Cohen-Grest model for the dynamics of supercooled liquids

Recent experiments have established that, at least for van der Waals glass formers, volume fluctuations contribute significantly to the slowing down of the dynamics near $T_g.$ Accordingly, we use the Cohen-Grest (CG) free-volume model to analyze dielectric relaxation data for six van der Waals liquids. The CG equation accurately describes the structural relaxation times over broader ranges of temperature than the more common Vogel-Fulcher relation. Moreover, the CG equation requires two less adjustable parameters when the data span the Stickel temperature $T_B$ associated with a change in the dynamics. The characteristic temperature $T_0$ of the CG model can be identified with $T_B,$ suggesting that the crossover reflects onset of percolation of the free volume. The CG parameters used to fit the structural relaxation times allow the free volume per liquidlike molecule to be calculated. These results, however, are at odds with free-volume estimates extracted from pressure-volume-temperature data.