Critical assessment of the equilibrium melting-based, energy distribution theory of supercooled liquids and application to jammed systems

Despite decades of intense study, the mechanisms underlying the extraordinary dynamics of supercooled liquids as they approach the glass transition remain, at best, mis-characterized, and at worst, misunderstood. A long standing endeavor is to understand the remarkable increase of the viscosity with supercooling. Recently, a new theory of supercooled liquids has been proposed that starts from first principles, using elementary statistical mechanics arguments, to derive a form for the viscosity that contains only a single fitting parameter in its simplest form. In this we demonstrate that this exact same form may be derived from a different starting point, and then critically examine its performance. In the process we find that functional form proposed fits the viscosity data of a diverse group of 45 liquids exceptionally well over a wide temperature range, and uncover a number of interesting correlations of the single parameter with various thermodynamic quantities, ultimately allowing for the prediction of low temperature viscosity from high temperature data. Additionally, we find that similar physical reasoning can be used to derive a similar, single parameter form for the viscosity of hard-sphere/jammed liquids. We demonstrate that this form accurately reproduces the viscosity of hard-spheres, suggesting an underlying universality in metastable dynamics.