Slow secondary relaxation in a free-energy landscape model for relaxation in glass-forming liquids

Within the framework of a free-energy landscape model for the relaxation in supercooled liquids the primary (alpha) relaxation is modeled by transitions among different free-energy minima. The Secondary (beta) relaxation then corresponds to intraminima relaxation. We consider a simple model for the reorientational motions of the molecules associated with both processes and calculate the dielectric susceptibility as well as the spin-lattice relaxation times. The parameters of the model can be chosen in a way that both quantities show a behavior similar to that observed in experimental studies on supercooled liquids. In particular we find that it is not possible to obtain a crossing of the time scales associated with alpha and beta relaxation. In our model these processes always merge at high temperatures and the cr process remains above the merging temperature. The relation to other models is discussed.