Breakdown of the Stokes–Einstein relation in Lennard-Jones glassforming mixtures with different interaction potential

Conservation of the Stokes-Einstein relation in supercooled water

The Stokes-Einstein (SE) relation is commonly regarded as being breakdown in supercooled water. However, this conclusion is drawn by testing the validity 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 simulations that the Stokes-Einstein relation is 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 only approximate relations; and (2) the effective hydrodynamic radius actually decreases with decreasing temperature, instead of being a constant as assumed in the SE variants.

Decoupled length scales for diffusivity and viscosity in glass-forming liquids

The growth of the characteristic length scales both for diffusion and viscosity is investigated by molecular dynamics utilizing the finite-size effect in a binary Lennard-Jones mixture. For those quantities relevant to the diffusion process (e.g., the hydrodynamic value and the spatial correlation function), a strong system-size dependence is found. In contrast, it is weak or absent for the shear relaxation process. Correlation lengths are estimated from the decay of the spatial correlation functions. We find the length scale for viscosity decouples from the one of diffusivity, featured by a saturated length even in high supercooling. This temperature-independent behavior of the length scale is reminiscent of the unapparent structure change upon supercooling, implying the manifestation of configuration entropy. Whereas for the diffusion process, it is manifested by relaxation dynamics and dynamic heterogeneity. The Stokes-Einstein relation is found to break down at the temperature where the decoupling of these lengths happens.

Heterogeneous diffusion, viscosity, and the Stokes-Einstein relation in binary liquids

We investigate the origin of the breakdown of the Stokes-Einstein relation (SER) between diffusivity and viscosity in undercooled melts. A binary Lennard-Jones system, as a model for a metallic melt, is studied by molecular dynamics. A weak breakdown at high temperatures can be understood from the collectivization of motion, seen in the isotope effect. The strong breakdown at lower temperatures is connected to an increase in dynamic heterogeneity. On relevant time scales some particles diffuse much faster than the average or than predicted by the SER. The van Hove self-correlation function allows one to unambiguously identify slow particles. Their diffusivity is even less than predicted by the SER. The time span of these particles being slow particles, before their first conversion to be a fast one, is larger than the decay time of the stress correlation. The contribution of the slow particles to the viscosity rises rapidly upon cooling. Not only the diffusion but also the viscosity shows a dynamically heterogeneous scenario. We can define a "slow" viscosity. The SER is recovered as the relation between slow diffusivity and slow viscosity.

A molecular dynamics simulations study on the relations between dynamical heterogeneity, structural relaxation, and self-diffusion in viscous liquids

We perform molecular dynamics simulations for viscous liquids to study the relations between dynamical heterogeneity, structural (α) relaxation, and self-diffusion. For atomistic models of supercooled water, polymer melts, and an ionic liquid, we characterize the space-time characteristics of dynamical heterogeneity by the degree of deviations from Gaussian displacement statistics (α2), the size of clusters comprising highly mobile particles (S(w)), and the length of strings consisting of cooperatively moving particles (L(w)). Comparison of our findings with previous simulation results for a large variety of viscous liquids, ranging from monoatomic liquids to silica melt, reveals a nearly universal decoupling between the time scales of maximum non-Gaussian parameter (τ(α2)) and the time constant of the α relaxation (τ(α)) upon cooling, explicitly, τ(α2) ∝τ(α)(3/4). Such uniform relation was not observed between the peak times of S(w) or L(w) and τ(α). On the other hand, the temperature-dependent time scale of maximum string length (τ(L)) follows the inverse of the self-diffusion coefficient (D) for various systems at sufficiently low temperatures, i.e., τ(L) ∝ D(-1). These observations are discussed in view of a breakdown of the Stokes-Einstein relation for the studied systems. It is found that the degree of deviation from this relation is correlated with the stretching of the α relaxation.

