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.
Monte Carlo investigation of a kinetic Ising model of the glass transition
A detailed Monte Carlo study of the equilibrium and dynamical properties of the two‐spin facilitated kinetic Ising model proposed by Fredrickson and Andersen (FA) is presented. The model Hamiltonian is that of a spin‐1/2 Ising model in an external magnetic field and, in the present study, contains no interactions between spins. The kinetic properties of the model are described by a master equation with single‐spin‐flip dynamics and highly cooperative flip rates. In particular, the rate at which a spin flips is chosen to be zero unless at least two of its neighbors are spin up. Monte Carlo simulations of the model on a square lattice demonstrate that although there is no evidence for a kinetic singularity (as predicted by FA), the model has dynamical properties much like those of viscous liquids. We find non‐Arrhenius temperature dependence of the average relaxation time and highly nonexponential decay of various relaxation functions. The expression derived by Adam and Gibbs is found to describe the relati...