Breakdown Of Stokes-Einstein Relation Research Articles

A molecular simulation study on transport properties of FAMEs in high-pressure conditions

Transport property prediction of fatty acid methyl esters (FAMEs) is essential to its utilisation as biodiesel and biolubricant which can work under high-pressure conditions. Equilibrium molecular simulation is performed to study the viscosity, diffusivity, density and molecular structure dynamics at conditions up to 300 MPa. Among the transport properties, convergence of the viscosity needs a sufficiently large number of independent replications of the simulation. The system size effect on diffusion coefficient should be taken into consideration in fitting the Stokes-Einstein relation. The capability of three different force fields on predicting transport properties is evaluated in terms of the united-atom molecular model and all-atom molecular model. The solidification of FAMEs under high pressure occurs with parallel molecular alignment. The spatial inhomogeneity results in the breakdown of Stokes-Einstein relation. A hybrid effective hydrodynamic radius is established on the linear relation between experimental viscosity and diffusion coefficient in molecular simulation. This provides a predictive method to estimate viscosity from molecular diffusion coefficient over a broad range of conditions provided that Stokes-Einstein relation applies.

Revisiting the breakdown of Stokes-Einstein relation in glass-forming liquids with machine learning

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.

Assessing relationships between self-diffusion coefficient and viscosity in Ni-Al alloys based on the pair distribution function

Based on the pair distribution function g(r), molecular dynamics simulations on NiAl and Ni3Al melts were carried out to investigate the relationships between self-diffusion coefficient and viscosity. The self-diffusion coefficients of Ni in melts and the viscosity of melts were calculated using the Einstein relation and Green-Kubo equation, respectively. Our result shows that there is a crossover in the self-diffusion coefficient and viscosity from high-temperature Arrhenius behavior to low-temperature non-Arrhenius behavior, and the crossover is accompanied by the breakdown of Stokes-Einstein relation (SER) and the onset of fractional Stokes-Einstein relation. The breakdown temperature of SER is nearly twice the glass-transition temperature and much higher than the mode-coupling critical temperature for both NiAl and Ni3Al melts. Further analyses based on g(r) suggest that temperature dependences of the pair correlation entropy and the partial pair correlation entropy of components may be used as probes for testing the validity of Stokes-Einstein relation and predicting its breakdown temperature.

Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation.

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 examine the existence of an upper critical dimension in this model by considering decoupling of transport rates through an effective fractional Stokes-Einstein relation, D∼τ-1+ω, with D and τ the diffusion constant of the probe particle and the relaxation time of the model liquid, respectively, and where ω>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 at least above d = 10 and argue that it may 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.

High temperature breakdown of the Stokes-Einstein relation in a computer simulated Cu-Zr melt.

Transport properties and the Stokes-Einstein (SE) relation in liquid Cu8Zr3 are studied by molecular dynamics simulation with a modified embedded atom potential. The critical temperature Tc of mode coupling theory (MCT) is derived as 930 K from the self-diffusion coefficient D and viscosity η. The SE relation breaks down around TSE = 1900 K, which is far above Tc. At temperatures below TSE, the product of D and η fluctuates around a constant value, similar to the prediction of MCT near Tc. The influence of the microscopic atomic motion on macroscopic properties is investigated by analyzing the time dependent liquid structure and the self-hole filling process. The self-holes for the two components are preferentially filled by atoms of the same component. The self-hole filling dynamics explains the different breakdown behaviors of the SE relation in Zr-rich liquid CuZr2 compared to Cu-rich Cu8Zr3. At TSE, a kink is found in the temperature dependence of both partial and total coordination numbers for the three atomic pair combinations and of the typical time of self-hole filling. This indicates a strong correlation between liquid structure, atomic dynamics, and the breakdown of SE relation. The previously suggested usefulness of the parameter d(D1/D2)/dT to predict TSE is confirmed. Additionally we propose a viscosity criterion to predict TSE in the absence of diffusion data.

Hopping and the Stokes-Einstein relation breakdown in simple glass formers.

