Fractional Stokes-Einstein Relation Research Articles

Molecular simulations of transport properties of polar hydrofluoroethers: Force field development, fractional Stokes-Einstein and free volume relations

Hydrofluoroethers (HFEs) having simultaneously hydrocarbon (HC) and fluorocarbon (FC) moieties connected through ether oxygen are polar chain molecules with dielectric properties, which makes them a good heat transfer medium, e.g., for cooling of electronics or magnetic devices. In this work, we report, validate, and test high level-ab initio derived force fields and we use partial charges fitted to the electrostatic potential surface (EPS) to reproduce the dipole moments. Computer simulations were performed over a wide range of temperatures and densities to calculate the transport coefficients in the condensed-phase and comparisons were made against available experimental data for five selected molecules; namely HFE-7000, HFE-7100, HFE −7200, HFE −7300, and HFE −7500. Furthermore, structural properties and enthalpy of vaporization were obtained from molecular simulations. Cohen and Turnbull formula for the translational self-diffusion coefficient was tested in the free-volume cast, which itself was correlated against the isothermal compressibility, which can explain the phenomenon of transport properties in liquids, D∝exp-γ/Vf/V∗. The fractional Stokes-Einstein relation was also tested to scale the self-diffusion coefficient vs viscosity in the form of (DT−1) ∝ (1/η)s, with s ranging between ≈ 0.89 and 0.92 for the five molecules in the reduced density range of ρσ3 = 0.56 to 0.75. Finally, the non-equilibrium molecular dynamics (NEMD) simulations of thermal conductivity was found to outperform the equilibrium Green-Kubo approach, but both with comparable accuracy.

Molecular Dynamics and Diffusion in Amorphous Solid Dispersions Containing Imidacloprid.

The main goal of this study is to develop an experimental toolbox to estimate the self-diffusion coefficient of active ingredients (AI) in single-phase amorphous solid dispersions (ASD) close to the glass transition of the mixture using dielectric spectroscopy (DS) and oscillatory rheology. The proposed methodology is tested for a model system containing the insecticide imidacloprid (IMI) and the copolymer copovidone (PVP/VA) prepared via hot-melt extrusion. For this purpose, reorientational and the viscoelastic structural (α-)relaxation time constants of hot-melt-extruded ASDs were obtained via DS and shear rheology, respectively. These were then utilized to extract the viscosity as well as the fragility index of the dispersions as input parameters to the fractional Stokes-Einstein (F-SE) relation. Furthermore, a modified version of Almond-West (AW) formalism, originally developed to describe charge diffusion in ionic conductors, was exercised on the present model system for the estimation of the AI diffusion coefficients based on shear modulus relaxation times. Our results revealed that, at the calorimetric glass-transition temperature (Tg), the self-diffusion coefficients of the AI in the compositional range from infinite dilution up to 60 wt % IMI content lied in the narrow range of 10-18-10-20 m2 s-1, while the viscosity values of the dispersions at Tg varied between 108 Pa s and 1010 Pa s. In addition, the phase diagram of the IMI-PVP/VA system was determined using the melting point depression method via differential scanning calorimetry (DSC), while mid-infrared (IR) spectroscopy was employed to investigate the intermolecular interactions within the solid dispersions. In this respect, the findings of a modest variation in melting point at different compositions stayed in agreement with the observations of weak hydrogen bonding interactions between the AI and the polymer. Moreover, IR spectroscopy showed the intermolecular IMI-IMI hydrogen bonding to have been considerably suppressed, as a result of the spatial separation of the AI molecules within the ASDs. In summary, this study provides experimental approaches to study diffusivity in ASDs using DS and oscillatory rheology, in addition to contributing to an enhanced understanding of the interactions and phase behavior in these systems.

Effect of water nanoconfinement on the dynamic properties of paramagnetic colloidal complexes.

The anomalous behavior of confined water at the nanoscale has remarkable implications in a number of nanotechnological applications. In this work, we analyze the effect of water self-diffusion on the dynamic properties of a solvated gadolinium-based paramagnetic complex, typically used for contrast enhancement in magnetic resonance imaging. In particular, we examine the effect of silica-based nanostructures on water behavior in the proximity of the paramagnetic complex via atomistic simulations, and interpret the resulting tumbling dynamics in the light of the local solvent modification based on the Lipari-Szabo formalism and of the fractional Stokes-Einstein relation. It is found that the local water confinement induces an increased "stiffness" on the outer sphere of the paramagnetic complex, which eventually reduces its tumbling properties. These model predictions are found to explain well the relaxivity enhancement observed experimentally by confining paramagnetic complexes into porous nanoconstructs, and thus offer mechanistic guidelines to design improved contrast agents for imaging applications.

Unified Description of Diffusion Coefficients from Small to Large Molecules in Organic-Water Mixtures.

