Stokes-Einstein Breakdown Research Articles

Noncanonical Relationship between Heterogeneity and the Stokes-Einstein Breakdown in Deep Eutectic Solvents.

The relationship between Stokes-Einstein breakdown (SEB) and dynamical heterogeneity (DH) is of paramount importance in the physical chemistry of complex fluids. In this work, we employ neutron scattering to probe the DH and SEB in a series of deep eutectic solvents (DESs) composed of acetamide and lithium salts. Quasielastic neutron scattering experiments reveal SEB in the jump diffusion of acetamide, represented by a fractional Stokes-Einstein relationship. Among these DESs, lithium perchlorate exhibits the most pronounced SEB while lithium bromide displays the weakest. Concurrently, elastic incoherent neutron scans identify that bromide DES is the most heterogeneous and perchlorate is the least. For the first time, our study unveils a counterintuitive incommensurate relationship between DH and SEB. Further, it reveals the intricate contrasting nature of the SEB-DH relationship when investigated in proximity to the glass-transition temperature and further away from it.

Thermodynamic response functions and Stokes-Einstein breakdown in superheated water under gigapascal pressure

Thermodynamic response functions and Stokes-Einstein breakdown in superheated water under gigapascal pressure

Breakdown of the Stokes-Einstein relation in supercooled liquids: A cage-jump perspective.

The breakdown of the Stokes-Einstein relation in supercooled liquids, which is the increase in the ratio τατD between the two macroscopic times for structural relaxation and diffusion on decreasing the temperature, is commonly ascribed to dynamic heterogeneities, but a clear-cut microscopic interpretation is still lacking. Here, we tackle this issue exploiting the single-particle cage-jump framework to analyze molecular dynamics simulations of soft disk assemblies and supercooled water. We find that τατD∝⟨tp⟩⟨tc⟩, where ⟨tp⟩ and ⟨tc⟩ are the cage-jump times characterizing slow and fast particles, respectively. We further clarify that this scaling does not arise from a simple term-by-term proportionality; rather, the relations τα∝⟨tp⟩⟨ΔrJ 2⟩ and τD∝⟨tc⟩⟨ΔrJ 2⟩ effectively connect the macroscopic and microscopic timescales, with the mean square jump length ⟨ΔrJ 2⟩ shrinking on cooling. Our work provides a microscopic perspective on the Stokes-Einstein breakdown and generalizes previous results on lattice models to the case of more realistic glass-formers.

Breakdown of the Stokes-Einstein Relation in Supercooled Water/Methanol Binary Mixtures: Explanation Using the Translational Jump-Diffusion Approach.

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.

Communication: Fast dynamics perspective on the breakdown of the Stokes-Einstein law in fragile glassformers.

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 ⟨u2⟩, 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 ⟨u2⟩. Two approximated expressions of the latter, with no and one adjustable parameter, respectively, are derived.

Slow Water Dynamics near a Glass Transition or a Solid Interface: A Common Rationale.

Performing molecular dynamics simulations, we investigate the enormous slowdowns of water dynamics when approaching a glass transition or a solid interface. We show that both effects can be described on common grounds within a theoretical framework, which was recently proposed by Schweizer et al. and considers coupled local hopping and elastic distortion. For confined water, we correctly describe the variation of the α-relaxation time, τα, as a function of both temperature and position with respect to the interface. Exploiting our knowledge of a cooperative length scale ξ(T) from the confinement studies, we quantitatively rationalize the glassy slowdown, τα(T), and the Stokes-Einstein breakdown of bulk water. For both confined and bulk liquid, variations of the α-relaxation time are intimately related to changes of the cage-rattling amplitude.

Diffusion-viscosity decoupling in supercooled glycerol aqueous solutions.

The diffusion of ferrocene methanol in supercooled glycerol-water mixtures has been measured over a wide viscosity range, which allowed analyzing the composition dependence of the Stokes-Einstein breakdown (diffusion-viscosity decoupling). The observed decoupling exhibits a common behavior for all studied compositions (glycerol mass fractions between 0.7 and 0.9), determined by the reduced temperature (T/Tg) of the mixtures. This result differs from that reported previously for the diffusion of glycerol in its aqueous solutions, where the reduced temperature for the decoupling decreases with increasing water content. We conclude that the contradictory results are only apparent, and they can be explained by the use of inconsistent extrapolated values of the viscosity of the glycerol-water mixtures in the supercooled region.

Distribution of diffusion constants and Stokes-Einstein violation in supercooled liquids.

