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The purpose of this paper is to discuss to which extent a microscopic version of the Stokes–Einstein (SE) relation without the hydrodynamic radius applies to liquid water. We demonstrate that the self-diffusion and shear viscosity data for five popular water models, recently reported by Ando [J. Chem. Phys. 159, 101102 (2023)], are in excellent agreement with the SE relation. The agreement with experimental results is also quite impressive. The limitations on the applicability of the SE relation are briefly discussed. [ABSTRACT FROM AUTHOR]

A vibrational model of transport properties of dense fluids assumes that solid-like oscillations of atoms around their temporary equilibrium positions dominate the dynamical picture. The temporary equilibrium positions of atoms do not form any regular structure and are not fixed, unlike in solids. Instead, they are allowed to diffuse and this is why liquids can flow. However, this diffusive motion is characterized by much longer time scales compared to those of solid-like oscillations. Although this general picture is not particularly new, only in a recent series of works it has been possible to construct a coherent and internally consistent quantitative description of transport properties such as self-diffusion, shear viscosity, and thermal conductivity. Moreover, the magnitudes of these transport coefficients have been related to the properties of collective excitations in dense fluids. Importantly, the model is simple and no free parameters are involved. Recent achievements are summarized in this overview. Application of the vibrational model to various single-component model systems such as plasma-related Coulomb and screened Coulomb (Yukawa) fluids, the Lennard-Jones fluid, and the hard-sphere fluid is considered in detail. Applications to real liquids are also briefly discussed. Overall, good to excellent agreement with available numerical and experimental data is demonstrated. Conditions of applicability of the vibrational model and a related question concerning the location of the gas–liquid dynamical crossover are discussed. [ABSTRACT FROM AUTHOR]

Relaxation processes over the static permittivity frequency region present in poly(propylene glycol) [PPG] of average molecular weights Mn = 425 and 725 have been investigated in the temperature range (285–320 K) and frequency range (1 Hz–1 MHz) using broadband dielectric spectroscopy. The data have been compared in the form of complex dielectric permittivity (ε*), electric modulus (M*), conductance (σ*), and impedance (Z*) spectra of PPG. From the comparative analysis of the spectra of all the complex quantities, the temperature-dependent relaxation processes caused by the presence of electrode polarization and ionic conduction effects were explored. The temperature dependence of various dielectric parameters such as dc conductivity (σdc), relaxation time due to electrode polarization (τEP), conductivity relaxation time (τσ), and their activation energies have been critically examined. It was observed that the dependence of dc conductivity (σdc) on the viscosity (η) or structural relaxation time (τα) of both PPGs satisfies the Stokes–Einstein–Nernst/Stokes–Einstein–Debye quite well. This behavior is similar to those reported in lithium percolate (LiClO4) electrolyte solutions in PPG solvents. This demonstrates that the electrical conduction behavior of unknown ions impurities existing in pure PPG and extremely low known concentration added ions in pure PPG is the same. [ABSTRACT FROM AUTHOR]

[Display omitted] Two-point microrheology (TPM) is used to infer material properties of complex fluids from the correlated motion of hydrodynamically interacting probes embedded in the medium. The mechanistic connection between probe motion and material properties is propagation of disturbance flows, encoded in current TPM theory for unconfined materials. However, confined media e.g. biological cells and particle-laden droplets, require theory that encodes confinement into the flow propagator (Green's function). To test this idea, we use Confined Stokesian Dynamics simulations to explicitly represent many-body hydrodynamic couplings between colloids and with the enclosing cavity at arbitrary concentration and cavity size. We find that previous TPM theory breaks down in confinement, and we identify and replace the underlying key elements. We put forth a Confined Generalized Stokes-Einstein Relation and report the viscoelastic spectrum. We find that confinement alters particle dynamics and increases viscosity, owing to hydrodynamic and entropic coupling with the cavity. The new theory produces a master curve for all cavity sizes and concentrations and reveals that for colloids larger than 0.005 times the enclosure size, the new model is required. [ABSTRACT FROM AUTHOR]

