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The Stokes-Einstein (SE) relation for pure liquids of various non-spherical molecules is examined using molecular dynamics simulation. The SE relation obeys generally the equation recently proposed...

A recent experiment has measured the viscosity of water down to approximately 244 K and up to 300 MPa. The correct viscosity and translational diffusivity data at various temperature–pressure (T–P)...

We investigate the origin of the violation of the Stokes-Einstein (SE) relation in two-dimensional Yukawa liquids. Using comprehensive molecular dynamics simulations, we identify the time scales supporting the violation of the SE relation $D\propto (\eta/T)^{-1}$, where $D$ is the self-diffusion coefficient and $\eta$ is the shear viscosity. We first compute the self-intermediate scattering function $F_s(k,t)$, the non-Gaussian parameter $\alpha_2$, and the autocorrelation function of the shear stress $C_{\eta}(t)$. The timescales obtained from these functions are included the structural relaxation time $\tau_{\alpha}$, the peak time of the non-Gaussian parameter $\tau_{\alpha_2}$, and the shear stress relaxation time $\tau_{\eta}$. We find that $\tau_{\eta}$ is coupled with $D$ for all temperatures indicating the SE preservation, however, $\tau_{\alpha}$ and $\tau_{\alpha_2}$ are decoupled with $D$ at low temperatures indicating the SE violation. Surprisingly, we find that the origins of this violation are related to the non-exponential behavior of the autocorrelation function of the shear stress and non-Gaussian behavior of the distribution function of particle displacements. These results confirm dynamic heterogeneity that occurs in two-dimensional Yukawa liquids that reflects the presence of regions in which dust particles move faster than the rest when the liquid cools to below the phase transition temperature.

A recent experiment has directly checked the validity of the Stokes-Einstein (SE) relation for pure water, pure methanol, and their binary mixtures of three different compositions at different temperatures. The effect of composition on the nature of breakdown of the SE relation is interesting. While in the majority of the systems, an increasing SE breakdown is observed with decreasing temperature, the breakdown is already significant at higher temperatures for the equimolar mixture. Violations of the SE relation in pure supercooled water at different temperatures and pressures have been previously explained using the translational jump-diffusion (TJD) approach, which provides a fundamental molecular basis, by directly connecting the SE breakdown with jump-diffusion of the molecules. We have used the same TJD approach for explaining the SE breakdown for the methanol/water binary mixtures of compositions studied in the experiment over a wide range of temperatures between 220 K and 300 K. We have understood that the jump-diffusion is the key responsible factor for the SE breakdown. The maximum jump-diffusion contribution gives rise to the early SE breakdown observed for the equimolar mixture observed in the experiment. This study, therefore, provides molecular insight into the SE breakdown for the supercooled water/methanol binary mixture, as found in the experiment.

The Stokes-Einstein (SE) relation has been considered as one of the hallmarks of dynamics in liquids. It describes that the diffusion constant D is proportional to ( τ / T )–1, where τ is the structural relaxation time and T is the temperature. In many glass-forming liquids, the breakdown of SE relation often occurred when the dynamics of the liquids becomes glassy, and its origin is still debated among many scientists. Using molecular dynamics simulations and support-vector machine method, it is found that the scaling between diffusion and relaxation fails when the total population of solid-like clusters shrinks at the maximal rate with decreasing temperature, which implies a dramatic unification of clusters into an extensive dominant one occurs at the time of breakdown of the SE relation. Our data leads to an interpretation that the SE violation in metallic glass-forming liquids can be attributed to a specific change in the atomic structures.

We have reported a new Stokes–Einstein relation (SER) for size determination and tested it by different nanoparticles. We assumed that the breakdown for SER results from local increases in viscosity. Here we investigate hydrodynamics of solvent near dendrimers to further test generality of our new theory. We discuss simulations of dendrimers in comparison to nanoparticles, experimental data on dendrimers from literature, and our theory. Local viscosity and local diffusivity of solvent near dendrimers are estimated by persistence times and exchange times, respectively. We find that the local dynamics of solvent near dendrimers of low density stay almost the same as that of bulk solvent. While the motions of solvent particles slow down near dendrimers of high density. This is similar with changes in local dynamics of solvent near nanoparticles. According to the causes we proposed for the deviation of SER, this is consistent with our findings that the SER works for the dendrimers of low density, while it fails for the dendrimers of high density. The new SER is then tested to predict size of the dendrimers accurately. Taking this together with the results for the nanoparticles, we believe that the new theory is general. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 1380–1392

