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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.

In low-temperature-supercooled liquids, below the ideal modecoupling theory transition temperature, hopping and continuous diffusion are seen to coexist. Here, we present a theory that shows explicitly the interplay between the two processes and shows that activated hopping facilitates continuous diffusion in the otherwise frozen liquid. Several universal features arise from nonlinear interactions between the continuous diffusive dynamics [described here by the mode coupling theory (MCT)] and the activated hopping (described here by the random first-order transition theory). We apply the theory to a specific system, Salol, to show that the theory correctly predicts the temperature dependence of the nonexponential stretching parameter, β, and the primary α relaxation timescale, τ. The study explains why, even below the mean field ergodic to nonergodic transition, the dynamics is well described by MCT. The nonlinear coupling between the two dynamical processes modifies the relaxation behavior of the structural relaxation from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Furthermore, the theory correctly predicts the observed variation of the stretching exponent β with the fragility parameter, D. These two predictions also allow the complexity growth to be predicted, in good agreement with the results of Capaccioli et al. complexity | glass transition | random first order T he glass transition is characterized by a number of interesting kinetic phenomena. Very slow and simultaneously nonexponential relaxation of time correlation functions over large time windows is one such important phenomenon. This relaxation is often approximated by the stretched exponential, KohlrauschWilliam-Watts (KWW) formula, φ(t) = exp(−(t/τ )) β , with both β and τ exhibiting nontrivial temperature dependence. The origin of the stretching is usually attributed to the presence of dynamic heterogeneity in the system (1, 2). The temperature dependence of the typical relaxation time can be described by the the Vogel-where τ VFT is the high-temperature relaxation time, T o is the VFT temperature, and D is the fragility index. The fragility index, D, determines the degree of deviation from the Arrhenius law that is appropriate for simple activated events. Experimental and theoretical model studies have shown that β and D are correlated (3-5). The temperature dependence of τ has also been described by phenomenological mode coupling theory (MCT) expression,, but this ultimately breaks down at low temperature. T fit c is referred to as the MCT transition temperature. Above T fit c , MCT is found to explain many experimental results (6-9), and below T fit c , the MCT picture of continuous diffusion fails eventually. It is conjectured that this breakdown is due to the ergodic to nonergodic transition in the dynamics and below T fit c activated dynamics becomes a dominant mode of transport. However in an elegant work, Brumer and Reichman (10) (BR) ...

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We present a study of two model liquids with different interaction potentials, exhibiting similar structure but significantly different dynamics at low temperatures. By evaluating the configurational entropy, we show that the differences in the dynamics of these systems can be understood in terms of their thermodynamic differences. Analyzing their structure, we demonstrate that differences in pair correlation functions between the two systems, through their contribution to the entropy, dominate the differences in their dynamics, and indeed overestimate the differences. Including the contribution of higher order structural correlations to the entropy leads to smaller estimates for the relaxation times, as well as smaller differences between the two studied systems.Many approaches towards understanding the dynamical behavior of liquids attempt to predict dynamics in terms of static structural correlations [1,2], often focussing on two-body correlation functions. In turn, it has been argued that the short range, repulsive interactions have a dominant role in determining the pair correlation function, with the attractions making a perturbative contribution. Such an approach was shown to be effective in predicting the pair correlation function for dense liquids interacting via. the Lennard-Jones (LJ) potential, by Weeks, Chandler and Andersen, who treated the LJ potential as a sum of a repulsive part (referred to subsequently as the WCA potential) and the attractive part [3]. If such a treatment carries over to the analysis of dynamics, the expectation would be that liquids with LJ and the corresponding WCA interactions should have similar dynamics. However, in a series of recent papers, Bertheir and Tarjus have shown that model liquids with LJ and WCA interactions, exhibiting fairly similar structure, exhibit dramatically different dynamics, characterized by a structural relaxation time, at low temperatures [4][5][6][7]. In order to analyze this "non-perturbative" effect of the attractive forces on the dynamics, Berthier and Tarjus studied a number of "microscopic" approaches to predict the dynamics, based on knowledge of the static pair correlations. They conclude that the approaches they analyze are unsuccessful in capturing the differences in dynamics between the LJ and WCA systems. Dyre and co-workers [8][9][10] have argued that the origins of these observations are not specifically in the inclusion or neglect of attractive interactions [10], but factors such as the inclusion of interactions of all first shell neighbors [8], and the presence or absence of scaling between systems/state points compared [9]. In particular, Pedersen and Dyre [9] identify a purely repulsive inverse-power-law (IPL) potential that has dynamics that can be mapped to the LJ case studied by Bertheir and Tarjus. These observations notwithstanding, the inability to capture the differences between the LJ and WCA system highlighted by Berthier and Tarjus by predictive approaches to dynamics remains an open issue. In this regard, it has been s...