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

Breakdown of the Stokes-Einstein relation in Stillinger-Weber silicon

We investigate the dynamical properties of liquid and supercooled liquid silicon, modeled using the Stillinger-Weber potential, to examine the validity of the Stokes-Einstein (SE) relation. Toward this end, we examine the relationship among various dynamical quantities, including (i) the macroscopic transport coefficients-self-diffusion coefficient D and viscosity η, (ii) relaxation time τα, and (iii) lengthscale dependent relaxation times τα(q) over a broad range of temperature T, pressure P, and density ρ covering both equilibrium and metastable liquid state points in the phase diagram. Our study shows a weak breakdown in the SE relation involving D and η, and the loci of the breakdown of the SE relation (SEB) are found in the high T liquid phase. The τα, when used as a proxy to η, shows a distinct breakdown in the SE relation, whose loci are found in the supercooled liquid phase. Interestingly, certain parts of the phase diagram show that the loci of onset of slow dynamics lie below the loci of SEB, suggesting a regime that exhibits Arrhenius but non-Fickian behavior. Computation of τα(q) enables us to extract the lengthscale associated with the Fickian to non-Fickian behavior using which we show that the breakdown of the SE relation occurs only below a specific lengthscale at a given temperature. Furthermore, we also compare the SEB loci with other features of the phase behavior, including the loci of compressibility maximum, density maximum, and diffusivity maximum.

Diffusivity of CO2 in H2O: A Review of Experimental Studies and Molecular Simulations in the Bulk and in Confinement

An in-depth review of the available experimental and molecular simulation studies of CO2 diffusion in H2O, which is a central property in important industrial and environmental processes, such as carbon capture and storage, enhanced oil recovery, and in the food industry is presented. The cases of both bulk and confined systems are covered. The experimental and molecular simulation data gathered are analyzed, and simple and computationally efficient correlations are devised. These correlations are applicable to conditions from 273 K and 0.1 MPa up to 473 K and 45 MPa. The available experimental data for diffusion coefficients of CO2 in brines are also collected, and their dependency on temperature, pressure, and salinity is examined in detail. Other engineering models and correlations reported in literature are also presented. The review of the simulation studies focuses on the force field combinations, the data for diffusivities at low and high pressures, finite-size effects, and the correlations developed based on the Molecular Dynamics data. Regarding the confined systems, we review the main methods to measure and compute the diffusivity of confined CO2 and discuss the main natural and artificial confining media (i.e., smectites, calcites, silica, MOFs, and carbon materials). Detailed discussion is provided regarding the driving force for diffusion of CO2 and H2O under confinement, and on the role of effects such as H2O adsorption on hydrophilic confining media on the diffusivity of CO2. Finally, an outlook of future research paths for advancing the field of CO2 diffusivity in H2O at the bulk phase and in confinement is laid out.

Mutual Diffusivities of Mixtures of Carbon Dioxide and Hydrogen and Their Solubilities in Brine: Insight from Molecular Simulations

H2-CO2 mixtures find wide-ranging applications, including their growing significance as synthetic fuels in the transportation industry, relevance in capture technologies for carbon capture and storage, occurrence in subsurface storage of hydrogen, and hydrogenation of carbon dioxide to form hydrocarbons and alcohols. Here, we focus on the thermodynamic properties of H2-CO2 mixtures pertinent to underground hydrogen storage in depleted gas reservoirs. Molecular dynamics simulations are used to compute mutual (Fick) diffusivities for a wide range of pressures (5 to 50 MPa), temperatures (323.15 to 423.15 K), and mixture compositions (hydrogen mole fraction from 0 to 1). At 5 MPa, the computed mutual diffusivities agree within 5% with the kinetic theory of Chapman and Enskog at 423.15 K, albeit exhibiting deviations of up to 25% between 323.15 and 373.15 K. Even at 50 MPa, kinetic theory predictions match computed diffusivities within 15% for mixtures comprising over 80% H2 due to the ideal-gas-like behavior. In mixtures with higher concentrations of CO2, the Moggridge correlation emerges as a dependable substitute for the kinetic theory. Specifically, when the CO2 content reaches 50%, the Moggridge correlation achieves predictions within 10% of the computed Fick diffusivities. Phase equilibria of ternary mixtures involving CO2-H2-NaCl were explored using Gibbs Ensemble (GE) simulations with the Continuous Fractional Component Monte Carlo (CFCMC) technique. The computed solubilities of CO2 and H2 in NaCl brine increased with the fugacity of the respective component but decreased with NaCl concentration (salting out effect). While the solubility of CO2 in NaCl brine decreased in the ternary system compared to the binary CO2-NaCl brine system, the solubility of H2 in NaCl brine increased less in the ternary system compared to the binary H2-NaCl brine system. The cooperative effect of H2-CO2 enhances the H2 solubility while suppressing the CO2 solubility. The water content in the gas phase was found to be intermediate between H2-NaCl brine and CO2-NaCl brine systems. Our findings have implications for hydrogen storage and chemical technologies dealing with CO2-H2 mixtures, particularly where experimental data are lacking, emphasizing the need for reliable thermodynamic data on H2-CO2 mixtures.

