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The authors explore the coupling between rotations and translations through electrostatic interactions with the medium and show that it leads to non-Gaussian translational dynamics and violation of Stokes-Einstein-Debye relation.

We examine the influence of the shape of dynamical heterogeneities on the Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations in quasi-two-dimensional suspensions of colloidal ellipsoids. For ellipsoids with repulsive interactions, both SE and SED relations are violated at all area fractions. On approaching the glass transition, however, the extent to which this violation occurs changes beyond a crossover area fraction. Quite remarkably, we find that it is not just the presence of dynamical heterogeneities but their change in the shape from stringlike to compact that coincides with this crossover. On introducing a suitable short-range depletion attraction between the ellipsoids, associated with the lack of morphological evolution of dynamical heterogeneities, the extent to which the SE and SED relations are violated remains unchanged even for deep supercooling.

An explicit expression of the Stokes-Einstein (SE) relation in molecular scale has been determined for pure Lennard-Jones (LJ) liquids on the saturated vapor line using a molecular dynamics calculation with the Green-Kubo formula, as $D{\ensuremath{\eta}}_{\mathrm{sv}}=kT{\ensuremath{\xi}}^{\ensuremath{-}1}{(N/V)}^{1/3}$, where $D$ is the self-diffusion coefficient, ${\ensuremath{\eta}}_{\mathrm{sv}}$ the shear viscosity, $k$ the Boltzmann constant, $T$ the temperature, $\ensuremath{\xi}$ the constant, and $N$ the particle number included in the system volume $V$. To this end, the dependence of $D$ and ${\ensuremath{\eta}}_{\mathrm{sv}}$ on packing fraction, $\ensuremath{\eta}$, and $T$ has been determined so as to complete their scaling equations. The equations for $D$ and ${\ensuremath{\eta}}_{\mathrm{sv}}$ in these states are ${m}^{\ensuremath{-}1/2}\phantom{\rule{0.16em}{0ex}}{(N/V)}^{\ensuremath{-}1/3}\phantom{\rule{0.16em}{0ex}}{\left(1\ensuremath{-}\ensuremath{\eta}\right)}^{4}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\epsilon}}^{\ensuremath{-}1/2}T$ and ${m}^{1/2}\phantom{\rule{0.16em}{0ex}}{(N/V)}^{2/3}\phantom{\rule{0.16em}{0ex}}{\left(1\ensuremath{-}\ensuremath{\eta}\right)}^{\ensuremath{-}4}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\epsilon}}^{1/2}{T}^{0}$, respectively, where $m$ and $\ensuremath{\epsilon}$ are the atomic mass and characteristic parameter of energy used in the LJ potentials, respectively. The equations can well describe the behaviors of $D$ and ${\ensuremath{\eta}}_{\mathrm{sv}}$ for both the LJ and the real rare-gas liquids. The obtained SE relation justifies the theoretical equation proposed by Eyring and Ree, although the value of $\ensuremath{\xi}$ is slightly different from that given by them. The difference of the obtained expression from the original SE relation, $D{\ensuremath{\eta}}_{\mathrm{sv}}=(kT/2\ensuremath{\pi}){\ensuremath{\sigma}}^{\ensuremath{-}1}$, where $\ensuremath{\sigma}$ means the particle size, is the presence of the ${\ensuremath{\eta}}^{1/3}$ term, since ${\left(N/V\right)}^{1/3}={\left(6/\ensuremath{\pi}\right)}^{1/3}{\ensuremath{\sigma}}^{\ensuremath{-}1}{\ensuremath{\eta}}^{1/3}$. Since the original SE relation is based on the fluid mechanics for continuum media, allowing the presence of voids in liquids is the origin of the ${\ensuremath{\eta}}^{1/3}$ term. Therefore, also from this viewpoint, the present expression is more justifiable in molecular scale than the original SE relation. As a result, the ${\ensuremath{\eta}}^{1/3}$ term cancels out the $\ensuremath{\sigma}$ dependence from the original SE relation. The present result clearly shows that it is not necessary to attribute the deviation from the original SE relation to any temperature dependence of particle size or to introduce the fractional SE relation for pure LJ liquids. It turned out that the $\ensuremath{\eta}$ dependence of both $D$ and ${\ensuremath{\eta}}_{\mathrm{sv}}$ is similar to that in the corresponding equations by the Enskog theory for hard sphere (HS) fluids, although the $T$ dependence is very different, which means that the difference in the behaviors of $D$ and ${\ensuremath{\eta}}_{\mathrm{sv}}$ between the LJ and HS fluids are traceable simply to their temperature dependence. Although the SE relation for the HS fluids also follows $D{\ensuremath{\eta}}_{\mathrm{sv}}=kT{\ensuremath{\xi}}^{\ensuremath{-}1}{(N/V)}^{1/3}$, the value of $\ensuremath{\xi}$ is significantly different from that for the LJ liquids.

