Brownian Motion of Molecular Probes in Supercooled Liquids

When a supercooled liquid approaches glass transition, viscous flow slows down greatly, but often the Brownian motion of a molecular probe in the host liquid does not slow down as much, causing the Stokes-Einstein relation to fail by orders of magnitude. Here we formulate a theory that relates the Brownian motion of the probe to two concurrent processes in the host liquid: viscous flow and molecular hopping. Molecular hopping prevails over viscous flow when the probe is small and the temperature is low. Our theory generalizes the Stokes-Einstein relation and fits the experimental data remarkably well.