Finite-Size Effects of Binary Mutual Diffusion Coefficients from Molecular Dynamics

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.

Transport Phenomena in Nano/Molecular Confinements

The transport of fluid and ions in nano/molecular confinements is the governing physics of a myriad of embodiments in nature and technology including human physiology, plants, energy modules, water collection and treatment systems, chemical processes, materials synthesis, and medicine. At nano/molecular scales, the confinement dimension approaches the molecular size and the transport characteristics deviates significantly from that at macro/micro scales. A thorough understanding of physics of transport at these scales and associated fluid properties is undoubtedly critical for future technologies. This compressive review provides an elaborate picture on the promising future applications of nano/molecular transport, highlights experimental and simulation metrologies to probe and comprehend this transport phenomenon, discusses the physics of fluid transport, tunable flow by orders of magnitude, and gating mechanisms at these scales, and lists the advancement in the fabrication methodologies to turn these transport concepts into reality. Properties such as chain-like liquid transport, confined gas transport, surface charge-driven ion transport, physical/chemical ion gates, and ion diodes will provide avenues to devise technologies with enhanced performance inaccessible through macro/micro systems. This review aims to provide a consolidated body of knowledge to accelerate innovation and breakthrough in the above fields.

Machine Learning-Based Upscaling of Finite-Size Molecular Dynamics Diffusion Simulations for Binary Fluids

Molecular diffusion coefficients calculated using molecular dynamics (MD) simulations suffer from finite-size (i.e., finite box size and finite particle number) effects. Results from finite-sized MD simulations can be upscaled to infinite simulation size by applying a correction factor. For self-diffusion of single-component fluids, this correction has been well-studied by many researchers including Yeh and Hummer (YH); for binary fluid mixtures, a modified YH correction was recently proposed for correcting MD-predicted Maxwell-Stephan (MS) diffusion rates. Here we use both empirical and machine learning methods to identify improvements to the finite-size correction factors for both self-diffusion and MS diffusion of binary Lennard-Jones (LJ) fluid mixtures. Using artificial neural networks (ANNs), the error in the corrected LJ fluid diffusion is reduced by an order of magnitude versus existing YH corrections, and the ANN models perform well for mixtures with large dissimilarities in size and interaction energies where the YH correction proves insufficient.

Estimates of Electrical Conductivity from Molecular Dynamics Simulations: How to Invest the Computational Effort

Although the electrical conductivity of an electrolyte can be estimated from the molecular dynamics trajectory, it is often a challenging task because of the need to obtain a substantial amount of data to ensure sufficient averaging. Here, we present an analysis on the convergence of results with the number of simulated trajectories. A series of molecular dynamics simulations have been performed for a model electrolyte (NaCl in water) and the Einstein relation has been used to calculate the electrical conductivity. The standard deviation of the conductivity estimates is relatively large compared to the mean value, and it has been shown that the off-diagonal contributions to the collective displacement of ions are responsible for large deviations between systems. It has been found that about 40 independent MD simulations may be required to reduce the errors. A procedure to improve the final estimate of the conductivity has been proposed.

Mutual Diffusivity of an n-Hexane-2,2-Dimethyl Butane Binary Mixture Confined to Zeolite Y

A molecular dynamic study of a mixture of n-hexane and 2,2-dimethyl butane (22DMB) confined to zeolite NaY has been carried out to understand the distinct diffusivity and mutual diffusivity. Results have been compared with the bulk mixture. For each of these mixtures, eight different runs were employed to compute distinct and mutual diffusivity. From the velocity auto- and cross-correlation functions between n-hexane and n-hexane, n-hexane and 22DMB, 22DMB and 22DMB, the self- and distinct diffusivity of the mixture has been computed. The thermodynamic factor and mutual diffusivity have been calculated. The ratio of D₁₁ to D_s is seen to be 1.11 and 0.75 for the confined mixture, while they are 1.21 and 0.79 for the bulk mixture at 200 and 300 K, respectively.

Effect of salt concentration on properties of mixed carbonate-based electrolyte for Li-ion batteries: a molecular dynamics simulation study

In this work, a computational framework is proposed by utilizing molecular dynamics simulation to explore the existing relation between molecular structure and ionic conductivity of the electrolyte system [LiPF₆+(EC+DMC 1:1)] consisting of a mixture of cyclic ethylene carbonate (EC) and acyclic dimethyl carbonate (DMC) solvents and lithium hexafluorophosphate (LiPF₆) salt to propose as a novel mixed organic solvent-based electrolytes to promote the performance of lithium-ion batteries (LIBs). To acquire a clear understanding of the structural and transport properties of the designed electrolytes, quantum chemistry (QC) calculations and molecular dynamics (MD) simulation are used. In the first step, the accurate molecular structures of the studied electrolytes in addition to their corresponding atomic partial charges are evaluated. The MD simulations are performed at 330 K varying the LiPF₆ concentration (0.5 M to 2.2 M). Analysis of the obtained results indicated that ionic diffusivity and conductivity of the electrolytes are dependent on the structure of solvated ions and lithium salt (LiPF₆) concentration. It is found that the obtained MD simulation results are in reasonable agreement with experimental results. Graphical abstract A representation of dependence of transport properties of electrolyte system [LiPF6 +(EC+DMC 1:1)] as function of salt concentration to be used in Lithium-ion batteries (LIBs).

