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

TL;DR

This study investigates how small light particles diffuse in a solvent of large heavy molecules, revealing persistent coupling, complex relaxation behaviors, and limitations of mode coupling theory at high mass ratios through simulations and theoretical analysis.

Contribution

It combines computer simulations and mode coupling theory to analyze diffusion dynamics of small particles in a large-mass solvent, highlighting the theory's limitations at high mass ratios.

Findings

Solute motion remains coupled to solvent dynamics even at large mass ratios.

The self-intermediate scattering function develops a stretched exponential decay at intermediate mass ratios.

Mode coupling theory underestimates diffusion and breaks down more severely at high mass ratios.

Abstract

We study 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 five 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, F_{s}(k,t) (where k is the wavenumber and t the time), develops a stretching at long time which could be fitted to a stretched exponential function with a k-dependent exponent, \beta. 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 five, the MCT calculations of the self-diffusion underestimates the simulated value by about 20 %, which appears to be reasonable because the conventional form of 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.