It is widely believed that the breakdown of the Stokes-Einstein (SE) relation between the translational diffusivity and the shear viscosity in supercooled liquids is due to the development of dynamic heterogeneity, i.e., the presence of both slow and fast moving particles in the system. In this study we directly calculate the distribution of the diffusivity for a model system for different temperatures in the supercooled regime. We find that with decreasing temperature, the distribution evolves from Gaussian to bimodal indicating that on the time scale of the typical relaxation time, mobile (fluid like) and less mobile (solid like) particles in the system can be unambiguously identified. We also show that less mobile particles obey the Stokes-Einstein relation even in the supercooled regime and it is the mobile particles which show strong violation of the Stokes-Einstein relation in agreement with the previous studies on different model glass forming systems. Motivated by some of the recent studies where an ideal glass transition is proposed by randomly pinning some fraction of particles, we then studied the SE breakdown as a function of random pinning concentration in our model system. We showed that degree of SE breakdown increases quite dramatically with increasing pinning concentration, thereby providing a new way to unravel the puzzles of SE violation in supercooled liquids in greater details.

Breakdown of the Stokes-Einstein relation in two, three, and four dimensions

The breakdown of the Stokes-Einstein (SE) relation between diffusivity and viscosity at low temperatures is considered to be one of the hallmarks of glassy dynamics in liquids. Theoretical analyses relate this breakdown with the presence of heterogeneous dynamics, and by extension, with the fragility of glass formers. We perform an investigation of the breakdown of the SE relation in 2, 3, and 4 dimensions in order to understand these interrelations. Results from simulations of model glass formers show that the degree of the breakdown of the SE relation decreases with increasing spatial dimensionality. The breakdown itself can be rationalized via the difference between the activation free energies for diffusivity and viscosity (or relaxation times) in the Adam-Gibbs relation in three and four dimensions. The behavior in two dimensions also can be understood in terms of a generalized Adam-Gibbs relation that is observed in previous work. We calculate various measures of heterogeneity of dynamics and find that the degree of the SE breakdown and measures of heterogeneity of dynamics are generally well correlated but with some exceptions. The two-dimensional systems we study show deviations from the pattern of behavior of the three- and four-dimensional systems both at high and low temperatures. The fragility of the studied liquids is found to increase with spatial dimensionality, contrary to the expectation based on the association of fragility with heterogeneous dynamics.

Communication: Fast and local predictors of the violation of the Stokes-Einstein law in polymers and supercooled liquids

The violation of the Stokes-Einstein (SE) law is investigated in a melt of linear chains by extensive molecular-dynamics simulations. It is found that the SE breakdown is signaled (with 5% uncertainty) by the monomer mean-square displacement <u(2)> on the picosecond time scale. On this time scale the displacements of the next-next-nearest neighbors are uncorrelated. It is shown that: (i) the SE breakdown occurs when <u(2)> is smaller than the breadth of the distribution of the square displacements to escape from the first-neighbors cage, (ii) the dynamical heterogeneity affects the form of the master curve of the universal scaling between the structural relaxation and <u(2)>.

Connection of translational and rotational dynamical heterogeneities with the breakdown of the Stokes-Einstein and Stokes-Einstein-Debye relations in water

We study the Stokes-Einstein (SE) and the Stokes-Einstein-Debye (SED) relations, Dt=kBT/6pietaR and Dr=kBT/8pietaR3, where Dt and Dr are the translational and rotational diffusivity, respectively, T is the temperature, eta the viscosity, kB the Boltzmann constant, and R the "molecular" radius. Our results are based on molecular dynamics simulations of the extended simple point charge model of water. We find that both the SE and SED relations break down at low temperature. To explore the relationship between these breakdowns and dynamical heterogeneities (DHs), we also calculate the SE and SED relations for subsets of the 7% "fastest" and 7% "slowest" molecules. We find that the SE and SED relations break down in both subsets, and that the breakdowns occur on all scales of mobility. Thus these breakdowns appear to be generalized phenomena, in contrast with a view where only the most mobile molecules are the origin of the breakdown of the SE and SED relations, embedded in an inactive background where these relations hold. At low temperature, the SE and SED relations in both subsets of molecules are replaced with "fractional" SE and SED relations, Dt approximately (tau/T)-xit and Dr approximately (tau/T)-xir, where xit approximately 0.84(<1) and xir approximately 0.75(<1). We also find that there is a decoupling between rotational and translational motion, and that this decoupling occurs in both the fastest and slowest subsets of molecules. Further, we find that, the decoupling increases upon cooling, but that the probability of a molecule being classified as both translationally and rotationally fastest also increases. To study the effect of time scale for SE and SED breakdown and decoupling, we introduce a time-dependent version of the SE and SED relations, and a time-dependent function that measures the extent of decoupling. Our results suggest that both the decoupling and SE and SED breakdowns originate at a time scale corresponding to the end of the cage regime, when diffusion starts. This is also the time scale when the DHs are more relevant. Our work also demonstrates that selecting DHs on the basis of translational or rotational motion more strongly biases the calculation of diffusion constants than other dynamical properties such as relaxation times.