Using the pair correlation function obtained via square well (SW) model [Mishra et al., 2015 Chem. Phys. 457 13], we calculate the pair excess entropy of liquid metals and determined the diffusion coefficients via Dzugutov’s excess entropy-diffusivity scaling relation. Further, the applicability of the Stokes-Einstein relation for SW potential is validated by comparing the computed shear viscosity coefficients ( η V ) of liquid metals with the available experimental data. Reduced η V of considered systems has been derived and scaled with the excess entropy. We compute isothermal compressibility, surface tension and surface entropy of the investigated liquids by using diffusion coefficient data obtained from excess entropy scaling law. It is found that the computed values are in good agreement with the corresponding experimental data. Thus, we demonstrate that the Dzugutov scheme can be applied successfully to SW liquid metals to correlate their microscopic structural functions with their surface and thermodynamic properties.

Molecular dynamics simulations were applied to investigate the Stokes-Einstein relation (SER) and the Rosenfeld entropy scaling law (ESL) in liquid Fe0.9Ni0.1 over a sufficiently broad range of temperatures (0.70

Molecular dynamics simulations of Ni36Zr64, Cu65Zr35 and Ni80Al20 were carried out over a broad range of temperature (900-3000 K) to investigate the Stokes-Einstein (SE) relation for glass-forming melts. Our results reproduce experimental structural and transport properties. Results show that the breakdown temperature of the SE relation (TSE) equals the dynamical crossover temperature (TA) and both are roughly twice the glass-transition temperature (Tg) for the three glass-forming melts (TSE = TA ≈ 2.0Tg). The product of the individual component self-diffusion coefficient and viscosity Dαη can be roughly regarded as a constant at the transition zone (a small temperature range around TSE) in which the temperature behaviors of self-diffusion coefficient and viscosity switch from high-temperature Arrhenius to a low-temperature VFT behavior. Below TSE, the decoupling of component diffusion coefficients was found. In particular, the decoupling of component diffusion coefficients can be ascribed to the decoupling of the partial pair structural correlation of components, which can be clearly reflected by the intersection of the high-temperature and low-temperature behaviors of the ratio between the partial pair correlation entropy of components (Sβ2/Sα2). Furthermore, the ratio between the partial pair correlation entropy of components may be used to predict the validity of the SE relation, in the absence of both transport coefficients and atomic coordinates.

It is well known that glass-forming liquids exhibit a number of anomalous dynamical phenomena, most notably a two-step relaxation in the self-intermediate scattering function and the breakdown of the Stokes-Einstein (SE) relation, as they are cooled toward the glass transition temperature. While these phenomena are generally ascribed to dynamic heterogeneity, specifically to the presence of slow- and fast-moving particles, a quantitative elucidation of the two-step relaxation and the violation of the SE relation in terms of these concepts has not been successful. In this work, we propose a classification of particles according to the rank order of their displacements (from an arbitrarily defined origin of time), and we divide the particles into long-distance (LD), medium-distance, and short-distance (SD) traveling particle groups. Using molecular-dynamics simulation data of the Kob-Andersen model, we show quantitatively that the LD group is responsible for the fast relaxation in the two-step relaxation process in the intermediate scattering function, while the SD group gives rise to the slow ($\ensuremath{\alpha}$) relaxation. Furthermore, our analysis reveals that ${\ensuremath{\tau}}_{\ensuremath{\alpha}}$ is controlled by the SD group, while the ensemble-averaged diffusion coefficient $D$ is controlled by both the LD and SD groups. The combination of these two features provides a natural explanation for the breakdown in the SE relation at low temperature. In addition, we find that the $\ensuremath{\alpha}$-relaxation time, ${\ensuremath{\tau}}_{\ensuremath{\alpha}}$, of the overall system is related to the relaxation time of the LD particles, ${\ensuremath{\tau}}_{\text{LD}}$, as ${\ensuremath{\tau}}_{\ensuremath{\alpha}}={\ensuremath{\tau}}_{0}exp(\mathrm{\ensuremath{\Omega}}{\ensuremath{\tau}}_{\text{LD}}/{k}_{\text{B}}T)$.