In thermal “passive” microrheology, the random Brownian motion of anisotropically shaped probe particles embedded within an isotropic viscoelastic material can be used to extract the material’s frequency-dependent linear viscoelastic modulus. We unite the existing theoretical frameworks for separately treating translational and rotational probe motion in a viscoelastic material by extending the generalized Stokes–Einstein relation (GSER) into a tensorial form that reflects simultaneous equilibrium translational and rotational fluctuations of one or more anisotropic probe particles experiencing viscoelastic drag. The tensorial GSER provides a formal basis for interpreting the complex Brownian motion of anisotropic probes in a viscoelastic material. Based on known hydrodynamic calculations of the Stokes mobility of highly symmetric shapes in a simple viscous liquid, we show simple examples of the tensorial GSER for spheroids and half-stick, half-slip Janus spheres.

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. [ABSTRACT FROM AUTHOR]

Dynamic light scattering (DLS) and nanoparticle tracking analysis (NTA) are widely used to determine the size of biological nanoparticles in liquid. In both cases, one first measures the nanoparticle diffusion coefficient and then converts it to the nanoparticle radius via the Stokes-Einstein relation. This relation is based on the no-slip boundary condition. Now, there is evidence that this condition can be violated in biologically relevant cases (e.g., for vesicles) and that in such situations the partial-slip boundary condition is more suitable. I show (i) how the latter condition can be employed in the context of DLS and NTA and (ii) that the use of the former condition may result in underestimation of the nanoparticle radius by about 10 nm compared with the nominal one. [ABSTRACT FROM AUTHOR]

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 (D / T) ∼ η t and D ∼ (T / η ) s 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. [ABSTRACT FROM AUTHOR]

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 on the ratio of the transverse and longitudinal sound velocities. In some cases, this ratio can be directly related to the pair interaction potential operating in fluids and thus there can be a certain level of predictivity regarding the value of this coefficient. This Research Note provides some evidence in favour of this observation. In particular, analysing the situation in several model systems such as one-component plasma, Yukawa, inverse-power-law, Lennard-Jones, and hard-sphere fluids, it is demonstrated that there are certain correlations between the interaction softness and the coefficient in SE relation. The SE coefficient is also re-evaluated for various liquid metals at the melting temperature, for which necessary data are available. [ABSTRACT FROM AUTHOR]

Molecular dynamic simulations were performed for liquid Al 72 Ni 16 Co 12 to study the transport properties and the Stokes-Einstein relation (SER). It was observed that the self-diffusion coefficient for Co is much lower and α -relaxation time is much longer than the other two elements. The viscosity as a function of temperature was obtained with a method of reversed non-equilibrium molecular dynamics simulation. The SER in terms of viscosity and α -relaxation time for all elements was evaluated. It is found that the effective diameter for Co increases abnormally with the decrease of the temperature. The breakdown of SER for Co between self-diffusion coefficient and viscosity or α -relaxation time happens in the whole temperature range covered in this work, whereas the breakdowns of SER for both Al and Ni occur respectively at 1500 K and 1200 K in term of viscosity and α -relaxation time, which are far above the critical temperature of mode coupling theory, T c , around 814 K according to transport properties, and 797 K based on the α -relaxation time. The decoupling of element dynamics and the dynamic heterogeneity are studied by calculating the ratio of the two diffusivities for different elements, D 1 / D 2 , and the non-Gaussian parameter. To check the structural-dynamics correlation, the total and partial pair correlation functions are calculated. It is proposed that for Co the decoupling of self-diffusion coefficient and viscosity or α -relaxation time persists at all temperatures due to the strong interactions between Co atoms. And the sudden increase of the dynamic heterogeneity, accompanied by a subtle change of liquid structure, is supposed to be the reason for the abnormal breakdown of SER for Al and Ni at a temperature far above T c. • Transport properties are computed and the abnormal breakdown of Stokes-Einstein relation for liquid Al-Ni-Co are evaluated. • The breakdown temperature is much higher than the critical temperature of mode coupling theory and the liquidus temperature. • The decoupling of element dynamics, the dynamic heterogeneity, and the structure-dynamics correlation are studied. [ABSTRACT FROM AUTHOR]

The Langevin equations (LE) and the Fokker−Planck (FP) equations are widely used to describe fluid behavior based on coarse-grained approximations of microstructure evolution. In this manuscript, we describe the relation between LE and FP as related to particle motion within a fluid. The manuscript introduces undergraduate students to two LEs, their corresponding FP equations, and their solutions and physical interpretation.

