Connection between the time distribution and length scale of dynamic heterogeneity explored by probe reorientations of different sizes

The rotational dynamics of fluorescent probes of different sizes in glass-forming materials were examined to correlate the time distribution and length scale of the dynamic heterogeneity (ζhet). As the size of the probe increased, the temperature dependence of the rotation correlation time (τc) shifted to longer times, and from this shift, the length scale associated with the glass transition (ζα) was estimated through the Debye-Stokes-Einstein (DSE) relationship and the length scale of the probe (ζsDFT) estimated from quantum mechanical calculations. The estimated ζα values roughly matched with ζhet obtained from calorimetric analysis but were considerably smaller than those deduced from 4D NMR, boson peak, and four-point dynamic susceptibility measurements but with a similar trend of decrease in the length scale upon the increase in the stretching exponent (β) of the system. Because β of the glass formers represents the time distribution of the system, and τc is related to the weighted average of the distribution, the length-scale distribution of the glass transition can be deduced by adopting the DSE relationship and assuming ζα is the weighted average of this distribution at the glass transition temperature. In such a case, the upper bound of the length scale and trend matches the experimentally obtained ζhet from 4D NMR, boson peak, and four-point dynamic susceptibility measurements. Furthermore, at a given temperature, as the probe size increased, the β value reported by the probe increased, whereas the temperature dependence of β, which strongly correlates with the fragility of the system, was independent of the probe size.