Role of Viscosity in Deviations from the Nernst-Einstein Relation

Deviations from the Nernst-Einstein relation are commonly attributed to ion-ion correlation and ion pairing. Despite the fact that these deviations can be quantified by either experimental measurements or molecular dynamics simulations, there is no rule of thumb to tell the extent of deviations. Here, we show that deviations from the Nernst-Einstein relation are proportional to the inverse viscosity by exploring the finite-size effect on transport properties under periodic boundary conditions. This conclusion is in accord with the established experimental results of ionic liquids.

ReaxFF molecular dynamics simulations of electrolyte-water systems at supercritical temperature

We have performed ReaxFF molecular dynamics simulations of alkali metal-chlorine pairs in different water densities at supercritical temperature (700 K) to elucidate the structural and dynamical properties of the system. The radial distribution function and the angular distribution function explain the inter-ionic structural and orientational arrangements of atoms during the simulation. The coordination number of water molecules in the solvation shell of ions increases with an increase in the radius of ions. We find that the self-diffusion coefficient of metal ions increases with a decrease in density under supercritical conditions due to the formation of voids within the system. The hydrogen bond dynamics has been interpreted by the residence time distribution of various ions, which shows Li⁺ having the highest water retaining capability. The void distribution within the system has been analyzed by using the Voronoi polyhedra algorithm providing an estimation of void formation within the system at high temperatures. We observe the formation of salt clusters of Na⁺ and K⁺ at low densities due to the loss of dielectric constants of ions. The diffusion of ions gets altered dramatically due to the formation of voids and nucleation of ions in the system.

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.

Mutual and Thermal Diffusivities as well as Fluid-Phase Equilibria of Mixtures of 1-Hexanol and Carbon Dioxide

This work contributes to an improved understanding of the fluid-phase behavior and diffusion processes in mixtures of 1-hexanol and carbon dioxide (CO₂) at temperatures around the upper critical end point (UCEP) of the system. Raman spectroscopy and dynamic light scattering were used to determine the composition at saturation conditions as well as Fick and thermal diffusivities. An acceleration of the Fick diffusive process up to CO₂ mole fractions of about 0.2 was found, followed by a strong slowing-down approaching vapor-liquid-liquid equilibrium or critical conditions. The acceleration of the Fick diffusive process vanished at temperatures much higher than the UCEP. Experimental Fick diffusivity data were compared with predictions from equilibrium molecular dynamics simulations and excess Gibbs energy calculations using interaction parameters from the literature. Both theoretical methods were not able to predict that the thermodynamic factor is equal to zero at the spinodal composition, stressing the need for new methodologies under such conditions. Thus, new sets of temperature-dependent interaction parameters were developed for the nonrandom two-liquid model, which improve the prediction of the Fick diffusion coefficient considerably. The link between the Fick diffusion coefficient and the nonrandomness of the liquid phases is also discussed.

Structural, Thermodynamic, and Transport Properties of Aqueous Reline and Ethaline Solutions from Molecular Dynamics Simulations

Deep eutectic solvents (DESs) are a new generation of green solvents, which are considered an environmentally friendly alternative to ionic liquids and volatile organic compounds. The addition of controlled amounts of water to DESs has a significant effect on their microscopic structure and thus on their thermodynamic and transport properties. In this way, DESs can be modified, leading to solvents with improved characteristics. In this work, molecular dynamics (MD) simulations are performed to obtain a better understanding of the relation between the microscopic structure, molecular interactions, and thermophysical properties of aqueous reline and ethaline solutions at temperatures ranging from 303.15 to 363.15 K. For both reline and ethaline solutions, the hydrogen bond (HB) networks disappear with increasing mass fraction of water, and the intensity of radial distribution function (RDF) peaks decreases. For a mass fraction of water of 40%, most of the HBs between the compounds of reline and ethaline are broken, and DESs are fully dissolved in water. Consequently, a monotonic decrease in viscosities and an increase in self-diffusion coefficients are observed. Ionic conductivities show a nonmonotonic behavior with increasing water content. Up to 60% water mass fraction, the ionic conductivities increase with increasing water content. A further increase in the mass fraction of water decreases conductivities. For all studied systems, the HB network and the peaks of RDFs show relatively small changes for water mass fractions below 5% and beyond 40%. The MD results show that viscosities decrease with temperature, while diffusivities and ionic conductivities increase. The effect of the temperature on the structure of DES-water mixtures is negligible.

