Diffusion of small light particles in a solvent of large massive molecules

Abstract

We study the diffusion of small light particles in a solvent which consists of large heavy particles. The intermolecular interactions are chosen to approximately mimic a water–sucrose (or water–polysaccharide) mixture. Both computer simulation and mode coupling theoretical (MCT) calculations have been performed for a solvent-to-solute size ratio 5 and for a large variation of the mass ratio, keeping the mass of the solute fixed. Even in the limit of large mass ratio the solute motion is found to remain surprisingly coupled to the solvent dynamics. Interestingly, at intermediate values of the mass ratio, the self-intermediate scattering function of the solute, Fs(k,t) (where k is the wave number and t is the time), develops a stretching at long time which could be fitted to a stretched exponential function with a k-dependent exponent, β. For very large mass ratio, we find the existence of two stretched exponentials separated by a power law type plateau. The analysis of the trajectory shows the coexistence of both hopping and continuous motions for both the solute and the solvent particles. It is found that for mass ratio 5, the MCT calculations of the self-diffusion underestimates the simulated value by about 20%, which appears to be reasonable because the conventional form of the MCT does not include the hopping mode. However, for larger mass ratio, MCT appears to breakdown more severely. The breakdown of the MCT for large mass ratio can be connected to a similar breakdown near the glass transition.