Diffusion coefficients in mixtures of organic molecules and water are needed for many applications, ranging from the environmental modeling of pollutant transport, air quality, and climate, to improving the stability of foods, biomolecules, and pharmaceutical agents for longer use and storage. The Stokes-Einstein relation has been successful for predicting diffusion coefficients of large molecules in organic-water mixtures from viscosity, yet it routinely underpredicts, by orders of magnitude, the diffusion coefficients of small molecules in organic-water mixtures. Herein, a unified description of diffusion coefficients of large and small molecules in organic-water mixtures, based on the fractional Stokes-Einstein relation, is presented. A fractional Stokes-Einstein relation is able to describe 98% of the observed diffusion coefficients from small to large molecules, roughly within the uncertainties of the measurements. The data set used in the analysis includes a wide range of radii of diffusing molecules, viscosities, and intermolecular interactions. As a case study, we show that the degradation of polycyclic aromatic hydrocarbons (PAHs) by O3 within organic-water particles in the planetary boundary layer is relatively short (≲1 day) when the viscosity of the particle is ≲102 Pa s. We also show that the degradation times predicted using the Stokes-Einstein relation and the fractional Stokes-Einstein relation can differ by up to a factor of 10 in this region of the atmosphere.

On the validity of the Stokes–Einstein relation for various water force fields

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 and 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.

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.

Predictions of diffusion rates of large organic molecules in secondary organic aerosols using the Stokes–Einstein and fractional Stokes–Einstein relations

Abstract. Information on the rate of diffusion of organic molecules within secondary organic aerosol (SOA) is needed to accurately predict the effects of SOA on climate and air quality. Diffusion can be important for predicting the growth, evaporation, and reaction rates of SOA under certain atmospheric conditions. Often, researchers have predicted diffusion rates of organic molecules within SOA using measurements of viscosity and the Stokes–Einstein relation (D∝1/η, where D is the diffusion coefficient and η is viscosity). However, the accuracy of this relation for predicting diffusion in SOA remains uncertain. Using rectangular area fluorescence recovery after photobleaching (rFRAP), we determined diffusion coefficients of fluorescent organic molecules over 8 orders in magnitude in proxies of SOA including citric acid, sorbitol, and a sucrose–citric acid mixture. These results were combined with literature data to evaluate the Stokes–Einstein relation for predicting the diffusion of organic molecules in SOA. Although almost all the data agree with the Stokes–Einstein relation within a factor of 10, a fractional Stokes–Einstein relation (D∝1/ηξ) with ξ=0.93 is a better model for predicting the diffusion of organic molecules in the SOA proxies studied. In addition, based on the output from a chemical transport model, the Stokes–Einstein relation can overpredict mixing times of organic molecules within SOA by as much as 1 order of magnitude at an altitude of ∼3 km compared to the fractional Stokes–Einstein relation with ξ=0.93. These results also have implications for other areas such as in food sciences and the preservation of biomolecules.

Supercooled liquids analogous fractional Stokes–Einstein relation in NaCl solution above room temperature**Project supported by the Foundation of Civil Aviation Flight University of China (Grant Nos. J2019-059 and JG2019-19).

The Stokes–Einstein relation and its two variants and 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. takes a fractional form within 300–800 K; a crossover is observed in both and . Both and are valid below the crossover temperature Tx, but take a fractional form for . 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 and its two variants should be critically evaluated to test the validity of the Stokes–Einstein relation.

Effects of Hydrogen Bonding on Diffusion of Aromatic Compounds in Acetone: An Experimental Investigation from 268.2 to 328.2 K.

Diffusion coefficients of pseudoplanar aromatic compounds at infinite dilution in acetone have been measured at different temperatures by the Taylor dispersion technique. The data of the polar solutes that can form hydrogen bonds with acetone are compared with those of the nonpolar ones incapable of hydrogen bonding to quantify the effects of hydrogen-bonded association on diffusion. The effects are further found to correlate strongly with the overall hydrogen-bonded acidity of the polar solutes containing proton-donating groups. For the nonpolar solutes in this study, the diffusivities at different temperatures can be expressed very well by the recently developed molecular-modified fractional Stokes-Einstein relation with only two constants. An innovative model for solute diffusion in liquid solutions, which is constructed by combining the molecular-hydrodynamic relation for nonpolar solutes with the overall hydrogen-bonded acidity scale for polar solutes, is introduced for representing the diffusivities of different types of disc-shaped molecules at various temperatures. An equation developed from this model is demonstrated to be capable of calculating a total of 191 diffusion data of both the hydrogen-bonded and the nonassociated aromatic solutes in acetone from 268.2 to 328.2 K to a standard deviation of 2.7%.

Fractional Stokes–Einstein relation in TIP5P water at high temperatures**Project supported by the National Natural Science Foundation of China (Grant No. 2153200) and the China Postdoctoral Science Foundation (Grant No. 2016M602712).

