Decoupling of tracer diffusion from viscosity in a supercooled liquid near the glass transition

Several experimental and computer simulation studies have found a partial decoupling between the diffusion coefficient of a small tagged particle from the viscosity of the medium in the supercooled liquid regime. In order to understand the microscopic origin of this decoupling, we have carried out detailed theoretical calculations of both quantities by using a self-consistent mode-coupling theory (MCT) which provides a microscopic treatment of coupled solute-solvent dynamics. We find that at low degree of supercooling, both the tracer diffusion coefficient $(D_t)$ and the viscosity $(\eta)$ of the medium vary similarly with a ratio close to the value given by the Stokes– Einstein relation with the slip boundary condition. However, at higher supercooling the viscosity increases faster than the decrease in the diffusion coefficient. This decoupling is found to depend strongly on both the size of the solute and the degree of supercooling, in agreement with the recent experimental results. The decoupling starts at a lower degree of supercooling for smaller sized tracers. The physical origin of the decoupling can be traced back to the faster increase of viscosity due to the appearance of a long-time tail in the dynamic structure factor. While the appearance of the long-time tail leads to a rapid increase of viscosity, the friction on the tracer molecule, whose motion occurs on a shorter time scale and smaller length scale, increases slowly, thus leading to the partial decoupling. However, when the size of the solute is the same as that of the solvent molecules, the straightforward application of MCT fails to predict the observed decoupling. It is shown here that this decoupling could be explained semi-quantitatively by extending the mode-oupling theory to include solvent inhomogeneity