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We present here a microscopic and self-consistent calculation of the self-diffusion coefficient of a small tagged particle in a dense liquid of much larger particles. In this calculation the solute motion is coupled to both the collective density fluctuation and the transverse current mode of the liquid. The theoretical results are found to be in good agreement with the known computer simulation studies for a wide range of solute-solvent size ratio. In addition, the theory can explain the anomalous enhancement of the self-diffusion over the Stokes-Einstein value for small solutes, for the first time. Further, we find that for large solutes the crossover to Stokes-Einstein behavior occurs only when the solute is 2-3 times bigger than the solvent molecules. The applicability of the present approach to the study of self-diffusion in supercooled liquids is discussed.

In this paper, we develop a model for the dynamics of water near a protein surface and compare with experimental results obtained with femtosecond resolution. The model consists of a layer of bound and free water molecules at the surface of the protein in dynamic equilibrium with each other, coupled to bulk water away from the protein surface. A previous model (Pal et al. J. Phys. Chem. B 2002, 106, 12376) considered the exchange in the layer without the coupling to the bulk. We find that water dynamics at the protein surface are described by two time scales, a fast, bulklike time scale, and a slower one more than 1 order of magnitude longer. The slow time scale, as in the previous model, is shown to be inversely proportional to the bound-to-free water conversion rate, k 2, but with a significant dependence on the free-to-bound conversion rate k 1, the diffusion of the free water molecules, and the thickness of the layer. This effect, identified as the feedback mechanism, is found to depend on the degree of orientation of the bound water molecules at the surface. The weight of the contribution of the slow component to the overall relaxation dynamics is shown to be inversely proportional to the slow decay time. For a heterogeneous surface with spatially varying k 2, the water dynamics in a probe region covering several sites is described by the cumulated effects from these water molecules, with the slow dynamics given by a sum of exponentials, with contributions inversely proportional to their respective decay times. To a very good degree, we find that this exponential behavior can be fitted to a single exponential; however, the apparent time scale does not represent that of any particular site. These conclusions are in good agreement with experimental results and provide important insight to the observed dynamical behavior.