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

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 (ξ_het). As the size of the probe increased, the temperature dependence of the rotation correlation time (τ_c) shifted to longer times, and from this shift, the length scale associated with the glass transition (ξ_α) was estimated through the Debye-Stokes-Einstein (DSE) relationship and the length scale of the probe (ξ_sDFT) estimated from quantum mechanical calculations. The estimated ξ_α values roughly matched with ξ_het 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 τ_c 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 ξ_α 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 ξ_het 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.