Abstract: The zeta potential (ζ) is the effective charge energy of a solvated protein, describing the magnitude of electrostatic interactions in solution. It is commonly used in the assessment of adsorption processes and dispersion stability. Predicting ζ from molecular structure would be useful to the structure‐based molecular design of drugs, proteins, and other molecules that hold charge‐dependent function while remaining suspended in solution. One challenge in predicting ζ is identifying the location of the slip plane (XSP), a distance from the protein surface where ζ is theoretically defined. This study tests the hypothesis that the XSP can be estimated by the Stokes–Einstein hydrodynamic radius (Rh), using globular hen egg white lysozyme as a model system. Although the XSP and Rh differ in their theoretical definitions, with the XSP being the position of the ζ during electrokinetic phenomena (e.g., electrophoresis) and the Rh being a radius pertaining to the edge of solvation during diffusion, they both represent the point where water and ions no longer adhere to a molecule. This work identifies the limited range of ionic strengths in which the XSP can be determined using diffusivity measurements and the Stokes–Einstein equation. In addition, a computational protocol is developed for determining the ζ from a protein crystal structure. At low ionic strengths, a hyperdiffusivity regime exists, requiring direct measurement of electrophoretic mobility to determine ζ. This work, therefore, supports a basic tenant of EDL theory that the electric double layer during diffusion and electrophoresis are equivalent in the Stokes–Einstein regime. [ABSTRACT FROM AUTHOR]

Abstract: Rheological properties of soft matter like polymer solutions/gels, colloidal dispersions, and biological materials have been extensively studied by macroscopic methods. Recently, a set of microrheometers has emerged as powerful tools to investigate the dynamics and structures of homogeneous or heterogeneous soft matter at the micro‐ or nanoscale. In this review, these microrheometers, including some novel hybrid microrheometers are summarized and compared. [ABSTRACT FROM AUTHOR]

The rotational diffusion of polyethylene glycol coated magnetic nanoparticles in serum albumin solutions was investigated in a range spanning 0 mg mL −1 to 200 mg mL −1 . Rotational diffusivities were determined from dynamic magnetic susceptibility measurements, which provide a non-optical means to probe rotation of nanoparticles in small volume samples. Experimental rotational diffusivities were compared to those estimated using the Stokes-Einstein relation and macroscopic measurements of the viscosity of the protein solutions. Excellent agreement was found between experimental measurements and theoretical predictions for serum albumin solutions buffered at physiological pH and for serum albumin solutions at acidic pH prepared using simple acids at physiological ionic strengths. For serum albumin solutions prepared using citrate buffer at acidic pH, we observed a discrepancy between the experimental rotational diffusivity and that predicted from the Stokes-Einstein relation. In contrast, when the pH was adjusted with a simple acid and salt at physiological ionic strength we observed agreement between the experimental rotational diffusivity and that predicted from the Stokes-Einstein relation. Because of the role of citrate ions in causing protein aggregation, we believe these observations suggest that dynamic magnetic susceptibility measurement of the rotational diffusivity of the nanoparticles is sensitive to gelation/crosslinking of proteins. [ABSTRACT FROM AUTHOR]

ABSTRACT 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 [ABSTRACT FROM AUTHOR]

