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Non-monotonic Size Dependence of Diffusion and Levitation Effect: A Mode Coupling Theory Analysis

We present a study of diffusion of small tagged particles in a solvent, using mode coupling theory (MCT) analysis and computer simulations. The study is carried out for various interaction potentials. For the first time, using MCT, it is shown that for strongly attractive interaction potential with soft core (allowing interpenetration between the solute-solvent pair) the diffusion exhibits a non-monotonic size dependence. This was earlier predicted in simulation and experimental studies and was connected to levitation effect [J. Phys. Chem. B 2005, 109, 5824-5835]. Our MCT analysis reveals that for weak or no attractive interactions, all the small solute particles studied here show levitation through the inter-solvent transient cage. However, for strong attractive interaction the levitation is not present for the smallest particle sizes. It is found that for systems where the interaction potential is hard, not allowing any interpenetration between the solute-solvent pair, the solute cannot explore the inter-solvent cage. Thus these systems will never show any non monotonic size dependence of diffusion. We also show that although levitation is a dynamic phenomena, the effect of levitation can be obtained in the radial distribution function.