In this Research Note the Zwanzig's formulation of the Stokes–Einstein (SE) relation for simple atomistic fluids is re-examined. It is shown that the value of the coefficient in SE relation depends...

A method for calculating the activation energy for the shear viscosity of a liquid from simulations at a single temperature is demonstrated. Importantly, the approach provides a route to the rigorous decomposition of the activation energy into contributions due to different motions and interactions, e.g., kinetic, Coulombic, and Lennard-Jones energies, that are otherwise not accessible. The method is illustrated by application to the case of liquid water under ambient conditions. The shear viscosity activation energy and its components are examined and compared to the analogous results for the time scales of diffusion and reorientation that have been previously calculated, providing a test of the Stokes-Einstein relation for water.

The validity of Stokes-Einstein (SE) relations in liquid noble metals namely Cu, Ag and Au over a wide temperature range has been studied using Dzugutov's scaling scheme and Faber's hard-sphere (HS) theory of transport coefficients. Basic ingredients of those theories are the temperature-dependent effective HS diameter and excess entropy. To determine them, we have applied variational modified hypernetted chain theory in conjunction with effective interionic interaction derived from embedded atomic method (EAM) with both temperature-dependent and independent adjustable parameters α and b. Obtained ingredients using α ( T ) and b ( T ) are close to the available experimental data than those obtained using fixed α and b with an empirical relation. Calculated transport coefficients are in good agreement with experimental data when scaling scheme with α ( T ) and b ( T ) has been considered. Simplified SE relations from transport coefficients hold when scaling scheme has been applied with α ( T ) and b ( T ) and lies around the slip boundary line.

The breakdown of the Stokes-Einstein relation (SER) in three model metallic liquids is investigated via molecular dynamics simulations. It is found that the breakdown of SER is closely correlated with the clustering behavior of well-packed atoms. When the SER breaks down, many cluster properties have almost the same value in these metallic liquids. At the breakdown temperature of SER, the temperature dependence of the number of clusters begins to deviate from a linear increase and the average number of well-packed atoms in the clusters reaches about 2, which indicates an increase in structure heterogeneity. Moreover, the size of the largest cluster shows a direct correlation with the SER. Therefore, our study provides a possible structural origin for the breakdown of SER in metallic liquids.

We report observations of breakdown of the Stokes-Einstein relation for the rotational diffusivity of polymer-grafted spherical nanoparticles in polymer melts. The rotational diffusivity of magnetic nanoparticles coated with poly(ethylene glycol) dispersed in poly(ethylene glycol) melts was determined through dynamic magnetic susceptibility measurements of the collective rotation of the magnetic nanoparticles due to imposed time-varying magnetic torques. These measurements clearly demonstrate the existence of a critical molecular weight for the melt polymer, below which the Stokes-Einstein relation accurately describes the rotational diffusivity of the polymer-grafted nanoparticles and above which the Stokes-Einstein relation ceases to apply. This critical molecular weight was found to correspond to a chain contour length that approximates the hydrodynamic diameter of the nanoparticles.

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 breakdown of the Stokes-Einstein (SE) law in fragile glassformers is examined by Molecular-Dynamics simulations of atomic liquids and polymers and consideration of the experimental data concerning the archetypical ortho-terphenyl glassformer. All the four systems comply with the universal scaling between the viscosity (or the structural relaxation) and the Debye-Waller factor < u(2)>, the mean square amplitude of the particle rattling in the cage formed by the surrounding neighbors. It is found that the SE breakdown is scaled in a master curve by a reduced < u(2)>. Two approximated expressions of the latter, with no and one adjustable parameter, respectively, are derived. Published by AIP Publishing.

In this paper the transport properties of water confined inside hydrophobic and hydrophilic nanotubes are compared for different nanotube radii and densities. While for wider nanotubes the nature of the wall plays no relevant role in the water mobility, for small nanotubes the hydrophobic confinement presents a peculiar behavior. As the density is increased the viscosity shows a huge increase associated with a small increase in the diffusion coefficient. This breakdown in the Stokes-Einstein relation for diffusion and viscosity was observed in the hydrophobic, but not in the hydrophilic nanotubes. The mechanism underlying this behavior is explained in terms of the structure of water under confinement. This result indicates that some of the features observed for water inside hydrophobic carbon nanotubes cannot be observed in other nanopores.

