Why diffusion decouples from viscosity near the glass transition
In plain words
In ordinary liquids, how fast a molecule wanders is inversely proportional to the viscosity, the Stokes-Einstein relation. Near the glass point molecules wander much faster than this rule predicts, and a quantitative explanation is missing.
Precise statement
Near $T_g$ in molecular liquids such as o-terphenyl, $D\eta/T$ exceeds its high-temperature value by roughly two to three orders of magnitude (approximate), and $D\sim \tau_{\alpha}^{-\xi}$ with a fractional exponent reported near 0.75 to 0.85. Predict the magnitude, temperature dependence and exponent $\xi$ from a theory of dynamic heterogeneity, and explain why rotational diffusion follows viscosity more closely than translational diffusion.
What would settle it
A theory that predicts $D(T)$, $\eta(T)$ and the decoupling exponent for a model liquid and agrees with simulations and with measurements on molecular glass formers.
Status in the literature
Unverified note
Attribution of the decoupling to dynamic heterogeneity is widely accepted qualitatively, but a quantitative prediction of the exponent is lacking (2026).