Quantifying Pore Width Effects on Diffusivity via a Novel 3D Stochastic Approach with Input from Atomistic Molecular Dynamics Simulations

The increased production of unconventional hydrocarbons emphasizes the need to understand the transport of fluids through narrow pores. Although it is well-known that confinement affects fluids structure and transport, it is not yet possible to quantitatively predict properties such as diffusivity as a function of pore width in the range of 1-50 nm. Such pores are commonly found not only in shale rocks but also in a wide range of engineering materials, including catalysts. We propose here a novel and computationally efficient methodology to obtain accurate diffusion coefficient predictions as a function of pore width for pores carved out of common materials, such as silica, alumina, magnesium oxide, calcite, and muscovite. We implement atomistic molecular dynamics (MD) simulations to quantify fluid structure and transport within 5 nm-wide pores, with particular focus on the diffusion coefficient within different pore regions. We then use these data as input to a bespoke stochastic kinetic Monte Carlo (KMC) model, developed to predict fluid transport in mesopores. The KMC model is used to extrapolate the fluid diffusivity for pores of increasing width. We validate the approach against atomistic MD simulation results obtained for wider pores. When applied to supercritical methane in slit-shaped pores, our methodology yields data within 10% of the atomistic simulation results, with significant savings in computational time. The proposed methodology, which combines the advantages of MD and KMC simulations, is used to generate a digital library for the diffusivity of gases as a function of pore chemistry and pore width and could be relevant for a number of applications, from the prediction of hydrocarbon transport in shale rocks to the optimization of catalysts, when surface-fluid interactions impact transport.

Diffusivities in 1-Alcohols Containing Dissolved H2, He, N2, CO, or CO2 Close to Infinite Dilution

The influence of the strength of intermolecular interactions on mass diffusive processes remains poorly understood for mixtures of associative liquids with dissolved gases. For contributing to a fundamental understanding of the interplay between liquid structures and mass diffusivities in such systems, dynamic light scattering, Raman spectroscopy, and molecular dynamics simulations were used in this work. As model systems, binary mixtures consisting of the gases hydrogen, helium, nitrogen, carbon monoxide, or carbon dioxide dissolved in ethanol, 1-hexanol, or 1-decanol were selected. Experiments and simulations were performed at macroscopic thermodynamic equilibrium close to infinite dilution of solute for temperatures between 303 and 423 K. The Fick diffusion coefficients and self-diffusivities of the gas solutes increase with increasing temperature, decreasing alkyl chain length of the 1-alcohols, and decreasing molar mass of the solutes except for helium and hydrogen showing the opposite behavior. The analysis of the liquid structure of the mixtures showed that the fraction of hydrogen-bonded alcohol molecules decreases with increasing alkyl chain length and temperature. From the obtained structure-property relationships, a new correlation was developed to predict mass diffusivities in binary mixtures consisting of n-alkanes or 1-alcohols with dissolved gases close to infinite dilution within 10% on average.

Development of the ReaxFF Methodology for Electrolyte-Water Systems

A new ReaxFF reactive force field has been developed for water-electrolyte systems including cations Li⁺, Na⁺, K⁺, and Cs⁺ and anions F^-, Cl^-, and I^-. The reactive force field parameters have been trained against quantum mechanical (QM) calculations related to water binding energies, hydration energies and energies of proton transfer. The new force field has been validated by applying it to molecular dynamics (MD) simulations of the ionization of different electrolytes in water and comparison of the results with experimental observations and thermodynamics. Radial distribution functions (RDF) determined for most of the atom pairs (cation or anion with oxygen and hydrogen of water) show a good agreement with the RDF values obtained from DFT calculations. On the basis of the applied force field, the ReaxFF simulations have described the diffusion constants for water and electrolyte ions in alkali metal hydroxide and chloride salt solutions as a function of composition and electrolyte concentration. The obtained results open opportunities to advance ReaxFF methodology to a wide range of applications involving electrolyte ions and solutions.

