contrast to usual heuristic equations with some free fit parameters. All parameters are material constants (melting point, Debye-temperature, and specific heat capacities) that are well known or that are measurable in the thermodynamic equilibrium. These parameters allow a complete approach to the non-Arrhenius behavior of the supercooled liquid. Furthermore, this fact includes that the fragility $F$ can be computed also by these equilibrium quantities. The results of the presented theory are examined by a representative number of various types of glass formers, e.g., ionic glasses, organic liquids, or polymers.