Fractional Stokes-Einstein and Debye-Stokes-Einstein relations in a network-forming liquid

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.     

Stokes-Einstein relation in supercooled aqueous solutions of glycerol

The diffusion of glycerol molecules decreases with decreasing temperature as its viscosity increases in a manner simply described by the Stokes-Einstein relation. Approaching the glass transition, this relation breaks down as it does with a number of other pure liquid glass formers. We have measured the diffusion coefficient for binary mixtures of glycerol and water and find that the Stokes-Einstein relation is restored with increasing water concentration. Our comparison with theory suggests that adding water postpones the formation of frustration domains.     

Hydrodynamic regimes of active rotators at fluid interfaces

We analyze the collective motion of suspensions of active rotators at low Reynolds numbers which interact hydrodynamically. We introduce a simple model for a rotator which allows us to classify the relevant dynamical regimes of the suspension. We characterize the collective velocity at which rotators displace and analyze its implications at long times, when these rotator suspensions diffuse. We analyze the differences with respect to diffusion in suspensions of passive particles, and assess the relevance of the Stokes-Einstein relation on rotators' diffusivity.     

Relation between self-diffusion and viscosity in dense liquids: new experimental results from electrostatic levitation

By using the technique of electrostatic levitation, the Ni self-diffusion, density, and viscosity of liquid Zr(64)Ni(36) have been measured in situ with high precision and accuracy. The inverse of the viscosity, η, measured via the oscillating drop technique, and the self-diffusion coefficient D, obtained from quasielastic neutron scattering experiments, exhibit the same temperature dependence over 1.5 orders of magnitude and in a broad temperature range spanning more than 800 K. It was found that Dη=const for the entire temperature range, contradicting the Stokes-Einstein relation.     

Experimental verification of the Stokes-Einstein relation in liquid Fe—FeS at 5 GPa

Experiments have been performed at 5 GPa on liquid Fe-FeS in order to determine Fe and S self-diffusivity as a function of temperature. The viscosity of the sample was then obtained using the Stokes-Einstein relation. The results are in excellent agreement with previous experiments where the viscosity of a material of the same composition under similar conditions was measured directly. These results support high, near-metallic, values of diffusivity and low viscosity in liquid Fe-S up to a few hundred K above the eutectic temperature, in contrast with some previous studies. Moreover, these results fully confirm the validity of the Stokes-Einstein relation between viscosity and diffusion coefficients for Fe_0.61S_0.39.     

The long time and Brownian limits for tagged particle motion in liquids

Formally exact theories of tagged particle motion in liquids are developed, based upon kinetic theory for hard spheres and mode coupling for smooth potentials. It is shown that the resulting equations are tractable in the long time and Brownian limits. The coefficient of the long time tail of the velocity correlation function is seen to differ from its low-density form by only the replacement of the low-density viscosity and diffusion constant by the true viscosity and diffusion constant. In the Brownian limit, the slip Stokes-Einstein law is obtained, with the true viscosity. The relation to other work is discussed.Supported by NSF Grant No. CHE81-11422 and by a Dreyfus Teacher-Scholar grant to TK.     

Observation of fractional Stokes-Einstein behavior in the simplest hydrogen-bonded liquid

Quasielastic neutron scattering has been used to investigate the single-particle dynamics of hydrogen fluoride across its entire liquid range at ambient pressure. For T>230 K, translational diffusion obeys the celebrated Stokes-Einstein relation, in agreement with nuclear magnetic resonance studies. At lower temperatures, we find significant deviations from the above behavior in the form of a power law with exponent xi=-0.71+/-0.05. More striking than the above is a complete breakdown of the Debye-Stokes-Einstein relation for rotational diffusion. Our findings provide the first experimental verification of fractional Stokes-Einstein behavior in a hydrogen-bonded liquid, in agreement with recent computer simulations [S. R. Becker, Phys. Rev. Lett. 97, 055901 (2006)10.1103/PhysRevLett.97.055901].     

