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 (ξhet). 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 (ξα) was estimated through the Debye-Stokes-Einstein (DSE) relationship and the length scale of the probe (ξsDFT) estimated from quantum mechanical calculations. The estimated ξα values roughly matched with ξhet 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 (ß) of the system. Because ß 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 ξα 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 ξhet from 4D NMR, boson peak, and four-point dynamic susceptibility measurements. Furthermore, at a given temperature, as the probe size increased, the ß value reported by the probe increased, whereas the temperature dependence of ß, which strongly correlates with the fragility of the system, was independent of the probe size.

Single molecule demonstration of Debye-Stokes-Einstein breakdown in polystyrene near the glass transition temperature.

Rotational-translational decoupling, in which translational motion is apparently enhanced over rotational motion in violation of Stokes-Einstein (SE) and Debye-Stokes-Einstein (DSE) predictions, has been observed in materials near their glass transition temperatures (Tg). This has been posited to result from ensemble averaging in the context of dynamic heterogeneity. In this work, ensemble and single molecule experiments are performed in parallel on a fluorescent probe in high molecular weight polystyrene near its Tg. Ensemble results show decoupling onset at approximately 1.15Tg, increasing to over three orders of magnitude at Tg. Single molecule measurements also show a high degree of decoupling, with typical molecules at Tg showing translational diffusion coefficients nearly 400 times higher than expected from SE/DSE predictions. At the single molecule level, higher degree of breakdown is associated with particularly mobile molecules and anisotropic trajectories, providing support for anomalous diffusion as a critical driver of rotational-translational decoupling and SE/DSE breakdown.