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We investigate the heterogeneity of dynamics, the breakdown of the Stokes-Einstein relation and fragility in a model glass forming liquid, a binary mixture of soft spheres with a harmonic interaction potential, for spatial dimensions from 3 to 8. Dynamical heterogeneity is quantified through the dynamical susceptibility $\chi_4$, and the non-Gaussian parameter $\alpha_2$. We find that the fragility, the degree of breakdown of the Stokes-Einstein relation, as well as heterogeneity of dynamics, decrease with increasing spatial dimensionality. We briefly describe the dependence of fragility on density, and use it to resolve an apparent inconsistency with previous results.

Organic aerosol can adopt a wide range of viscosities, from liquid to glass, depending on the local humidity. In highly viscous droplets, the evaporation rates of organic components are suppressed to varying degrees, yet water evaporation remains fast. Here, we examine the coevaporation of semivolatile organic compounds (SVOCs), along with their solvating water, from aerosol particles levitated in a humidity-controlled environment. To better replicate the composition of secondary aerosol, nonvolatile organics were also present, creating a three-component diffusion problem. Kinetic modeling reproduced the evaporation accurately when the SVOCs were assumed to obey the Stokes-Einstein relation, and water was not. Crucially, our methodology uses previously collected data to constrain the time-dependent viscosity, as well as water diffusion coefficients, allowing it to be predictive rather than postdictive. Throughout the study, evaporation rates were found to decrease as SVOCs deplete from the particle, suggesting path function type behavior.

The Stokes–Einstein (SE) equation is often applied as an approximation of self-diffusion coefficients D of molecular species based on the shear viscosity of fluids. The SE relation gives rough esti...

Although water is the most ubiquitous liquid it shows many thermodynamic and dynamic anomalies. Some of the anomalies further intensify in the supercooled regime. While many experimental and theoretical studies have focused on the thermodynamic anomalies of supercooled water, fewer studies explored the dynamical anomalies very extensively. This is due to the intricacy of the experimental measurement of the dynamical properties of supercooled water. Violation of the Stokes–Einstein relation (SER), an important relation connecting the diffusion of particles with the viscosity of the medium, is one of the major dynamical anomalies. In absence of experimentally measured viscosity, researchers used to check the validity of SER indirectly using average translational relaxation time or α-relaxation time. Very recently, the viscosity of supercooled water was accurately measured at a wide range of temperatures and pressures. This allowed direct verification of the SER at different temperature-pressure thermodynamic state points. An increasing breakdown of the SER was observed with decreasing temperature. Increasing pressure reduces the extent of breakdown. Although some well-known theories explained the above breakdown, a detailed molecular mechanism was still elusive. Recently, a translational jump-diffusion (TJD) approach has been able to quantitatively explain the breakdown of the SER in pure supercooled water and an aqueous solution of methanol. The objective of this article is to present a detailed and state-of-the-art analysis of the past and present works on the breakdown of SER in supercooled water with a specific focus on the new TJD approach for explaining the breakdown of the SER.

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)...

The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-H\"uckel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy ${s}_{\mathrm{ex}}$ can be used as a suitable indicator of the validity of the SE relation. In all cases considered the onset of SE relation validity occurs at approximately ${s}_{\mathrm{ex}}\ensuremath{\lesssim}\ensuremath{-}2$. In addition, we demonstrate that the line separating gaslike and liquidlike fluid behaviours on the phase diagram is roughly characterized by ${s}_{\mathrm{ex}}\ensuremath{\simeq}\ensuremath{-}1$.

Measuring accurate translational self-diffusion coefficients (Dt ) by NMR techniques with modern spectrometers has become rather routine. In contrast, the derivation of reliable molecular information therefrom still remains a nontrivial task. In this paper, two established approaches to estimating molecular size in terms of hydrodynamic volume (VH ) or molecular weight (M) are compared. Ad hoc designed experiments allowed the critical aspects of their application to be explored by translating relatively complex theoretical principles into practical take-home messages. For instance, comparing the Dt values of three isosteric Cp2 MCl2 complexes (Cp=cyclopentadienyl, M=Ti, Zr, Hf), having significantly different molecular mass, provided an empirical demonstration that VH is the critical molecular property affecting Dt . This central concept served to clarify the assumptions behind the derivation of Dt =ƒ(M) power laws from the Stokes-Einstein equation. Some pitfalls in establishing log (Dt ) versus log (M) linear correlations for a set of species have been highlighted by further investigations of selected examples. The effectiveness of the Stokes-Einstein equation itself in describing the aggregation or polymerization of differently shaped species has been explored by comparing, for example, a ball-shaped silsesquioxane cage with its cigar-like dimeric form, or styrene with polystyrene macromolecules.