We investigate the dimensional dependence of dynamical fluctuations related to dynamic heterogeneity in supercooled liquid systems using kinetically constrained models. The $d$-dimensional spin-facilitated East model with embedded probe particles is used as a representative super-Arrhenius glass forming system. We investigate the existence of an upper critical dimension in this model by considering decoupling of transport rates through an effective fractional Stokes-Einstein relation, $D\sim{\tau}^{-1+\omega}$, with $D$ and $\tau$ the diffusion constant of the probe particle and the relaxation time of the model liquid, respectively, and where $\omega > 0$ encodes the breakdown of the standard Stokes-Einstein relation. To the extent that decoupling indicates non mean-field behavior, our simulations suggest that the East model has an upper critical dimension which is at least above $d=10$, and argue that it may be actually be infinite. This result is due to the existence of hierarchical dynamics in the East model in any finite dimension. We discuss the relevance of these results for studies of decoupling in high dimensional atomistic models., Comment: 7 pages, 7 figures

The translational self-diffusion coefficient and the shear viscosity of water are related by the fractional Stokes–Einstein relation. We report extensive novel molecular dynamics simulations for the self-diffusion coefficient and the shear viscosity of water. The SPC/E and TIP4P/2005 water models are used in the temperature range 220–560 K and at 1 or 1,000 bar. We compute the fractional exponents t, and s that correspond to the two forms of the fractional Stokes–Einstein relation (Formula presented.) and (Formula presented.) respectively. We analyse other available experimental and numerical simulation data. In the current analysis two temperature ranges are considered (above or below 274 K) and in both cases deviations from the Stokes–Einstein relation are observed with different values for the fractional exponents obtained for each temperature range. For temperatures above 274 K, both water models perform comparably, while for temperatures below 274 K TIP4P/2005 outperforms SPC/E. This is a direct result of the ability of TIP4P/2005 to predict water densities more accurately and thus predict more accurately the water self-diffusion coefficient and the shear viscosity.

In many glass-forming liquids, fractional Stokes-Einstein relation (SER) is observed above the glass transition temperature. However, the origin of such phenomenon remains elusive. Using molecular dynamics simulations, we investigate the break- down of SER and the onset of fractional SER in a model of metallic glass-forming liquid. We find that SER breaks down when the size of the largest cluster consisting of trapped atoms starts to increase sharply at which the largest cluster spans half of the simulations box along one direction, and the fractional SER starts to follows when the largest cluster percolates the entire system and forms 3-dimentional network structures. Further analysis based on the percolation theory also confirms that percolation occurs at the onset of the fractional SER. Our results directly link the breakdown of the SER with structure inhomogeneity and onset of the fraction SER with percolation of largest clusters, thus provide a possible picture for the break- down of SER and onset of fractional SER in glass-forming liquids, which is is important for the understanding of the dynamic properties in glass-forming liquids.

International audience; It is becoming common practice to consider that the Stokes-Einstein relation D/T similar to eta(-1) usually works for liquids above their melting temperatures although there is also experimental evidence for its failure. Here we investigate numerically this commonly-invoked assumption for simple liquid metals as well as for their liquid alloys. Using ab initio molecular dynamics simulations we show how entropy scaling relationships developed by Rosenfeld can be used to predict the conditions for the validity of the Stokes-Einstein relation in the liquid phase. Specifically, we demonstrate the Stokes-Einstein relation may break down in the liquid phase of some liquid alloys mainly due to the presence of local structural ordering as evidenced in their partial two-body excess entropies. Our findings shed new light on the understanding of transport properties of liquid materials and will trigger more experimental and theoretical studies since excess entropy and its two-body approximation are readily obtainable from standard experiments and simulations.

