Liquid State Elasticity and the Onset of Activated Transport in Glass Formers

We show that the crossover temperature to activated transport in glass-forming liquids can be predicted using their finite-frequency elastic constants and the fusion entropy. The latter quantities determine the size of the vibrational motions of chemically rigid molecular units in the liquid as a function of temperature. Using the notion that, at the crossover, the "Lindemann ratio" of this vibrational displacement to the corresponding lattice spacing is nearly system-independent, one can estimate the crossover temperature. For nine specific substances, the resulting predictions are consistent with experimental estimates of the dynamical crossover temperature and also with the predictions of the random first order transition (RFOT) theory for the onset of barrierless transport owing to fractal correlated rearrangements that occur at a critical configurational entropy. In particular, the fragility index is found to inversely correlate with the ratio of the crossover and glass transition temperatures. This prediction agrees with most observations except for boron oxide B2O3, which deviates from the common trend. This exception is argued to result from additional local ordering with lowering temperature in B2O3. Finally, we show that taking into account the temperature dependence of the elastic constants is crucial for accurate estimates of the crossover temperature.