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.

The Stokes-Einstein (SE) relation is commonly regarded as being breakdown in supercooled water. However, this conclusion is drawn upon testing the validities of some variants of the SE relation rather than its original form, and it appears conflicting with the fact that supercooled water is in its local equilibrium. In this work, we show by molecular dynamics simulation that both the Einstein and Stokes relations are indeed conserved in supercooled water. The inconsistency between the original SE relation and its variants comes from two facts: (1) the substitutes of the shear viscosity in the SE variants are wavevector-dependent, so it is only a cursory approximation; (2) the effective hydrodynamic radius actually decreases with decreasing temperature, instead of being a constant as assumed in the SE variants. Besides supercooled water, this inconsistency may also exist in other supercooled liquids.

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.

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.

One of the rarely used ways of determining the overall motion correlation time of proteins is method based on the Maxwell effect. This effect consists in the appearance of a stimulated birefringence in liquids or solutions and induced by the mechanical force like shear stress in a streamline flow. To determine the overall motion correlation time for protein in dilute solution is sufficient to know the molecular mass and the ratio of the principal axes of protein, and an intrinsic viscosity. The intrinsic viscosity has been measured using an Ubbelohde-type capillary microviscometer immersed in a water-bath controlled thermostatically in the range from 5°C to 45°C for six mammalian albumins. To check the influence of solution pH on the overall motion correlation time the intrinsic viscosity value of the human serum albumin in solutions at the isoelectric point and beyond of it was measured. The thus obtained correlation times were compared with the times determined on the basis of the Debye-Stokes-Einstein equation.

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.

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

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.

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.

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.

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.

Various relaxation procedure in the supercooled state of D-xylose have been investigated using dielectric spectroscopy over a wide frequency (1 mHz – 10 MHz) and temperature range (140-350 K). The main relaxation process (α) that is accountable for the glass transition phenomena, another secondary relaxation process is also visible below glass transition temperature. The attached hydroxymethyl (-CH2OH) side group to the sugar ring might be responsible for this process. In addition, we have applied Coupling model to find the location of intermolecular relaxation below the glass transition temperature (Tg). The dependence of various dielectric parameters viz. τα, τβ, τγ and τβ cm on temperature have been critically examined. The current experimental result shows that, log10 σdc vs. log10 τα dependence is nonlinear and hence can be described with the fractional Stokes-Einstein-Debye relation.

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.

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.

One of hallmark features of glass forming ultraviscous liquids is the decoupling between translational and orientational dynamics. This report presents studies of this phenomenon in glycerol, a canonical molecular glass former, heading for the impact of two exogenic factors: high pressures up to extreme 1.5 GPa and silver (Ag) nanoparticles (NP). The analysis is focused on the fractional Debye-Stokes-Einstein (FDSE) relation $\sigma(T,P)*(\tau(T,P))^S = const$, linking DC electric conductivity $(\sigma)$ and primary $(\alpha)$ relaxation time $(\tau_\alpha)$. In glycerol and its nanocolloid (glycerol with Ag-NP) under atmospheric pressure only the negligible decoupling $(S = 1)$ was detected. However, in the compressed nanocolloid a well-defined transformation (at P = 1.2 GPa) from $S \thickapprox 1$ to the very strongly decoupled dynamics $(S \thickapprox 0.5)$ occurred. For comparison, in pressurized 'pure' glycerol the stretched shift from $S \thickapprox 1$ to $S \thickapprox 0.7$ took place. This report presents also the general discussion of FDSE behavior in ultraviscous liquids, including the new link between FDSE exponent, fragility and the apparent activation enthalpy and volume.

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

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.