Predicting Gaseous Solute Diffusion in Viscous Multivalent Ionic Liquid Solvents

Calculating solute diffusion in dense, viscous solvents can be particularly challenging in molecular dynamics simulations due to the long time scales involved. Here, a new scaling approach is developed for predicting solute diffusion based on analyses of CO2 and SO2 diffusion in two different multivalent ionic liquid solvents. Various scaling approaches are initially evaluated, including single and separate thermostats for the solute and solvent, as well as the application of the Arrhenius relationship and the Speedy-Angell power law. A very strong logarithmic correlation is established between the solvent-accessible surface area and solute diffusion. This relationship, reflecting Danckwerts' surface renewal theory and the Vrentas-Duda free volume model, presents a valuable method for estimating diffusion behavior from short simulation trajectories at elevated temperatures. The approach may be beneficial for enhancing predictive modeling in similar challenging systems and should be more broadly evaluated.

Diffusion of hydrocarbons diluted in supercritical carbon dioxide

Mutual diffusion of six hydrocarbons (methane, ethane, isobutane, benzene, toluene or naphthalene) diluted in supercritical carbon dioxide ([Formula: see text]) is studied by molecular dynamics simulation near the Widom line, i.e., in the temperature range from 290 to 345 K along the isobar 9 MPa. The [Formula: see text] + aromatics mixtures are additionally sampled at 10 and 12 MPa and an experimental database with Fick diffusion coefficient data for those systems is provided. Taylor dispersion experiments of [Formula: see text] with benzene, toluene, n-dodecane and 1,2,3,4-tetrahydronaphthalene are conducted along the [Formula: see text] 10 MPa isobar. Maxwell-Stefan and Fick diffusion coefficients are analyzed, together with the thermodynamic factor that relates them. It is found that the peculiar behavior of the Fick diffusion coefficient of some [Formula: see text] mixtures in the extended critical region is a consequence of the thermodynamic factor minimum due to pronounced clustering on the molecular scale. Further, the strong dependence of the Fick diffusion coefficient on the molecular mass of the solute as well as the breakdown of the Stokes-Einstein relation near the Widom line are confirmed. Eleven correlations for the prediction of the Fick diffusion coefficient of [Formula: see text] mixtures are assessed. An alternative two-step approach for the prediction of the infinite dilution Fick diffusion coefficient of supercritical [Formula: see text] mixtures is proposed. It requires only the state point in terms of temperature and pressure (or density) as well as the molecular solute mass as input parameters. First, entropy scaling is applied to estimate the self-diffusion coefficient of [Formula: see text]. Subsequently, this coefficient is used to determine the infinite dilution Fick diffusion coefficient of the mixture, based on the finding that these two diffusion coefficients exhibit a linear relationship, where the slope depends only on the molecular solute mass.

Structure-Thermodynamic Relationship of a Polysaccharide Gel (Alginate) as a Function of Water Content and Counterion Type (Na vs Ca)