We perform ab initio molecular dynamics simulations to study structural and transport properties in liquid $\mathrm{A}{\mathrm{l}}_{1\ensuremath{-}x}\mathrm{C}{\mathrm{u}}_{x}$ alloys, with copper composition $x\ensuremath{\le}0.4$, in relation to the applicability of the Stokes-Einstein (SE) equation in these melts. To begin, we find that self-diffusion coefficients and viscosity are composition dependent, while their temperature dependence follows an Arrhenius-type behavior, except for $x=0.4$ at low temperature. Then, we find that the applicability of the SE equation is also composition dependent, and its breakdown in the liquid regime above the liquidus temperature can be related to different local ordering around each species. In this case, we emphasize the difficulty of extracting effective atomic radii from interatomic distances found in liquid phases, but we see a clear correlation between transport properties and local ordering described through the structural entropy approximated by the two-body contribution. We use these findings to reformulate the SE equation within the framework of Rosenfeld's scaling law in terms of partial structural entropies, and we demonstrate that the breakdown of the SE relation can be related to their temperature dependence. Finally, we also use this framework to derive a simple relation between the ratio of the self-diffusivities of the components and the ratio of their partial structural entropies.

International audience; We investigate the conditions for the validity of the Stokes-Einstein relation that connects diffusivity to viscosity in melts using entropy-scaling relationships developed by Rosenfeld. Employing ab initio molecular dynamics simulations to determine transport and structural properties of liquid Al-1 Cu--x(x) alloys (with composition x

International audience; We use ab initio molecular dynamics simulations to study the transport properties and the validity of the Stokes-Einstein relation in Al-rich liquid alloys with Ni, Cu, and Zn as alloying elements. First, we show that the composition and temperature dependence of their transport properties present different behaviors, which can be related to their local structural ordering. Then, we evidence that the competition between the local icosahedral ordering and the local chemical ordering may cause the breakdown of the Stokes-Einstein relation even in the liquid phase. We demonstrate that this breakdown can be captured by entropy-scaling relationships developed by Rosenfeld and using the two-body excess entropy. Our findings provide a unique framework to study the relation between structure, thermodynamics, and dynamics in metallic melts and pave the way towards the explanation of various complex transport properties in metallic melts. Published by AIP Publishing.

International audience; Using reverse non-equilibrium molecular dynamics simulations, we report the calculation of the shear viscosity and the tracer diffusion coefficient of a binary Lennard-Jones mixture that is known as a model glass-former. Several remarkable temperatures are well reproduced in our calculations, i.e. TS (the onset of slow dynamics), Tc (the critical temperature predicted by the mode-coupling theory) and TK (the Kauzmann temperature). A breakdown of the Stokes-Einstein relation is found at temperature TS. We propose that, at low temperatures below TS, the size of single-particle positional fluctuations between particle-hopping events corresponds to the length measured by the Stokes-Einstein relation, which is equated to the hydrodynamic radius of particles at high temperatures.

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition -- like that of other statistical systems -- is exact when the spatial dimension $d\rightarrow\infty$, the evolution of systems properties with $d$ may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions, $d=2,3$. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes--Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step towards describing dynamic facilitation in the framework of the mean-field theory of glasses., 27 pages, 13 figures (including supplementary information) - final version accepted for publication on PNAS

We study the motion of a tracer particle injected in facilitated models which are used to model supercooled liquids in the vicinity of the glass transition. We consider the East model, FA1f model and a more general class of non-cooperative models. For East previous works had identified a fractional violation of the Stokes-Einstein relation with a decoupling between diffusion and viscosity of the form $D\sim\tau^{-\xi}$ with $\xi\sim 0.73$. We present rigorous results proving that instead $\log(D)=-\log(\tau)+O(\log(1/q))$, which implies at leading order $\log(D)/\log(\tau)\sim -1$ for very large time-scales. Our results do not exclude the possibility of SE breakdown, albeit non fractional. Indeed extended numerical simulations by other authors show the occurrence of this violation and our result suggests $D\tau\sim 1/q^\alpha$, where $q$ is the density of excitations. For FA1f we prove fractional Stokes Einstein in dimension $1$, and $D\sim\tau^{-1}$ in dimension $2$ and higher, confirming previous works. Our results extend to a larger class of non-cooperative models., Comment: 6 pages, 2 figures; v2: revised version, to appear in EPL