A new analysis based on selectively probing of sub-population in a heterogeneous system from a fluorescence intensity autocorrelation is proposed that determines the relation between viscosity decoupling and dynamic heterogeneity in a better way. [Display omitted] • A novel analysis is developed for identifying dynamic heterogeneity from viscosity decoupling in a better way. • The analysis enabled probing of slower, moderate, and faster moving species from the same measurement. • Four versatile solvent systems are studied as a proof of concept. • Contrary to the traditional consensus, viscosity decoupling does not ensure dynamic heterogeneity. • A difference in the extent of viscosity decoupling for different sub-populations might be a superior criterion. Generally, dynamic heterogeneity in a media is identified by recognizing the viscosity decoupling of the dynamics (i.e., p ≠ 1 in the equation log τ x = p log η T + log C). While dynamically heterogeneous media will show a breakdown from the Stokes-Einstein (SE) relationship (p ≠ 1), the vice-versa is not automatically true. One should be cautious in relating viscosity decoupling to dynamic heterogeneity. Herein, we developed a novel analysis for identifying dynamic heterogeneity in a better way. The analysis is based on selective probing of different diffussion time-regimes in a heterogeneous system from a single measurement and observing their temperature evolution. To prove our concept, we studied temperature dependent translational diffusion of a fluorophore using fluorescence correlation spectroscopy. We used two molecular liquids and two complex deep eutectic solvents in our study. All four solvents show viscosity decoupling, albeit to a different extent. Following the previous knowledge, this could be explained by dynamic heterogeneity in all these solvents. However, our analysis suggests that two molecular liquids, DMF and glycerol, are dynamically homogenous and the two DESs, acetamide/urea and lauric-acid/menthol, are dynamically heterogeneous. We conclude that difference in the extent of viscosity decoupling for different diffusion time-regimes might be a better criteria to identify dynamic heterogeneity, compared to the traditional way. We believe that the newly developed approach will be a step-forward in determining the dynamic heterogeneity from viscosity decoupling. [ABSTRACT FROM AUTHOR]

The glass transition is the most enduring grand-challenge problem in contemporary condensed matter physics. Here, we review the contribution of colloid experiments to our understanding of this problem. First, we briefly outline the success of colloidal systems in yielding microscopic insights into a wide range of condensed matter phenomena. In the context of the glass transition, we demonstrate their utility in revealing the nature of spatial and temporal dynamical heterogeneity. We then discuss the evidence from colloid experiments in favor of various theories of glass formation that has accumulated over the last two decades. In the next section, we expound on the recent paradigm shift in colloid experiments from an exploratory approach to a critical one aimed at distinguishing between predictions of competing frameworks. We demonstrate how this critical approach is aided by the discovery of novel dynamical crossovers within the range accessible to colloid experiments. We also highlight the impact of alternate routes to glass formation such as random pinning, trajectory space phase transitions and replica coupling on current and future research on the glass transition. We conclude our review by listing some key open challenges in glass physics such as the comparison of growing static length scales and the preparation of ultrastable glasses that can be addressed using colloid experiments. [ABSTRACT FROM PUBLISHER]

We report an ab initio study of structural and dynamic properties of liquid copper as a function of temperature. In particular, we have evaluated the temperature dependence of the self-diffusion coefficient from the velocity autocorrelation function as well the temperature dependence of the viscosity from the transverse current correlation function. We show that LDA based results are in close agreement with experimental data for both the self-diffusion coefficient and the viscosity over the temperature range investigated. Our 1ndings are then used to test empirical approaches like the Stokes-Einstein relation and the excess entropy scaling law widely used in the literature. We show that the Stokes-Einstein relation is valid for the liquid phase and that the excess entropy scaling law proposed by Dzugutov is legitimate only if a self-consistent method for determining the packing fraction of the hard sphere reference liquid is used within the Carnahan-Starling approach to express the excess entropy. [ABSTRACT FROM AUTHOR]

A polarisable ion model is parameterised for the whole series of molten alkali halides by using first-principles calculations based on density functional theory. Viscosity, electrical conductivity and thermal conductivity are determined using molecular dynamics simulations via the Green–Kubo formulae and confronted to experimental results. The calculated transport coefficients are generally in much better agreement than those obtained with the empirical Fumi–Tosi potentials. The inclusion of polarisation effects significantly decreases the viscosity and thermal conductivity, while it increases the electrical conductivity. The individual dynamics of the ions is analysed using the Stokes–Einstein relation. The anion behaviour is always well represented using the slip boundary condition, while for cations there is an apparent shift from slip to stick condition when the ionic radius decreases. This difference is interpreted by subtle changes in their coordinating environment, which are maximised in the case of Li+cation. [ABSTRACT FROM PUBLISHER]

