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We present diffusion coefficient and shear viscosity data for the Lennard-Jones fluid along nine isochores above the critical density, each involving a temperature variation of roughly two orders of magnitude. The data are analyzed with respect to the Stokes-Einstein (SE) relation, which breaks down gradually at high temperatures. This is rationalized in terms of the fact that the reduced diffusion coefficient D and the reduced viscosity η are both constant along the system’s lines of constant excess entropy (the isomorphs). As a consequence, Dη is a function of T/TRef(ρ) in which T is the temperature, ρ is the density, and TRef(ρ) is the temperature as a function of the density along a reference isomorph. This allows one to successfully predict the viscosity from the diffusion coefficient in the studied region of the thermodynamic phase diagram.We present diffusion coefficient and shear viscosity data for the Lennard-Jones fluid along nine isochores above the critical density, each involving a temperature variation of roughly two orders of magnitude. The data are analyzed with respect to the Stokes-Einstein (SE) relation, which breaks down gradually at high temperatures. This is rationalized in terms of the fact that the reduced diffusion coefficient D and the reduced viscosity η are both constant along the system’s lines of constant excess entropy (the isomorphs). As a consequence, Dη is a function of T/TRef(ρ) in which T is the temperature, ρ is the density, and TRef(ρ) is the temperature as a function of the density along a reference isomorph. This allows one to successfully predict the viscosity from the diffusion coefficient in the studied region of the thermodynamic phase diagram.

The Stokes-Einstein relation (SER) is one of the most robust and widely employed results from the theory of liquids. Yet sizable deviations can be observed for self-solvation, which cannot be explained by the standard hydrodynamic derivation. Here, we revisit the work of Masters and Madden [J. Chem. Phys. 74, 2450-2459 (1981)], who first solved a statistical mechanics model of the SER using the projection operator formalism. By generalizing their analysis to all spatial dimensions and to partially structured solvents, we identify a potential microscopic origin of some of these deviations. We also reproduce the SER-like result from the exact dynamics of infinite-dimensional fluids., 20 pages

The authors employed the equilibrium molecular dynamics technique to calculate the self-diffusion coefficient and the shear viscosity for simple fluids that obey the Lennard-Jones 6-12 potential in order to investigate the validity of the Stokes-Einstein (SE) relation for pure simple fluids. They performed calculations in a broad range of density and temperature in order to test the SE relation. The main goal of this work is to exactly calculate the constant, here denominated by alpha, present in the SE relation. Also, a modified SE relation where a fluid density is raised to a power in the usual expression is compared to the classical expression. According to the authors' simulations slip boundary conditions (alpha=4) can be satisfied in some state points. An intermediate value of alpha=5 was found in some regions of the phase diagram confirming the mode coupling theory. In addition depending on the phase diagram point and the definition of hydrodynamics radius, stick boundary condition (alpha=6) can be reproduced. The authors investigated the role of the hydrodynamic radius in the SE relation using three different definitions. The authors also present calculations for alpha in a hard-sphere system showing that the slip boundary conditions hold at very high density. They discuss possible explanations for their results and the role of the hydrodynamic radius for different definitions in the SE relation.

The Stokes–Einstein and Stokes–Einstein–Debye relations hold well in nonsupercooled liquids; however, sizeable deviations from the former appear in supercooled liquids, leading to a ‘‘decoupling’’ of translational diffusion from viscosity and reorientational relaxation. We attribute this breakdown and this ‘‘decoupling’’ to the existence of structured domains in the supercooled liquid.

International audience; The breakdown of the Stokes-Einstein relation was investigated for three glass-forming models composed of mixtures of Lennard-Jones A-B particles, which have been constructed by modifying the shape of the interaction potential between A particles. By performing molecular dynamics simulations, we show that these mixtures intrinsically possess different organizations. The breakdown of the Stokes-Einstein relation particularly occurs at different temperatures for each type of particles and it is directly related to the dynamical decoupling between A and B particles and the formation or not of paths where fast particles show jumplike motions. The effective size of each particles and the fraction of slow and fast particles were also determined. Similarity with silicate glasses including mixed alkali effect is discussed. © 2009 American Institute of Physics.

The expressions for the friction coefficient of a diffusing particle, obtained from a completely molecular theory in a previous paper, are solved for a Brownian particle in a compressible fluid. In appropriate limits the exact forms of the hydrodynamic friction coefficients in the slip and stick limits are reproduced. The use of the hydrodynamic results in describing the velocity autocorrelation function (VACF) of a molecule is discussed.

Empirically motivated modifications of the Stokes–Einstein formula, in which the diffusion coefficient is inversely proportional to a fractional power of the viscosity, are discussed. We suggest that the results should be analyzed in terms of an effective hydrodynamic radius.