A molecular explanation of the transition from viscous to hopping mechanism of mass transport in the supercooled liquid near the glass transition

Abstract

When the viscosity of a supercooled liquid becomes large, the mechanism of mass transport is known to undergo a change from viscosity dependent, Stokes-Einstein behavior to an activated hopping dominated, almost viscosity independent behavior. This change is known to occur rather sharply near the temperature T_c where the mode coupling theory predicts singularities in the transport properties of the liquid. However, the origin of this change in the transport mechanism is not well-understood. Here we suggest a simple microscopic interpretation of this crossover. Our analysis is based on a scaled particle theory calculation of the activation energy for hopping and the non-Markovian rate theory of activated barrier crossing. We find that as the liquid is progressively supercooled, the activation barrier for hopping increases rapidly which makes the curvature at the barrier top also to increase. At high densities the latter gives almost a viscosity independent hopping rate which becomes more dominant at large viscosities where the collective diffusion becomes inefficient. The suddenness of the crossover is because as the density is increased, the hopping rate also decreases rapidly because of the increase in the activation energy, and a rapid increase in viscosity is required to tilt the balance in favor of the hopping mechanism. The latter can only happen at a dynamic singularity where the viscosity undergoes a sharp increase. The present analysis also offers an explanation of the decoupling of structural relaxation from the viscosity at large values of latter-such a decoupling has been suggested recently by Angell. Our analysis also provides a tentative explanation of the recent simulation results of Keyes and co-workers.