The determination of particle size by dynamic light scattering uses the Stokes-Einstein relation, which can break down for nanoscale objects. Here, we employ a molecular dynamics simulation of fully solvated 1-5 nm carbon nanoparticles for the refinement of the experimental data obtained for nanodiamonds in water by using dynamic light scattering. We performed molecular dynamics simulations in differently sized boxes and calculated nanoparticles diffusion coefficients using the velocity autocorrelation function and mean-square displacement. We found that the predictions of the Stokes-Einstein relation are accurate for nanoparticles larger than 3 nm while for smaller nanoparticles the diffusion coefficient should be corrected and different boundary conditions should be taken into account. [ABSTRACT FROM AUTHOR]

An explicit analytical expression has been obtained for vertical detachment energy (VDE) that can be used to calculate the same over a wide range (both stable and unstable regions) of cluster sizes including the bulk from the knowledge of VDE for a finite number of stable clusters (n= 16–23). The calculated VDE for the bulk is found to be very good in agreement (within 1%) with the available experimental result and the domain of instability lies betweenn= 0 andn= 15 for the hydrated clusters, PO3 ?4·nH2O. The minimum number (n0) of water molecules needed to stabilise the phosphate anion is 16. We are able to explain the origin of solvent–berg model and anomalous conductivity from the knowledge of first stable cluster. We have also provided a scheme to calculate the radius of the solvent–berg for phosphate anion. The calculated conductivity using Stokes–Einstein relation and the radius of solvent–berg is found to be very good in agreement (within 4%) with the available experimental results. [ABSTRACT FROM AUTHOR]

We study the effects of the solvation structure on the diffusion of a large particle in a binary mixture. Using our recently developed perturbation theory, we calculate the diffusion coefficient of a large hard-sphere solute particle immersed in a binary solvent mixture of hard spheres with two different sizes. The calculation results show that the Stokes–Einstein (SE) relation breaks down in the hard-sphere system. When the size ratio of binary solvent spheres is three or more, the deviation from the SE relation increases with the packing fraction of larger solvent spheres. In contrast, at the size ratio of two, the diffusion coefficient approaches the value predicted by the SE relation as larger solvent spheres are added. We show that the large deviation from the SE relation is caused by the high density of larger solvent spheres around the solute sphere. [ABSTRACT FROM AUTHOR]

We present an overview on the applicability of fluorescence correlation spectroscopy (FCS) for the accurate determination of translational diffusion coefficients and thus, via the Stokes-Einstein relation, of molecular size. We consider several of the most common sources of optical aberrations and their impact on the outcome of conventional FCS measurements. We describe also a new variant of FCS, dual-focus FCS, which is robust against most of the considered aberrations, and we report reference values of diffusion coefficients for several fluorescent dyes across the visible spectrum. [ABSTRACT FROM AUTHOR]