Fractional Stokes–Einstein relation described by D ∼ (τ/T)ξ is observed in supercooled water, where D is the diffusion constant, τ the structural relaxation time, T the temperature, and the exponent ξ ≠ −1. In this work, the Stokes–Einstein relation in TIP5P water is examined at high temperatures within 400 K–800 K. Our results indicate that the fractional Stokes–Einstein relation is explicitly existent in TIP5P water at high temperatures, demonstrated by the two usually adopted variants of the Stokes–Einstein relation, D ∼ τ−1 and D ∼ T/τ, as well as by D ∼ T/η, where η is the shear viscosity. Both D ∼ τ−1 and D ∼ T/τ are crossed at temperature Tx = 510 K. The D ∼ τ−1 is in a fractional form as D ∼ τξ with ξ = −2.09 for T ≤ Tx and otherwise ξ = −1.25. The D ∼ T/τ is valid with ξ = −1.01 for T ≤ Tx but in a fractional form for T > Tx. The Stokes–Einstein relation D ∼ T/η is satisfied below Tx = 620 K but in a fractional form above Tx. We propose that the breakdown of D ∼ T/η may result from the system entering into the super critical region, the fractional forms of D ∼ τ−1 and D ∼ T/τ are due to the disruption of the hydration shell and the local tetrahedral structure as well as the increase of the shear viscosity.

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.

Structural origin of fractional Stokes-Einstein relation in glass-forming liquids

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.

Concentration-dependent structure and dynamics of aqueous LiCl solutions: A molecular dynamics study

Herein we employ molecular dynamics simulation technique to appreciate the microscopic structural and dynamic changes in the aqueous solution of LiCl when the electrolyte concentration is varied from dilute to high concentration. As a function of the LiCl concentration, we connect changes in the local order, entropy and transport properties and intend to relate them with experimentally determined phase diagram and the glass forming regime of the solution. We observe that a pronounced monotonic decrease in diffusivities of water, Li+ and Cl− is accompanied by an increase in the viscosity with increasing LiCl concentration that marks out a low-mobility regime in approximate agreement with the experimental glass-forming composition region. The fractional Stokes-Einstein relation is obeyed in the temperature regime studied here. The ionic conductivity shows a non-monotonic dependence on composition and pronounced negative deviations from the Nernst-Einstein relation are notable in the glass-forming regime. The breakdown of the hydrogen-bonded network of water as a function of the LiCl concentration along various isotherms is clearly indicated by the tetrahedral order parameter distributions, ensemble-averaged tetrahedral order (⟨qtet⟩) and triplet correlation functions. Further insights into the changes in the structure of the aqueous solution with increasing LiCl concentration is provided using radial distribution functions (RDFs) and corresponding coordination numbers. A useful connection between the structure and thermodynamics is provided by the pair entropy, computed from the atomic pair RDFs. We anticipate that these structure-thermodynamic-transport relations to be qualitatively the same for other alkali halide-water systems. Similarities and differences with binary ionic melts, e.g. LiF-BeF2, MgO-SiO2, with tunable tetrahedrality are also discussed.

Understanding the Stokes–Einstein relation in supercooled liquids using random pinning

The breakdown of the Stokes–Einstein relation in supercooled liquids is believed to be one of the hallmarks of glass transition. The phenomenon has been studied in depth over many years in efforts to understand the microscopic mechanism, without much success. Recently it was found that the violation of the Stokes–Einstein relation in supercooled liquids can be tuned by randomly pinning a set of particles in their equilibrium positions. This observation suggested a possible framework where the breakdown of the Stokes–Einstein relation in the dynamics of supercooled liquids can be studied in a systematic manner. We have performed extensive molecular dynamics simulations to understand this phenomenon by analysing the structure of appropriately defined sets of dynamically slow and fast particle clusters. The breakdown of the Stokes–Einstein relation is found to become predominant once the cluster formed by the slow particles percolates the entire system size. Finally we propose a possible close connection between fractal dimensions of these clusters and the exponents associated with the fractional Stokes–Einstein relation.

Structural signatures evidenced in dynamic crossover phenomena in metallic glass-forming liquids

Molecular dynamics simulations were performed to investigate dynamic evolution in metallic glass-forming liquids during quenching from high temperature above melting point down to supercooled region. Two crossover temperatures TA and TS (TA > TS) are identified, and their physical meanings are clarified. TA and TS are found to be not only the sign of dynamic crossover phenomena but also the manifestation of two key structure correlation lengths ξs. As temperature decreases below TA, ξs goes beyond the nearest-neighbor distance, resulting in the Arrhenius-to-non-Arrhenius transition of structural relaxation time and the failure of Stokes-Einstein (SE) relation. As TS is traversed, the increase rate of ξs reaches the maximum, leading to the simultaneous appearance of dynamical heterogeneity and fractional SE relation. It is further found that structure correlation increases much faster than dynamic correlation, playing a role of structural precursor for dynamic evolution in liquids. Thus, a structural link is established for deeper understanding dynamic crossover phenomena.