Self-diffusion in microemulsions and micellar size

Self-diffusion of all components of two different microemulsions have been measured. Application of Stokes-Einstein equations for surfactant and oil gives a simple relation connecting their size and self-diffusion coefficients. Using the measured self-diffusion coefficients and dimensions of oil molecules known from elsewhere, the size of the surfactant droplets was estimated. This approach turns out to be advantageous in practical determination of droplet size in microemulsions.     

An Enskog repeated-ring kinetic equation; Long-time tails and the Brownian limit

A kinetic equation for the motion of a particle of arbitrary size and mass through a moderately dense gas is derived and discussed. The “long-time tail” of the velocity correlation function is calculated and found to agree with existing results. For a Brownian particle, the theory gives the Stokes-Einstein law for the self-diffusion coefficient, with the shear viscosity given by its Enskog value.     

Limits of the validity of the mass ratio independence of the Stokes—Einstein relation: molecular dynamics calculations and comparison with the Enskog theory

Detailed molecular dynamics simulations have been carried out to investigate the mass ratio dependence of the tracer self-diffusion coefficient D ₂ in binary, atomic Lennard-Jones mixtures as a function of density n and length diameter ratio σ₂₂/σ₁₁. For a compact representation of our results an exponential approach is employed. The results are compared with the Stokes-Einstein relation, which predicts no mass ratio dependence, and the Enskog theory. The validity ranges regarding the mass ratio dependence for Enskog and Stokes-Einstein like behaviour are given as well as the mass ratio dependence in the crossover regions between these two cases. For length parameter ratios σ₂₂/₁₁ <1, the Stokes-Einstein prediction is not valid for mass ratios 1/16≤m₂/m₁ ≤50. For length parameter ratios σ₂₂/σ₁₁>2 and for mass ratios m₂/m₁ < 1, the Stokes-Einstein regime (regarding the mass ratio dependence) is reached for smaller densities than for the same system but m₂/m₁ >1.     

Dielectric and transport properties of a supercooled symmetrical molten salt

The liquid-glass transition of the restricted primitive model for a symmetrical molten salt is studied using mode-coupling theory. The transition at high densities is predicted to obey the Lindemann criterion for melting, and the charge-density peak found in neutron-scattering experiments on ionic glass formers is qualitatively reproduced. Frequency-dependent dielectric functions, shear viscosities, and dynamical conductivities of the supercooled liquid are presented. Comparing the latter to the diffusion constant, we find that mode-coupling theory reproduces the Nernst-Einstein relation. The Stokes-Einstein radius is found to be approximately equal to the particle radius only near the high-density glass transition.     

Molecular dynamics simulation of self-diffusion coefficients for liquid metals

The temperature-dependent coefficients of self-diffusion for liquid metals are simulated by molecular dynamics meth ods based on the embedded-atom-method （EAM） potential function. The simulated results show that a good inverse linear relation exists between the natural logarithm of self-diffusion coefficients and temperature, though the results in the litera ture vary somewhat, due to the employment of different potential functions. The estimated activation energy of liquid metals obtained by fitting the Arrhenius formula is close to the experimental data. The temperature-dependent shear-viscosities obtained from the Stokes-Einstein relation in conjunction with the results of molecular dynamics simulation are generally consistent with other values in the literature.     

Effects of solute-solvent and solvent-solvent attractive interactions on solute diffusion

A study is reported on the diffusion process of a solute molecule in a Lennard-Jones-like liquid near the triple point by a molecular dynamics simulation. Systematic changes were made to the strength of the solute-solvent or solvent-solvent attractive interaction in order to elucidate its effects on the diffusion coefficient. When the solute-solvent attractive interaction is enhanced, the diffusion coefficient of the solute becomes much smaller than that predicted by the Stokes-Einstein relationship with a stick boundary condition. The generalized friction coefficient on the solute molecule was investigated, and the attractive force between solute and solvent is found to be the main cause for the enhancement of the friction. When the attractive interaction between solvent molecules is weakened, the diffusion coefficient of a solute does not change, whereas that of a solvent does. Compared with the shear viscosity of the solvent, the diffusion coefficient of the solute breaks the Stokes-Einstein relationship, whereas the Stokes-Einstein relationship appears to hold in the case of the solvent molecule.     

