Temperature dependence of relaxation times and the length scale of cooperative motion for glass-forming liquids

When considered in the framework of a dynamic scaling model, the length scale of cooperative motion of all glass-forming liquids appears to have a universal temperature dependence. This model also predicts relaxation times with a system-specific temperature dependence, as the product of the universal cooperative length scale raised to the sixth power and a non-universal thermally activated process. In the glassy state, the length scale for cooperative motion can become temperature-independent, so the model predicts relaxation times to have an Arrhenius temperature dependence. As expected by the model, the same activation energy is observed both above and below the glass transition. At sufficiently high temperatures the model ceases to apply to relaxation times, and the crossover to a high-T Arrhenius temperature dependence provides an experimental estimate of the caging temperature. We also report an approximate power law relation between the fragility index and the cooperative length scale at the glass transition.