Biofilms are the predominant mode of microbial life on Earth, and so a deep understanding of microbial communities─and their impacts on environmental processes─requires a firm understanding of biofilm properties. Because of the importance of biofilms to their microbial inhabitants, microbes have evolved different ways of engineering and reconfiguring the matrix of extracellular polymeric substances (EPS) that constitute the main non-living component of biofilms. This ability makes it difficult to distinguish between the biotic and abiotic origins of biofilm properties. An important route toward establishing this distinction has been the study of simplified models of the EPS matrix. This study builds on such efforts by using atomistic simulations to predict the nanoscale (≤10 nm scale) structure of a model EPS matrix and the sensitivity of this structure to interpolymer interactions and water content. To accomplish this, we use replica exchange molecular dynamics (REMD) simulations to generate all-atom configurations of ten 3.4 kDa alginate polymers at a range of water contents and Ca-Na ratios. Simulated systems are solvated with explicitly modeled water molecules, which allows us to capture the discrete structure of the hydrating water and to examine the thermodynamic stability of water in the gels as they are progressively dehydrated. Our primary findings are that (i) the structure of the hydrogels is highly sensitive to the identity of the charge-compensating cations, (ii) the thermodynamics of water within the gels (specific enthalpy and free energy) are, surprisingly, only weakly sensitive to cation identity, and (iii) predictions of the differential enthalpy and free energy of hydration include a short-ranged enthalpic term that promotes hydration and a longer-ranged (presumably entropic) term that promotes dehydration, where short and long ranges refer to distances shorter or longer than ∼0.6 nm between alginate strands.

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

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.

Enhanced local viscosity around colloidal nanoparticles probed by equilibrium molecular dynamics simulations

Nanofluids-dispersions of nanometer-sized particles in a liquid medium-have been proposed for a wide variety of thermal management applications. It is known that a solid-like nanolayer of liquid of typical thicknesses of 0.5-1 nm surrounding the colloidal nanoparticles can act as a thermal bridge between the nanoparticle and the bulk liquid. Yet, its effect on the nanofluid viscosity has not been elucidated so far. In this article, we compute the local viscosity of the nanolayer using equilibrium molecular dynamics based on the Green-Kubo formula. We first assess the validity of the method to predict the viscosity locally. We apply this methodology to the calculation of the local viscosity in the immediate vicinity of a metallic nanoparticle for a wide range of solid-liquid interaction strength, where a nanolayer of thickness 1 nm is observed as a result of the interaction with the nanoparticle. The viscosity of the nanolayer, which is found to be higher than its corresponding bulk value, is directly dependent on the solid-liquid interaction strength. We discuss the origin of this viscosity enhancement and show that the liquid density increment alone cannot explain the values of the viscosity observed. Rather, we suggest that the solid-like structure of the distribution of the liquid atoms in the vicinity of the nanoparticle contributes to the nanolayer viscosity enhancement. Finally, we observe a failure of the Stokes-Einstein relation between viscosity and diffusion close to the wall, depending on the liquid-solid interaction strength, which we rationalize in terms of the hydrodynamic slip.

Settling dynamics of nanoparticles in simple and biological media

The biological response of organisms exposed to nanoparticles is often studied in vitro using adherent monolayers of cultured cells. In order to derive accurate concentration-response relationships, it is important to determine the local concentration of nanoparticles to which the cells are actually exposed rather than the nominal concentration of nanoparticles in the cell culture medium. In this study, the sedimentation-diffusion process of different sized and charged gold nanoparticles has been investigated in vitro by evaluating their settling dynamics and by developing a theoretical model to predict the concentration depth profile of nanoparticles in solution over time. Experiments were carried out in water and in cell culture media at a range of controlled temperatures. The optical phenomenon of caustics was exploited to track nanoparticles in real time in a conventional optical microscope without any requirement for fluorescent labelling that potentially affects the dynamics of the nanoparticles. The results obtained demonstrate that size, temperature and the stability of the nanoparticles play a pivotal role in regulating the settling dynamics of nanoparticles. For gold nanoparticles larger than 60 nm in diameter, the initial nominal concentration did not accurately represent the concentration of nanoparticles local to the cells. Finally, the theoretical model proposed accurately described the settling dynamics of the nanoparticles and thus represents a promising tool to support the design of in vitro experiments and the study of concentration-response relationships.

Dynamic heterogeneity, cooperative motion, and Johari-Goldstein β -relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition

We investigate the Johari-Goldstein (JG)β -relaxation process in a model metallic glass-forming (GF) material (Al 90 Sm 10 ), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JGβ -relaxation timeτ J G and the lifetime of the mobile particle clustersτ M , defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between theα -relaxation timeτ α and the lifetime of immobile particle clustersτ I M . Moreover, we find that the average diffusion coefficient D nearly coincides withD A l of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides withτ J G to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JGβ -relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JGβ -relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find thatAl 90 Sm 10 exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.

