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 (\ensuremath{\alpha}) relaxation is modeled by transitions among different free-energy minima. The secondary (\ensuremath{\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 \ensuremath{\alpha} and \ensuremath{\beta} relaxation. In our model these processes always merge at high temperatures and the \ensuremath{\alpha} process remains above the merging temperature. The relation to other models is discussed.