Abstract: Our theoretical analysis of the transport of an “inert” (without specific interactions with the solvent) species inside a very viscous medium has led to the conclusion that the classical Stokes–Einstein description is not valid for these systems. Instead of it, the model of a perfectly sliding sphere was proposed for such systems, which results in the Sutherland formula for the diffusion coefficient, D = k B T/4πηa. It is assumed that “the hydrodynamic radius”, a, in this expression for very viscous ionic liquids (ILs) may be identified with the crystallographic radius of the species, as it is valid for the Stokes–Einstein relation, D = k B T/6πηa, for the ferrocene (Fc) transport in “normal” (molecular) organic solvents. For experimental verification of these predictions the procedure based on combination of electrochemical and spectral measurements proposed in our previous paper [M.A, Vorotyntsev, V.A. Zinovyeva, D.V. Konev, M. Picquet, L. Gaillon, C. Rizzi, J. Phys. Chem. B 113 (2009) 1085] has been applied to study Fc properties for a set of its solutions in another ionic liquid (IL), [BMIM][BF4]. Both the Fc oxidation current in voltammetry and the maximum absorption in the visible range (at 440nm) have found to be proportional to the concentration of the solute Fc. The extinction coefficient of the Fc+IL solution at 440nm, 88.1±3.2M−1 cm−1, is within the same narrow range of the values for Fc solutions in [BMIM][NTf2] and numerous molecular organic solvents. The value of the diffusion coefficient of Fc in [BMIM][BF4], (8.8±0.85) 10−8 cm2/s, is about two times smaller than that in [BMIM][NTf2], (1.7±0.2)×10−7 cm2/s. The values of the product of the diffusion coefficient and the dynamic viscosity of the medium are close to one another for these two ILs and to the theoretical value of the product for the perfectly sliding sphere, k B T/4πa, thus confirming this model for Fc in ILs as well as that the Stokes-Einstein formula is not applicable for these systems. It has been proposed to calculate “the Sutherland coefficient”, θ = k B T/πDηa, as the criterion of the compatibility of the experimental value of D with predictions of the general theory of “the partially sticking sphere” (including its particular cases of the sticking and sliding spheres). [Copyright &y& Elsevier]

A general model for the diffusive dynamics of rigid particles in a viscous solvent is studied. The model applies to particles of arbitrary shape and allows for arbitrary cross- and self-coupling between translational and rotational degrees of freedom. Scaling and perturbation techniques are used to characterize the dynamics at time scales relevant to different classic experimental methods. It is shown that translational and rotational motion can be treated as independent at these time scales and can be described by simplified diffusion models, provided that certain geometric and hydrodynamic parameters associated with a particle are small. These parameters are estimated for DNA molecules of different length using a sequence-dependent geometric model based on x-ray crystallography and a numerical boundary element technique. Our results suggest that, for short DNA fragments up to about a persistence length, translational data can be accurately analyzed using a simplified model characterized by a scalar, orientationally averaged diffusion coefficient, but not rotational data. Indeed, the accurate analysis of rotational data may require a model which accounts for self-coupling and other possible effects at the rotational time scale. [ABSTRACT FROM AUTHOR]

In microrheology, the local and bulk mechanical properties of a complex fluid are extracted from the motion of probe particles embedded within it. In passive microrheology, particles are forced by thermal fluctuations and probe linear viscoelasticity, whereas active microrheology involves forcing probes externally and can be extended out of equilibrium to the nonlinear regime. Here we review the development, present state, and future directions of this field. We organize our review around the generalized Stokes-Einstein relation (GSER), which plays a central role in the interpretation of microrheology. By discussing the Stokes and Einstein components of the GSER individually, we identify the key assumptions that underpin each, and the consequences that occur when they are violated. We conclude with a discussion of two techniques-multiple particle-tracking and nonlinear microrheology- that have arisen to handle systems in which the GSER breaks down. [ABSTRACT FROM AUTHOR]

Diffusion coefficient and shear viscosity are calculated for fluids containing molecules modelled as chains of tangent hard spheres. A formula for the Stokes-Einstein relation is proposed for hard chain fluids to calculate the shear viscosity from the diffusion coefficient. The numerical results show a good agreement between theoretical values and molecular dynamics results [ABSTRACT FROM AUTHOR]

• Diffusion in dense supercritical methane is examined from the freezing density scaling perspective. • High pressure behavior of the self-diffusion coefficient is consistent with the freezing density scaling. • Stokes–Einstein relation without the hydrodynamic radius holds in a wide pressure and density regime. • Unexpected violation of the Stokes–Einstein relation occurs at highest pressures and densities. • Viscosity coefficient leading to this violation exceeds the expectations based on the freezing density scaling. The new results on the diffusion in dense supercritical methane reported by Ranieri et al. [Nature Communications 12 , 1958 (2021)] are examined from the freezing density scaling perspective. It is demonstrated that the high pressure behaviour of the self-diffusion coefficient is consistent with the freezing density scaling of dense Lennard-Jones and hard sphere fluids. It is also observed that the Stokes–Einstein relation of the form D η (Δ / k B T) = α SE holds in a wide pressure and density regime, where it is expected to hold (here D and η are the diffusion and shear viscosity coefficients, Δ is the intermolecular separation and k B T is the temperature). Unexpected violation occurs at highest densities in the vicinity of the freezing point, where the coefficient α SE reaches values ≃ 10 % higher than the upper theoretically expected limit. [ABSTRACT FROM AUTHOR]

