(774b) Relation Between Transient Localization and Long-Time Viscous Relaxation In Glasses?

Glass forming liquids exhibit upon cooling a striking divergence in the magnitude of the characteristic time-scales of transient local elastic vibration and long-time viscous relaxation. This divergence is apparently a universal feature of glass-forming liquids. A model generally relating these high and low frequency processes would both offer great practical benefits from the standpoint of design and characterization of glass-forming materials and could have a fundamental impact on our understanding of glass formation. Recent attempts to develop such a relation have been based, following classical studies of Eyring and coworkers, on simple transition state framework models that posit structural relaxation to consist of numerous local ‘cage escape’ events, with the further assumption that particles are enthalpically localized by a harmonic potential. More recently, Leporini and coworkers have extended the earlier approach of Hall and Wolynes in this framework by incorporating dynamic heterogeneity. On this basis they have suggested a universal relation between the Debye-Waller factor (a local vibrational length scale) and the structural alpha relaxation time, without any free parameters that reflect the specific nature of the material in question. 

Despite some apparent reported successes of this type of argument, the universality of these proposed relations as well as the physical basis of their modeling assumptions remain unclear. Accordingly, we freshly examine the success of models of this class in the context of several experimental and simulated systems. We find that no universal equation can relate the Debye-Waller factor to the alpha relaxation time without minimally taking into account the fragility of the glass-forming liquid. We tentatively explore an alternative transition state theory approach that generalizes the work of Hall and Wolynes simply by accounting for the anharmonicity of the local intermolecular potential. This model yields an improved fitting of our relaxation data with apparently physically meaningful parameters. Despite this success, we consider the transition state framework of this and other models to be rather idealized, and we discuss conceptual shortcomings of this class of approach.