Dynamic heterogeneity in crossover spin facilitated model of supercooled liquid and fractional Stokes-Einstein relation.

Kinetically constrained models have gained much interest as models that assign the origins of interesting dynamic properties of supercooled liquids to dynamical facilitation mechanisms that have been revealed in many experiments and numerical simulations. In this work, we investigate the dynamic heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the model that linearly interpolates between the strong liquid-like behavior and the fragile liquid-like behavior by an asymmetry parameter b. When the asymmetry parameter is sufficiently small, smooth fragile-to-strong transition is observed both in the relaxation time and the diffusion constant. Using these physical quantities, we investigate fractional Stokes-Einstein relations observed in this model. When b is fixed, the system shows constant power law exponent under the temperature change, and the exponent has the value between that of the Frederickson-Andersen model and the East model. Furthermore, we investigate the dynamic length scale of our systems and also find the crossover relation between the relaxation time. We ascribe the competition between energetically favored symmetric relaxation mechanism and entropically favored asymmetric relaxation mechanism to the fragile-to-strong crossover behavior.

Is there a fractional breakdown of the Stokes-Einstein relation in kinetically constrained models at low temperature?

We study the motion of a tracer particle injected in facilitated models which are used to model supercooled liquids in the vicinity of the glass transition. We consider the East model, FA1f model and a more general class of non-cooperative models. For East previous works had identified a fractional violation of the Stokes-Einstein relation with a decoupling between diffusion and viscosity of the form with . We present rigorous results proving that instead , which implies at leading order for very large time scales. Our results do not exclude the possibility of SE breakdown, albeit non-fractional. Indeed extended numerical simulations by other authors show the occurrence of this violation and our result suggests , where q is the density of excitations. For FA1f we prove a fractional Stokes-Einstein relation in dimension 1, and in dimension 2 and higher, confirming previous works. Our results extend to a larger class of non-cooperative models.

High Pressure as a Key Factor to Identify the Conductivity Mechanism in Protic Ionic Liquids

In this Letter we report the relation between ionic conductivity and structural relaxation in supercooled protic ionic liquids (PILs) under high pressure. The results of high-pressure dielectric and volumetric measurements, combined with rheological and temperature-modulated differential scanning calorimetry experiments, have revealed a fundamental difference between the conducting properties under isothermal and isobaric conditions for three PILs with different charge transport mechanisms (Grotthuss vs vehicle). Our findings indicate a breakdown of the fractional Stokes-Einstein relation and Walden rule when the ionic transport is controlled by fast proton hopping. Consequently, we demonstrate that the studied PILs exhibit significantly higher conductivity than one would expect taking into account that they are in fact a mixture of ionic and neutral species. Thus, the examined herein samples represent a new class of "superionic" materials desired for many advanced applications.

Glass Forming Ability and Alloying Effect of a Noble-Metal-Based Glass Former

This work addresses the question on how the glass-forming ability (GFA) of a binary Pd-Ni metallic glass can be enhanced by the alloying effect of Pt. The structural features and slow dynamics of liquid and glassy states on both alloys are investigated by molecular dynamics simulations. Both alloys show typical features of glassy dynamics, namely, the non-Arrhenian behavior of diffusion and relaxation and the fractional Stokes-Einstein relation validity at low temperatures. On the basis of the analysis of the dynamical susceptibilities, we demonstrate that there is a strong influence of the alloying effect on the collective motion of the species, revealing that the GFA of the binary liquid increases with Pt alloying.

The dynamic crossover in water does not require bulk water

Many of the anomalous properties of water may be explained by invoking a second critical point that terminates the coexistence line between the low- and high-density amorphous states in the liquid. Direct experimental evidence of this point, and the associated polyamorphic liquid-liquid transition, is elusive as it is necessary for liquid water to be cooled below its homogeneous-nucleation temperature. To avoid crystallization, water in the eutectic LiCl solution has been studied but then it is generally considered that "bulk" water cannot be present. However, recent computational and experimental studies observe cooperative hydration in which case it is possible that sufficient hydrogen-bonded water is present for the essential characteristics of water to be preserved. For femtosecond optical Kerr-effect and nuclear magnetic resonance measurements, we observe in each case a fractional Stokes-Einstein relation with evidence of the dynamic crossover appearing near 220 K and 250 K respectively. Spectra obtained in the glass state also confirm the complex nature of the hydrogen-bonding modes reported for neat room-temperature water and support predictions of anomalous diffusion due to "worm-hole" structure.