Abstract: 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 . We discuss the validity of the Vogel–Fulcher–Tammann in both regions. The breakdown of the Stokes–Einstein relation below is presented, indicating that the diffusion coefficient of a tracer becomes decoupled from the viscosity through an exponent , 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. [Copyright &y& Elsevier]

Abstract: The translational diffusion constant, D, has been measured for each of the 1-alkenes 1-C6H12, 1-C8H16, 1-C12H24, and 1-C14H28 in each of the even n-alkanes n-C6H14–n-C14H30; the D values have also been measured for 1-C10H20 in each of the even n-alkanes n-C8H18–n-C14H30. Cyclohexene has been studied in each of the even n-alkanes n-C8H18–n-C14H30 and cyclohexane. Deviations from the Stokes–Einstein (SE) relation (D = k B T/6πηr) were found. For a given solute, the hydrodynamic radius r decreased as the viscosity η increased. Analyses of literature data for n-alkane solutes in n-alkane solvents, including self-diffusion, also gave values of r that decreased as η increased. These solvent-dependent r values are discussed in terms of the relative sizes of the solutes and solvents. The data also were analyzed using D/T = A/η p (p =1 for the SE relation). The p values for the 1-alkenes and the n-alkane solutes with six or more carbon atoms were all <1 and were not a strong function of size; those for the 1-alkenes ranged from 0.637±0.027 for 1-hexene to 0.725±0.017 for 1-tetradecene. The p values for the analogous n-alkane solutes were roughly the same and indicated that the similar shapes and polarities of the two types of hydrocarbon play key roles in determining their diffusion. In the n-alkane solvents, the p value of the more globular cyclohexene is somewhat larger than those of both 1-hexene and n-hexane. [Copyright &y& Elsevier]

Abstract: Self-diffusion coefficients for a dense fluid of particles interacting with a square-well potential employing high temperature approximation have been described. Further, the dependence of the diffusion coefficient and shear viscosity on the excess entropy have been analyzed for a square-well potential. Hence, scaling laws of diffusion coefficients and shear viscosity have been described separately for square-well fluids. [Copyright &y& Elsevier]

We propose a simple hybrid model for the shear viscosity of isotopic fluid mixtures by coupling the contribution of the Stokes-Einstein relation with the existing linear model of Roults's law for the shear viscosity. The calculated values of shear viscosity using this simple hybrid model are found to be in excellent agreement with the molecular dynamics (MD) simulation results. The calculated value of the shear viscosity obtained from the theoretical model as well as the MD simulation increases with increasing mass ratio. [ABSTRACT FROM AUTHOR]

Abstract: The tracer diffusivities of 22Na and 45Ca in two high-quality silica glasses produced by the Deutsche Glastechnische Gesellschaft as standard glasses I and II have been measured in the temperature range between 473 K and 783 K. The temperature dependences of the tracer diffusion coefficients in both glasses follow Arrhenius laws. The diffusion of 22Na is more than six orders of magnitude faster than the diffusion of 45Ca. The ionic conductivity was determined by frequency-dependent impedance spectroscopy and the conductivity diffusion coefficient D σ was deduced from the dc conductivity via the Nernst–Einstein relation. The temperature dependences of D σ for both glasses follow also Arrhenius functions. The activation parameters and pre-exponential factors for tracer diffusion and for conductivity diffusion were determined. The activation enthalpy of 22Na and the activation enthalpy of the dc conductivity are equal, showing that the conductivity of standard glasses is due to the motion of Na ions. The viscosity diffusivities D η were determined from available viscosity data using the Stokes–Einstein relation. They are considerably slower than both tracer diffusivities. The Haven ratios HR are temperature independent for both glasses. The diffusivities of 22Na and 45Ca in soda-lime glasses increase with increasing Na2O content. [Copyright &y& Elsevier]