Slow dynamics of a tagged particle in a supercooled liquid

The ergodicity-nonergodicity (ENE) transition of the self-consistent mode-coupling theory (MCT) is marked by the point at which the time correlation of collective density fluctuations is not zero in the long-time limit. The nonergodic state, reaching beyond the ENE transition of simple MCT, is characterized by a finite shear modulus. The MCT, formulated in the current set of papers, predicts that the single-particle density correlation, unlike the collective density correlation, decays to zero at long times on either side of the ENE transition. The self-diffusion coefficient remains finite. This differs from the existing MCT results in which both collective and single-particle correlations are simultaniously frozen at the ENE transition. We discuss in this paper mechanisms by which a sharp fall in self-diffusion coefficient may occur within the present model. This overdamping or the so-called adiabatic approximation for the supercooled state does not maintain microscopic momentum conservation. Within this approximation, the self-diffusion constant approaches zero at the ENE transition point. This approximate result, which is similar to the prediction of the existing MCT models, further illustrates the process of cage formation with increase of density. At a qualitative level, our analysis shows that the self-diffusion process depends on the structure as well as short-time transport properties of the supercooled liquid. We solve the integral equations for the nonergodicity parameters to analyze the full implications of the adiabatic approximation.

Communication: Non-monotonic evolution of dynamical heterogeneity in unfreezing process of metallic glasses

The relaxation dynamics in unfreezing process of metallic glasses is investigated by the activation-relaxation technique. A non-monotonic dynamical microstructural heterogeneities evolution with temperature is discovered, which confirms and supplies more features to flow units concept of glasses. A flow unit perspective is proposed to microscopically describe this non-monotonic evolution of the dynamical heterogeneities as well as its relationship with the deformation mode development of metallic glasses.

Explicit expression for the Stokes-Einstein relation for pure Lennard-Jones liquids

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

Molecular dynamics study of coagulation in silica-nanocolloid-water-NaCl systems based on the atomistic model

In the present work, large scale molecular dynamics (MD) simulations of nanocolloidal silica in aqueous NaCl solutions were performed using a fully atomistic model to study the microscopic structures and dynamics of the systems that lead to aggregation or gelation. Our attention is focused on the self-organizations that occur in the structures of the colloidal silica and water for various concentrations of NaCl. As the salt concentration increased, coagulation developed through the direct bonding of SiO4 units. The trend was explained by the systematic changes in the pair correlation functions related to the barrier height in the potential of mean force [J. G. Kirkwood, J. Chem. Phys., 1935, 3, 300]. Network structures of silica were visualised, and their fractal dimensions were examined by computing the running coordination numbers of Si-Si pairs and also by the analysis of two dimensional images. The calculated dimension by the former method was comparable to the experimental observations for the aggregation of silica colloids, and at longer length scales, super-aggregation was evident in the gelation process. The result from the 2D images is found to be insensitive to the differences in the structure. Clear changes in both the structure and mobility of the water were observed as the NaCl concentration increased, suggesting the importance of the solvent structures to these processes, although such a feature is lacking in the conventional models and most simulations of colloids.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

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

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

Several routes to the glassy states in the one component soft core system: revisited by molecular dynamics

Molecular dynamics simulations have been performed to study the glass transition for the soft core system with a pair potential φ(n)(r) = ε(σ∕r)(n) of n = 12. Using the compressibility factor, PV/Nk(B)T=P̃(ρ*), its phase diagram can be represented as a function of a reduced density, ρ∗ = ρ(ε∕k(B)T)(3∕n), where ρ = Nσ(3)∕V. In the present work, NVE relaxations to the glassy or crystalline states starting from the unstable states in the phase diagram have been revisited in details and compared with other processes. Relaxation processes can be characterized by the time dependence of the dynamical compressibility factor (PV/Nk(B)T)(t) (≡g(ρ(t)*)) on the phase diagram. In some cases, g(ρ(t)*) reached a crystal branch in the phase diagram; however, metastable states are found in many cases. With connecting points for the metastable states in the phase diagram, we can define a glass branch where the dynamics of particles are almost frozen. The structures observed there have common properties characterized as glasses. Although overlaps of glass forming process and nanocrystallization process are observed in some cases, these behaviors are distinguishable to each other by the characteristics of structures. There are several routes to the glass branch and we suggest that all of them are the glass transition.