The Stokes–Einstein relation D ∼ T / η and its two variants D ∼ τ − 1 and D ∼ T / τ follow a fractional form in supercooled liquids, where D is the diffusion constant, T the temperature, η the shear viscosity, and τ the structural relaxation time. The fractional Stokes–Einstein relation is proposed to result from the dynamic heterogeneity of supercooled liquids. In this work, by performing molecular dynamics simulations, we show that the analogous fractional form also exists in sodium chloride (NaCl) solutions above room temperature. D ∼ τ − 1 takes a fractional form within 300–800 K; a crossover is observed in both D ∼ T / τ and D ∼ T / η . Both D ∼ T / τ and D ∼ T / η are valid below the crossover temperature T x , but take a fractional form for T > T x . Our results indicate that the fractional Stokes–Einstein relation not only exists in supercooled liquids but also exists in NaCl solutions at high enough temperatures far away from the glass transition point. We propose that D ∼ T / η and its two variants should be critically evaluated to test the validity of the Stokes–Einstein relation.

The tracer diffusion coefficients, D-12, are fundamental properties for the design and simulation of rate-controlled processes. Nowadays, under the scope of the biorefinery concept and strict environmental legislation, the D-12 values are increasingly necessary for extractions, reactions, and chromatographic separations carried out at supercritical conditions, particularly using carbon dioxide. Hence, the main objective of this work is the development of accurate and simple models for the pure prediction of D-12 values in supercritical CO2. Two modified Stokes-Einstein equations (mSE(1) and mSE(2)) are proposed and validated using a large database comprehending extremely distinct molecules in terms of size, molecular weight, polarity and sphericity. The global deviations achieved by the mSE1 (Eqs. (2) and (13)) and mSE(2) (Eqs. (5), (13), (3), (4)) models are only 6.38% and 6.75%, respectively, in contrast to the significant errors provided by well known predictive correlations available in the literature: Wilke-Chang, 12.17%; Tyn-Calus, 17.01%; Scheibel, 19.04%; Lusis-Ratcliff, 27.32%; Reddy-Doraiswamy, 79.34%; Lai-Tan, 25.82%. Furthermore, the minimum and maximum deviations achieved by the new models are much smaller than those of the reference equations adopted for comparison. In conclusion, our mSE(1) and mSE(2) models can be recommended for the prediction of tracer diffusivities in supercritical CO2. (C) 2013 Elsevier B.V. All rights reserved.

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.

The redox properties of a rhenium-tetrazolato complex, namely fac-[Re(CO)3(phen)L] (where L is 5-(4′- cyanophenyl)tetrazolate), have been studied by cyclic voltammetry in a range of common room temperature ionic liquids (RTILs) with different anions and cations. In all eight RTILs, one reduction and two oxidation peaks are observed. It is believed that the reduction peak corresponds to ligand reduction and the two oxidation peaks are two one-electron oxidations of the metal from Re(I) to Re(II) and Re(II) to Re(III). The redox potentials of the metal oxidations appear to be unchanged with the solvent; however, the potential for the reduction peak is more negative in RTILs containing the [P14,6,6,6]+ cation, suggesting a stabilization effect of the electrogenerated intermediate with the other RTIL cations studied (imidazolium and pyrrolidinium). Potential step chronoamperometric experiments were used to calculate diffusion coefficients of the complex in RTILs, and it was found that fac-[Re(CO)3(phen)L] diffuses very slowly through the RTIL medium. A plot of diffusion coefficient against the inverse of viscosity of the RTIL solvent showed a linear trend, suggesting that the Stokes− Einstein relationship generally applies for this complex in RTILs, but the coefficient on the denominator is likely to be closer to 4 (the “slip” limit) than 6 (the “stick” limit) when taking into account the hydrodynamic radius.

The fractional Stokes–Einstein relation postulates a direct relationship between conductivity and shear flow. Like viscosity, the electrical resistivity of a glass-forming liquid exhibits a non-Arrhenius scaling with temperature. However, while both viscosity and resistivity are non-Arrhenius, here we show that these two properties follow distinct functional forms. Through analysis of 821 unique silicate liquids, we show that viscosity is best represented using the Mauro–Yue–Ellison–Gupta–Allan (MYEGA) model, whereas the resistivity of the same compositions more closely follows the Avramov–Milchev (AM) equation. Our results point to two fundamentally different mechanisms governing viscous flow and conductivity and therefore cast doubt on the general validity of the fractional Stokes–Einstein relation.