Abstract: The short-time self-diffusion of highly charged colloids is studied theoretically. Generalized Langevin equations for the momenta of colloids are derived from a statistical–mechanical point of view. The mean-square displacement of colloids is then calculated for short times. The finite size effect of small ions on short-time self-diffusion of colloids is thus investigated. The short-time self-diffusion coefficient is shown to decrease as the ratio of a single diffusion coefficient of a colloid to that of a small ion increases. The dependence of the short-time dynamics on charges and volume fractions is also discussed. The present theory is valid even for such small ions which do not satisfy the so-called Stokes–Einstein relation. For medium size of small ions which satisfy that relation, the validity of the theory is confirmed by Brownian-dynamics simulations. [Copyright &y& Elsevier]

Molecular dynamics simulations in the NVT ensemble were performed for a repulsive system of bead-spring polymer chains with angle constraints. The diffusion coefficients of spherical penetrants were measured for different size penetrants as the angle constraints were varied. The scaling of the diffusion coefficient with penetrant size varies as a function of chain stiffness from liquid-like behavior to polymeric behavior. Free volume distributions were calculated from both simulation and PRISM theory. It is found that free volume distributions and mean void size are constant with chain stiffness although the diffusion coefficient changes by a factor of two. This suggests that while free volume is necessary for diffusion to occur, binary collisions and chain relaxation also play a role in determining penetrant diffusion. The relative contributions of these factors to the diffusion coefficient may change as a function of chain stiffness. [Copyright &y& Elsevier]

In this paper we develop a random walk model on a lattice for coordinate-dependent diffusion at constant temperature. We employ here a coordinate-dependent waiting time of the random walker to get coordinate dependence of diffusion. Such a modeling of the coordinate dependence of diffusion keeps the local isotropy of the process of diffusion intact which is consistent with the nature of thermal noise. The presence of a confining conservative force is modeled by appropriately breaking the isotropy of the jumps of the random walker to its nearest lattice points. We show that the equilibrium is characterized by the position distribution which is of a modified Boltzmann form as is obtained for an Itô process. We also argue that, in such systems with coordinate-dependent diffusivity, the modified Boltzmann distribution correctly captures the transition over a potential barrier as opposed to the Boltzmann distribution. • Local Stokes–Einstein relation for coordinate dependent diffusion. • Modified Boltzmann distribution for equilibrium under coordinate dependent diffusion. • Barrier overcoming process under coordinate dependent diffusion. [ABSTRACT FROM AUTHOR]

We evaluate the microscopic correlation functions in Al 1−x Cu x melts (x= 0.10, 0.17, 0.25, 0.33 and 0.40) in the attractive and repulsive region of the square well (SW) potential under the mean spherical model (MSM) principle. We derive the temperature and concentration dependent transport coefficients through the computed structural functions and verify the Dzugutov's scaling law in Al 1−x Cu x liquid alloys. The liquid Al-Cu alloys follow the Stokes–Einstein relation especially in Al-rich melts. The concentration–concentration fluctuations in the long-wavelength limit, i.e. S C C (0) and the Warren–Cowley short-range order parameters, α 1 have been computed which explains the compound forming behavior in this melts. S C C (0) is also employed to determine the thermodynamic factor for calculating inter-diffusion coefficients from Darken's approach in liquid alloys. The temperature variation of diffusion coefficients are being applied for the computation of activation energy in liquid Al-Cu alloys by following Arrhenius equation. The theoretically evaluated activation energies of the alloys are in fair agreement with reported values. The composition dependent surface tension is determined and compared with the available experimental results which are in satisfactory agreement. Thus we establish a closer relationship between structure, transport and surface properties in Al 1−x Cu x melts without using any adjusting parameters. • Microscopic correlation functions have been derived. • Temperature dependent transport coefficients were computed using structure factors. • A universal scaling law was tested for liquid binary alloys using square well potential. • Activation energy of diffusion were derived and computed. • Shear viscosity have been computed using diffusion data. [ABSTRACT FROM AUTHOR]