Tracer diffusion in glassforming liquids

In the last decades, a wide collection of experimental evidence has been found in the study of supercooled glassformers on the existence of a crossover between two dynamical regimes at a temperature T_c. We discuss the validity of the Vogel-Fulcher-Tammann in both regions. The breakdown of the Stokes-Einstein relation below T_c is presented, indicating that the diffusion coefficient of a tracer becomes decoupled from the viscosity through an exponent ξ, and the diffusion process is intensified. We verify that a temperature shift on the diffusion coefficient introduces the same effect as the Stokes-Einstein breakdown equation. We present the dependence of this exponent on the ratio between the radii of the tracer and the host liquid molecule.     

Glass transition of the monodisperse Gaussian core model

We numerically investigate the dynamical properties of the one-component Gaussian core model in supercooled states. We find that nucleation is increasingly suppressed with increasing density. The system concomitantly exhibits glassy, slow dynamics characterized by the two-step stretched exponential relaxation of the density correlation and a drastic increase of the relaxation time. We also find a weaker violation of the Stokes-Einstein relation and a smaller non-Gaussian parameter than in typical model glass formers, implying weaker dynamic heterogeneities. Additionally, the agreement of the simulation data with the prediction of mode-coupling theory is exceptionally good, indicating that the nature of the slow dynamics of this ultrasoft particle fluid is mean-field-like. This fact may be understood as a consequence of the long-range nature of the interaction.     

Particle dynamics in polymer-metal nanocomposite thin films on nanometer-length scales

X-ray photon correlation spectroscopy was used in conjunction with resonance-enhanced grazing-incidence small-angle x-ray scattering to probe slow particle dynamics and kinetics in gold/polystyrene nanocomposite thin films. Such enhanced coherent scattering enables, for the first time, measurement of the particle dynamics at wave vectors up to approximately 1 nm(-1) (or a few nanometers spatially) in a disordered system, well in the regime where entanglement, confinement, and particle interaction dominate the dynamics and kinetics. Measurements of the intermediate structure factor f(q,t) indicate that the particle dynamics differ from Stokes-Einstein Brownian motion and are explained in terms of viscoelastic effects and interparticle interactions.     

Fermi-like behavior of weakly vibrated granular matter

Vertical movement of zirconia-yttria stabilized 2 mm balls is measured by a laser facility at the surface of a vibrated 3D granular matter under gravity. Realizations z(t) are measured from the top of the container by tuning the fluidized gap with a 1D measurement window in the direction of the gravity. The statistics obeys a Fermi-like configurational approach which is tested by the relation between the dispersions in amplitude and velocity. We introduce a generalized equipartition law to characterize the ensemble of particles which cannot be described in terms of a Brownian motion. The relation between global granular temperature and the external excitation frequency is established.     

Self-diffusion of tris-naphthylbenzene near the glass transition temperature

We present a direct measurement of self-diffusion of a single-component glass-forming liquid at the glass transition temperature. Forward recoil spectrometry is used to measure the concentration profiles of deuterio and protio 1,3-bis-(1-naphthyl)-5-(2-naphthyl)benzene (TNB) following annealing-induced diffusion in a vapor-deposited bilayer. These experiments extend the range of measured diffusion coefficients in TNB by 6 orders of magnitude. The results indicate a decoupling of translational diffusion coefficients from viscosity or rotation. At T(g), D(T) is 400 times larger than expected from the Stokes-Einstein equation.     

Rotational diffusion microrheology

Examining the rotational diffusion of a microparticle suspended in a soft material opens up exciting new opportunities for locally probing the frequency-dependent linear viscoelastic shear modulus, G*(omega). We study the one-dimensional rotational diffusion of a wax microdisk in an aqueous polymer entanglement network using light streak tracking. By measuring the disk's time-dependent mean square angular displacement, , we predict the polymer solution's G*(omega) using a rotational generalized Stokes-Einstein relation. The good agreement of the predicted modulus with mechanical measurements confirms this new microrheological approach.