Dynamic scaling approach to glass formation

Experimental data for the temperature dependence of relaxation times are used to argue that the dynamic scaling form, with relaxation time diverging at the critical temperature [Formula Presented] as [Formula Presented] is superior to the classical Vogel form. This observation leads us to propose that glass formation can be described by a simple mean-field limit of a phase transition. The order parameter is the fraction of all space that has sufficient free volume to allow substantial motion, and grows logarithmically above [Formula Presented] Diffusion of this free volume creates random walk clusters that have cooperatively rearranged. We show that the distribution of cooperatively moving clusters must have a Fisher exponent [Formula Presented] Dynamic scaling predicts a power law for the relaxation modulus [Formula Presented] where z is the dynamic critical exponent relating the relaxation time of a cluster to its size. Andrade creep, universally observed for all glass-forming materials, suggests [Formula Presented] Experimental data on the temperature dependence of viscosity and relaxation time of glass-forming liquids suggest that the exponent ν describing the correlation length divergence in this simple scaling picture is not always universal. Polymers appear to universally have [Formula Presented] (making [Formula Presented] However, other glass-formers have unphysically large values of [Formula Presented] suggesting that the availability of free volume is a necessary, but not sufficient, condition for motion in these liquids. Such considerations lead us to assert that [Formula Presented] is in fact universal for all glass- forming liquids, but an energetic barrier to motion must also be overcome for strong glasses.