Dynamic Crossover in Polymers , Role of Molecular Weight
One of the most characteristic features of glass-forming liquids is the sharp slowing down of relaxation times, τ, upon cooling. In these materials relaxation dynamics exhibit a non-Arrhenius temperature dependence usually described by Vogel-Fulcher-Tamman (VFT) relation [1]. However, for majority of glassforming liquids it is impossible to fit data in the entire temperature range with a single set of VFT parameters. Above some characteristic temperature it is necessary to use another set of VFT parameters. Existence of this dynamic crossover was predicted by the mode-coupling theory (MCT) [2]. The theory predicts a transition from a liquidlike to a solidlike dynamics on a molecular time and length scale at some specific temperature, TC, above the glass transition temperature Tg. The dynamic crossover becomes even more evident with the use of derivative analysis proposed by Stickel et al [3] 2 , where x is the relaxation time or frequency. If
Relaxation in complex systems
The phenomenon of slow relaxation is discussed with emphasis on finding a general explanation of its ubiquity. After a review of the phenomenon, possible causes are considered both at the microscopic level and from a configuration space viewpoint. Quenched randomness and strongly constrained dynamics appear most important microscopically. In configuration space the central requirement seems to be the existence of many valleys connected sparsely in a hierarchical way. Recent toy models are shown to fit into this overall picture.
Relaxation behaviour in ultrametric spaces
The authors model transport in random media through random walks on ultrametric spaces, which allow them to account for energetic randomness. They monitor the relaxation patterns for the trapping and target annihilation problems and show that the relaxation depends qualitatively on temperature.