"In Silico" Seawater

Many important processes affecting the earth's climate are determined by the physical properties of seawater. In addition, desalination of seawater is a significant source of drinking water for the human population living in coastal areas. Since the physical properties of seawater governing these processes depend on the molecular interactions among its components, a deeper knowledge of seawater at the molecular level would contribute to a better understanding of these phenomena. However, in strong contrast with the situation in other areas such as biomolecules or materials science, molecular simulation studies reporting the physical properties of seawater are currently lacking. This is probably due to the usual perception of the seawater composition being too complex to approach. This point of view ignores the fact that physical properties of seawater are dependent on a single parameter representing the composition, namely the salinity. This is because the relative proportions of any two major constituents of seasalt are always the same. Another obstacle to performing molecular simulations of seawater could have been the unavailability of a satisfactory force field representing the interactions between water molecules and dissolved substances. However, this drawback has recently been overcome with the proposal of the Madrid-2019 force field. In this work we show for the first time that molecular simulation of seawater is feasible. We have performed molecular dynamics simulations of a system, the composition of which is close to the average composition of standard seawater and with the molecular interactions given by the Madrid-2019 force field. In this way we are able to provide quantitative or semiquantitative predictions for a number of relevant physical properties of seawater for temperatures and salinities from the oceanographic range to those relevant to desalination processes. The computed magnitudes include static (density), dynamical (viscosity and diffusion coefficients), structural (ionic hydration, ion-ion distribution functions), and interfacial (surface tension) properties.

Diffusivity of α-, β-, γ-cyclodextrin and the inclusion complex of β-cyclodextrin: Ibuprofen in aqueous solutions; A molecular dynamics simulation study

Cyclodextrins (CDs) are widely used in drug delivery, catalysis, food and separation processes. In this work, a comprehensive simulation study on the diffusion of the native α-, β- and γ-CDs in aqueous solutions is carried out using Molecular Dynamics simulations. The effect of the system size on the computed self-diffusivity is investigated and it is found that the required correction can be as much as 75% of the final value. The effect of the water force field is examined and it is shown that the q4md-CD/TIP4P/2005 force field combination predicts the experimentally measured self-diffusion coefficients of CDs very accurately. The self-diffusion coefficients of the three native CDs were also computed in aqueous-NaCl solutions using the Joung and Cheatham (JC) and the Madrid-2019 force fields. It is found that Na+ ions have higher affinity towards the CDs when the JC force field is used and for this reason the predicted diffusivity of CDs is lower compared to simulations using the Madrid-2019 force field. As a model system for drug delivery and waste-water treatment applications, the diffusion of the β-CD:Ibuprofen inclusion complex in water is studied. In agreement with experiments for similar components, it is shown that the inclusion complex and the free β-CD have almost equal self-diffusion coefficients. Our analysis revealed that this is most likely caused by the almost full inclusion of the ibuprofen in the cavity of the β-CD. Our findings show that Molecular Dynamics simulation can be used to provide reasonable diffusivity predictions, and to obtain molecular-level understanding useful for industrial applications of CDs.

Generalized Form for Finite-Size Corrections in Mutual Diffusion Coefficients of Multicomponent Mixtures Obtained from Equilibrium Molecular Dynamics Simulation

The system-size dependence of computed mutual diffusion coefficients of multicomponent mixtures is investigated, and a generalized correction term is derived. The generalized finite-size correction term was validated for the ternary molecular mixture chloroform/acetone/methanol as well as 28 ternary LJ systems. It is shown that only the diagonal elements of the Fick matrix show system-size dependency. The finite-size effects of these elements can be corrected by adding the term derived by Yeh and Hummer (J. Phys. Chem. B2004, 108, 15873–15879). By performing an eigenvalue analysis of the finite-size effects of the matrix of Fick diffusivities we show that the eigenvector matrix of Fick diffusivities does not depend on the size of the simulation box. Only eigenvalues, which describe the speed of diffusion, depend on the size of the system. An analytic relation for finite-size effects of the matrix of Maxwell–Stefan diffusivities was developed. All Maxwell–Stefan diffusivities depend on the system size, and the required correction depends on the matrix of thermodynamic factors.