A mode coupling theory analysis of microscopic friction in the macroscopic limit

In order to understand the physical origin of the cross-over of solute diffusion to the hydrodynamic regime, we present an analytical and numerical calculation of the microscopic friction obtained from the mode coupling theory (MCT) at the limit of large solute size. In this limit we have shown that in the MCT expression of the microscopic friction/diffusion the contribution from the density mode vanishes and the current contribution to the diffusion reduces to the famous Stokes–Einstein form. Our numerical calculation shows that along with the size of the solute if we accordingly change the mass and the solute–solvent interaction parameters then cross-over to the current dominated regime happens early.