Power Law Behavior of Dynamics in Simple Glass Formers

Simulation results for the diffusive behavior of polymer chain/ penetrant systems are analyzed. Both freely jointed and freely rotating chains are studied. In all cases, the characteristic times, $\tau $, extracted from the diffusion constants are found to be single valued functions of the packing fraction, $\eta $. The functions $\tau (\eta )$ are found to be power-laws with exponents that are sensitive to both chain stiffness and particle type. For a specific system type, all measures of motion extrapolate to zero (or infinity) at a single $\eta _{0}$. In addition, ($\eta _{0}-\eta )$ can be interpreted as a ``scalar metric'' of the ``distance'' to the glass ``transition.''