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

Thermodynamic scaling of α-relaxation time and viscosity stems from the Johari-Goldstein β-relaxation or the primitive relaxation of the coupling model

By now it is well established that the structural α-relaxation time, τ(α), of non-associated small molecular and polymeric glass-formers obey thermodynamic scaling. In other words, τ(α) is a function Φ of the product variable, ρ(γ)/T, where ρ is the density and T the temperature. The constant γ as well as the function, τ(α) = Φ(ρ(γ)/T), is material dependent. Actually this dependence of τ(α) on ρ(γ)/T originates from the dependence on the same product variable of the Johari-Goldstein β-relaxation time, τ(β), or the primitive relaxation time, τ(0), of the coupling model. To support this assertion, we give evidences from various sources itemized as follows. (1) The invariance of the relation between τ(α) and τ(β) or τ(0) to widely different combinations of pressure and temperature. (2) Experimental dielectric and viscosity data of glass-forming van der Waals liquids and polymer. (3) Molecular dynamics simulations of binary Lennard-Jones (LJ) models, the Lewis-Wahnström model of ortho-terphenyl, 1,4 polybutadiene, a room temperature ionic liquid, 1-ethyl-3-methylimidazolium nitrate, and a molten salt 2Ca(NO(3))(2)·3KNO(3) (CKN). (4) Both diffusivity and structural relaxation time, as well as the breakdown of Stokes-Einstein relation in CKN obey thermodynamic scaling by ρ(γ)/T with the same γ. (5) In polymers, the chain normal mode relaxation time, τ(N), is another function of ρ(γ)/T with the same γ as segmental relaxation time τ(α). (6) While the data of τ(α) from simulations for the full LJ binary mixture obey very well the thermodynamic scaling, it is strongly violated when the LJ interaction potential is truncated beyond typical inter-particle distance, although in both cases the repulsive pair potentials coincide for some distances.

Transport properties and Stokes-Einstein relation in a computer-simulated glass-forming Cu33.3Zr66.7melt

Molecular dynamics simulation with a modified embedded atom potential was used to study transport properties and the Stokes-Einstein relation of a glass-forming Cu${}_{33.3}$Zr${}_{66.7}$ metallic melt. Upon cooling, at high temperatures, the self-diffusion coefficients of the two species evolve nearly parallel, whereas they diverge below 1600 K. The viscosity as function of temperature is calculated from the Green-Kubo equation. The critical temperature of mode coupling theory ${T}_{\mathrm{c}}$ is found as 1030 K, from both the transport properties and the \ensuremath{\alpha}-relaxation time. It is found that the Stokes-Einstein relation between viscosity and diffusivity breaks down at around 1600 K, far above ${T}_{\mathrm{c}}$ and even above the melting temperature. The temperature dependence of the effective diameter in the Stokes-Einstein relation correlates closely with the first derivative of the ratio of the self-diffusion coefficients of the two components. We propose that the onset of Stokes-Einstein relation breakdown could be predicted quantitatively by the divergence behavior of diffusion coefficients, and the breakdown of Stokes-Einstein relation is ascribed to the sudden increase of the dynamic heterogeneity.

MOLECULAR-DYNAMICS STUDIES OF BIATOMIC SUPERCOOLED LIQUIDS: INTERMITTENCY, STICK-SLIP TRANSITION AND THE BREAKDOWN OF THE STOKES-EINSTEIN LAWS

The transport and the relaxation properties of a biatomic supercooled liquid are studied by molecular-dynamics methods. Both translational and rotational jumps are evidenced. At lower temperatures their waiting-time distributions decay as a power law at short times. The Stokes-Einstein relation (SE) breaks down at a temperature which is close to the onset of the intermittency. A precursor effect of the SE breakdown is observed as an apparent stick-slip transition. The breakdown of Debye-Stokes-Einstein law for rotational motion is also observed. On cooling, the changes of the rotational correlation time τ1 and the translational diffusion coefficient at low temperatures are fitted by power laws over more than three and four orders of magnitude, respectively. A less impressive agreement is found for τl with l = 2 - 4 and the rotational diffusion coefficient.