We generalize to higher spatial dimensions the Stokes--Einstein relation (SER) and the leading correction to diffusivity in periodic systems, and validate them using numerical simulations. Using these results, we investigate the evolution of the SER violation with dimension in simple hard sphere glass formers. The analysis suggests that the SER violation disappears around dimension d=8, above which SER is not violated. The critical exponent associated to the violation appears to evolve linearly in 8-d below d=8, as predicted by Biroli and Bouchaud [J. Phys.: Cond. Mat. 19, 205101 (2007)], but the linear coefficient is not consistent with their prediction. The SER violation evolution with d establishes a new benchmark for theory, and a complete description remains an open problem., 20 pages, 10 figures

Breakdown of Stokes-Einstein relation in supercooled liquids is believed to be one of the hallmarks of glass transition. The phenomena is studied in depth over many years to understand the microscopic mechanism without much success. Recently it was found that violation of Stokes-Einstein relation in supercooled liquids can be tuned very systematically by pinning randomly a set of particles in their equilibrium positions. This observation suggested a possible framework where breakdown of Stokes-Einstein relation in the dynamics of supercooled liquids can be studied with precise control. We have done extensive molecular dynamics simulations to understand this phenomena by analyzing the structure of appropriately defined set of dynamically slow and fast particles clusters. We have shown that the Stokes-Einstein breakdown actually become predominant once the cluster formed by the slow particles percolate the entire system size. Finally we proposed a possible close connection between fractal dimensions of these clusters and the exponents associated with the fractional Stokes-Einstein relation., submitted to JStat ( special issue on The role of structure in glassy and jammed systems )

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.

Molecular Dynamics simulations of high density hard sphere fluids clearly show a breakdown of the Stokes-Einstein equation (SE). This result has been conjectured to be due to the presence of mobile particles, i.e., ones which have the propensity to "hop" distances which are integer multiples of the interparticle distance. We conclusively show that, even though the whole liquid violates the SE equation at high densities, the sedentary particles, i.e., ones complementary to the "hoppers", obey the SE relationship. These results strongly support the notion that the unusual dynamics of fluids near vitrification are caused exclusively by the presence of hopping particles.

Background In all amyloid diseases, protein aggregates have been implicated fully or partly, in the etiology of the disease. Due to their significance in human pathologies, there have been unprecedented efforts towards physiochemical understanding of aggregation and amyloid formation over the last two decades. An important relation from which hydrodynamic radii of the aggregate is routinely measured is the classic Stokes-Einstein equation. Here, we report a modification in the classical Stokes-Einstein equation using a mixture theory approach, in order to accommodate the changes in viscosity of the solvent due to the changes in solute size and shape, to implement a more realistic model for Aβ aggregation involved in Alzheimer’s disease. Specifically, we have focused on validating this model in protofibrill lateral association reactions along the aggregation pathway, which has been experimentally well characterized. Results The modified Stokes-Einstein equation incorporates an effective viscosity for the mixture consisting of the macromolecules and solvent where the lateral association reaction occurs. This effective viscosity is modeled as a function of the volume fractions of the different species of molecules. The novelty of our model is that in addition to the volume fractions, it incorporates previously published reports on the dimensions of the protofibrils and their aggregates to formulate a more appropriate shape rather than mere spheres. The net result is that the diffusion coefficient which is inversely proportional to the viscosity of the system is now dependent on the concentration of the different molecules as well as their proper shapes. Comparison with experiments for variations in diffusion coefficients over time reveals very similar trends. Conclusions We argue that the standard Stokes-Einstein’s equation is insufficient to understand the temporal variations in diffusion when trying to understand the aggregation behavior of Aβ 42 proteins. Our modifications also involve inclusion of improved shape factors of molecules and more appropriate viscosities. The modification we are reporting is not only useful in Aβ aggregation but also will be important for accurate measurements in all protein aggregation systems.

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.

An empirical relation between diffusion coefficients and viscosities is proposed which interpolates between the kinetic theory of dilute gases and the Stokes-Einstein equation of liquids. This extended Stokes-Einstein-relationship is tested with experimental examples. It is useful for studies of reaction processes over large density ranges.

Environmental concern has been recently more and more directed towards the emission of soot particles from engines and flames, because of the carcinogenic properties of such particulates which are carried deeply inside the lungs. New methods of in situ measurements of soot diameters are thus desired in order to study the phenomenon of soot growing or to continuously control emission from various devices. Such measurements carried out by means of Diffusion Broadening Spectroscopy (DBS) are here reported.