Characterized by conceptual simplicity, a semiempirical formula based on the Stokes–Einstein equation and microfriction theory was constructed for correlating tracer diffusivities and, alternativel...

The Stokes–Einstein equation relates the self-diffusion constant of a liquid with the mobility of its constituents. In water, however, the relation has to be modified for temperatures below ∼290 K. A combined experimental and numerical investigation suggests that this behaviour results from a specific change in the local water structure. The Stokes–Einstein relation has long been regarded as one of the hallmarks of transport in liquids. It predicts that the self-diffusion constant D is proportional to (τ/T)−1, where τ is the structural relaxation time and T is the temperature. Here, we present experimental data on water confirming that, below a crossover temperature T×≈ 290 K, the Stokes–Einstein relation is replaced by a ‘fractional’ Stokes–Einstein relation D∼(τ/T)−ζ with ζ≈3/5 (refs 1, 2, 3 4, 5, 6). We interpret the microscopic origin of this crossover by analysing the OH-stretch region of the Fourier transform infrared spectrum over a temperature range from 350 down to 200 K. Simultaneous with the onset of fractional Stokes–Einstein behaviour, we find that water begins to develop a local structure similar to that of low-density amorphous solid H2O. These data lead to an interpretation that the fractional Stokes–Einstein relation in water arises from a specific change in the local water structure. Computer simulations of two molecular models further support this interpretation.

The voltammetry for the reduction of oxygen at a microdisk electrode is reported in six commonly used RTILs: [C(4)mim][NTf(2)], [C(4)mpyrr][NTf(2)], [C(4)dmim][NTf(2)], [C(4)mim][BF(4)], [C(4)mim][PF(6)], and [N(6,2,2,2)][NTf(2)], where [C(4)mim](+) is 1-butyl-3-methylimidazolium, [NTf(2)](-) is bis(trifluoromethanesulfonyl)imide, [C(4)mpyrr](+) is N-butyl-N-methylpyrrolidinium, [C(4)dmim](+) is 1-butyl-2,3-methylimidazolium, [BF(4)](-) is tetrafluoroborate, [PF(6)](-) is hexafluorophosphate, and [N(6,2,2,2)](+) is n-hexyltriethylammonium at varying scan rates (50-4000 mV s(-1)) and temperatures (293-318 K). Diffusion coefficients, D, of oxygen are deduced at each temperature from potential-step chronoamperometry, and diffusional activation energies are calculated. Oxygen solubilities are also reported as a function of temperature. In the six ionic liquids, the Stokes-Einstein relationship (D proportional, variant eta(-1)) was found to apply only very approximately for oxygen. This is considered in relationship to the behavior of other diverse solutes in RTILs.

Cadmium selenide nanoparticles are found to diffuse approximately 200 times faster in a polymeric liquid than predicted by the Stokes-Einstein relation. This remarkable behavior is hypothesized to be due to the nanoparticles being smaller than the entanglement mesh to create a frictional drag that does not follow continuum expectations, in line with a theoretical calculation presented before. This is one of the first demonstrations of X-ray photo correlation spectroscopy applied to polymeric liquids, which we use to explain the simultaneous 60% viscosity reduction of the mixture through a proposed constraint release mechanism.

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.

The deviations from Stokes-Einstein hydrodynamics of small solutes are more pronounced in ionic liquids than in conventional solvents (J. Phys. Chem. B 2013 117 (39), 11697). Small neutral solutes diffuse much faster than expected, whereas small charged solutes diffuse much slower. This article attempts to establish a link between the local friction experienced by tracer solutes and the polar/apolar structure of ionic liquids. We find that small neutral solutes probe locally "stiff" (mostly charged, high electrostriction) regions and locally "soft" (mostly apolar, low electrostriction) regions. These regions of high and low friction are associated with cage and jump regimes. Enhanced neutral tracer mobility in the low friction regions associated with the cationic apolar component has an important bearing on the large positive deviations from Stokes-Einstein behavior. In contrast, diminished charged tracer mobility involves long caging dynamics separated by jump events often triggered by the loss and recovery of counterions.