Our extended electrical conductivity and viscosity measurements have revealed a general fractional power relation between them in pure and mixed ionic melts: $\ensuremath{\sigma}T\ensuremath{\propto}(T/\ensuremath{\eta}{)}^{m}$ ( $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.8\ifmmode\pm\else\textpm\fi{}0.1$ for all melts) where $\ensuremath{\eta}$ is a shear viscosity of a melt. This relation has been observed in 9 orders of magnitude range of viscosity for the well known ionic melt ${\mathrm{Ca}}_{2}{\mathrm{K}}_{3}({\mathrm{NO}}_{3}{)}_{7}$. This fractional interdependence is considered to be a macroscopic manifestation of a basic difference in elementary mechanisms of charge and momentum transport in ionic melts.

We study the breakdown of the Stokes-Einstein (SE) and Debye-Stokes-Einstein (DSE) relations for translational and rotational motion in a prototypical model of a network-forming liquid, the ST2 model of water. We find that the emergence of ``fractional'' SE and DSE relations at low temperature is ubiquitous in this system, with exponents that vary little over a range of distinct physical regimes. We also show that the same fractional SE relation is obeyed by both mobile and immobile dynamical heterogeneities of the liquid.

The Stokes-Einstein equation is applied to the water self-diffusion coefficient D in human serum albumin protein solutions. A linear trend for D as a function of T/\ensuremath{\eta} is found for all the protein concentrations investigated. However, the indication of a violation of the Stokes-Einstein equation is found in the protein concentration dependence of the effective hydrodynamic radius of water. The deviation of the experimental NMR water self-diffusion and viscosity data from the hydrodynamic Stokes-Einstein relation is found to be consistent with an enhancement of the solvent structure in the vicinity of the protein surface.

Finite temperature and athermal simulations are used to determine the viscosity mu and diffusivity D for systems undergoing shear flow at shear rate gamma and temperature T. Athermal simulations show that mu approximately gamma(-1) and D approximately gamma due to strain-activated relaxations, leading to an athermal Stokes-Einstein-like relation muD=C(ASE). Finite temperature simulations show that at high T the Stokes-Einstein relation muD=C(SE)T is followed, and as T decreases muD diverges in the Newtonian limit, but muD reaches the constant value C(ASE) for finite gamma. These different behaviors of muD suggest that particle dynamics are fundamentally different as jamming is approached by reducing a driving force as opposed to cooling, and that dynamic heterogeneities play a different role in shear-induced dynamics.

Deviations from a Stokes-Einstein relation between the self-diffusion coefficient D and shear viscosity eta for liquid metals near freezing are shown to correlate with a net transit parameter xi introduced recently by Wallace [Phys. Rev. E 58, 538 (1998)] in a two-parameter model of D. Brief comments are made on the single exception of In, for the seven liquid metals for which suitable experimental data are available. [S1063-651X(99)07108-1].

The diffusion coefficient $D$ and the Ostwald solubility $\ensuremath{\alpha}$ have been measured for $^{133}\mathrm{Xe}$ atoms in water-sucrose solutions ranging in viscosity $\ensuremath{\eta}$ from 1 to 289 cP, i.e., 0.68% sucrose by weight. In water $D(20\ifmmode^\circ\else\textdegree\fi{}\mathrm{C})=(1.32\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{2}$/sec, in agreement with the Stokes-Einstein (SE) law. Over the entire range studied the observed dependence is $D\ensuremath{\propto}{\ensuremath{\eta}}^{\ensuremath{-}0.63\ifmmode\pm\else\textpm\fi{}0.02}$, significantly departing from the SE law. In water $\ensuremath{\alpha}(20\ifmmode^\circ\else\textdegree\fi{}\mathrm{C})=0.108\ifmmode\pm\else\textpm\fi{}0.005$. For water-sucrose solutions $\ensuremath{\alpha}$ is approximately proportional to the volume fraction of water in solution.

The autocorrelation function of the density of a tagged particle is studied using the Mori formalism. The variables used are the collective conserved variables, the tagged-particle density, and bilinear products thereof. The case of point particles is considered in two dimensions, and, in three dimensions, self-diffusion by a particle of arbitrary size is treated. It is found that the bilinear-hydrodynamic approach automatically separates the self-diffusion coefficient of the tagged particle into a nonhydrodynamic part, and a hydrodynamic part which resembles the Stokes-Einstein law. In two dimensions, it is found that the mean-square displacement of a particle increases as $t\mathrm{ln}t$, and that certain natural redefinitions of the diffusion and friction coefficients leave Einstein's law invariant. In three dimensions, for a large particle, the Stokes-Einstein law is reproduced. The relation between the well-known ${t}^{(\frac{\ensuremath{-}3}{2})}$ "tails" on correlation functions, and the Stokes-Einstein law, is discussed.

The diffusion coefficient associated with the order-parameter fluctuations near the critical point of fluids is expected to vanish asymptotically as $D=\frac{\mathrm{RkT}}{6\ensuremath{\pi}\ensuremath{\eta}\ensuremath{\xi}}$, where $\ensuremath{\eta}$ is the viscosity, $\ensuremath{\xi}$ the correlation length, and $R$ a universal constant. Our experiments, using 3-methylpentane-nitroethane, yield $R=1.02\ifmmode\pm\else\textpm\fi{}0.06$, in agreement with the mode-coupling theory of critical fluctuations, but in disagreement with the value $\frac{R}{6\ensuremath{\pi}}=\frac{1.2}{6\ensuremath{\pi}}\ensuremath{\simeq}\frac{1}{5\ensuremath{\pi}}$, recently suggested by several investigators.