Correlations Between Short- and Long-time Relaxation in Colloidal Supercooled Liquids and Glasses*

The spatiotemporal dynamics of short- (β) and long-time (α) structural relaxation are measured experimentally as a function of packing fraction, φ, in a series of quasi-two-dimensional binary-sphere colloidal supercooled liquids and glasses. The relaxation times associated with both long-time dynamic heterogeneity and short-time intra-cage motion grow by orders of magnitude with increasing φ, and interestingly, the two relaxation times are strongly correlated and suggest power law behavior. Moreover, microscopic analysis of the spatiotemporal dynamics revealed that the fraction of overlapping clusters of most-mobile particles at the long and short timescale increases with φ. Furthermore, the minimum spatial separation between the closest non-overlapping clusters of most-mobile particles across the two distinct timescales shows an exponential distribution. This allows extraction of φ-dependent characteristic length scale that further connects dynamics on short- and long timescales and increases with packing.