Thermodynamic Analysis of n-Hexane-Ethanol Binary Mixtures Using the Kirkwood-Buff Theory

A complete thermodynamic analysis of mixtures consisting of molecules with complex chemical constitution can be rather demanding. The Kirkwood-Buff theory of solutions allows the estimation of thermodynamic properties, which cannot be directly extracted from atomistic simulations, such as the Gibbs energy of mixing (Δ_mix G). In this work, we perform molecular dynamics simulations of n-hexane-ethanol binary mixtures in the liquid state under two temperature-pressure conditions and at various mole fractions. On the basis of the recently published methodology of Galata [ Fluid Phase Equilib. 2018 , 470 , 25 - 37 ] , we first calculate the Kirkwood-Buff integrals in the isothermal-isobaric ( NpT) ensemble, identifying how system size affects their estimation. We then extract the activity coefficients, excess Gibbs energy, excess enthalpy, and excess entropy for the n-hexane-ethanol binary mixtures we simulate. We employ two approaches for quantifying composition fluctuations: one based on counting molecular centers of mass and a second one based on counting molecular segments. Results from the two approaches are practically indistinguishable. We compare our results against predictions of vapor-liquid equilibria obtained in a previous simulation work using the same force field, as well as with experimental data, and find very good agreement. In addition, we develop a simple methodology to identify the hydrogen bonds between ethanol molecules and analyze their effects on mixing properties.

Correction of diffusion calculations when using two types of non-rectangular simulation boxes in molecular simulations

Although simulation boxes used in molecular dynamics are normally chosen to be cubic or rectangular, two other cell shapes that are very familiar to crystallographers-the truncated octahedron and the rhombic dodecahedron-could also be used because they are also space-filling cells. Due to their spherical nature, these boxes have been intentionally applied in simulations of biomolecular solutions and liquid structures. Indeed, due to the advantages of running many molecular dynamic codes in parallel, simulations based on these non-rectangular boxes have been growing in popularity in recent years. In this work, the effects of using these two types of boxes on diffusion are explored for the first time, and an appropriate correction formula is derived theoretically within the framework of hydrodynamics. In addition, the range of validity for the correction formula is evaluated by performing molecular dynamic simulations on argon at three different densities.

Optimizing Nonbonded Interactions of the OPLS Force Field for Aqueous Solutions of Carbohydrates: How to Capture Both Thermodynamics and Dynamics

Knowledge on thermodynamic and transport properties of aqueous solutions of carbohydrates is of great interest for process and product design in the food, pharmaceutical, and biotechnological industries. Molecular simulation is a powerful tool to calculate these properties, but current classical force fields cannot provide accurate estimates for all properties of interest. The poor performance of the force fields is mainly observed for concentrated solutions, where solute–solute interactions are overestimated. In this study, we propose a method to refine force fields, such that solute–solute interactions are more accurately described. The OPLS force field combined with the SPC/Fw water model is used as a basis. We scale the nonbonded interaction parameters of sucrose, a disaccharide. The scaling factors are chosen in such a way that experimental thermodynamic and transport properties of aqueous solutions of sucrose are accurately reproduced. Using a scaling factor of 0.8 for Lennard-Jones energy parameters (ϵ) and a scaling factor of 0.95 for partial atomic charges (q), we find excellent agreement between experiments and computed liquid densities, thermodynamic factors, shear viscosities, self-diffusion coefficients, and Fick (mutual) diffusion coefficients. The transferability of these optimum scaling factors to other carbohydrates is verified by computing thermodynamic and transport properties of aqueous solutions of d-glucose, a monosaccharide. The good agreement between computed properties and experiments suggests that the scaled interaction parameters are transferable to other carbohydrates, especially for concentrated solutions.

Shear Viscosity Computed from the Finite-Size Effects of Self-Diffusivity in Equilibrium Molecular Dynamics

A method is proposed for calculating the shear viscosity of a liquid from finite-size effects of self-diffusion coefficients in Molecular Dynamics simulations. This method uses the difference in the self-diffusivities, computed from at least two system sizes, and an analytic equation to calculate the shear viscosity. To enable the efficient use of this method, a set of guidelines is developed. The most efficient number of system sizes is two and the large system is at least four times the small system. The number of independent simulations for each system size should be assigned in such a way that 50%–70% of the total available computational resources are allocated to the large system. We verified the method for 250 binary and 26 ternary Lennard-Jones systems, pure water, and an ionic liquid ([Bmim][Tf₂N]). The computed shear viscosities are in good agreement with viscosities obtained from equilibrium Molecular Dynamics simulations for all liquid systems far from the critical point. Our results indicate that the proposed method is suitable for multicomponent mixtures and highly viscous liquids. This may enable the systematic screening of the viscosities of ionic liquids and deep eutectic solvents.

Interplay of structure and diffusion in ternary liquid mixtures of benzene + acetone + varying alcohols

The Fick diffusion coefficient matrix of ternary mixtures containing benzene + acetone + three different alcohols, i.e., methanol, ethanol, and 2-propanol, is studied by molecular dynamics simulation and Taylor dispersion experiments. Aiming to identify common features of these mixtures, it is found that one of the main diffusion coefficients and the smaller eigenvalue do not depend on the type of alcohol along the studied composition path. Two mechanisms that are responsible for this invariant behavior are discussed in detail, i.e., the interplay between kinetic and thermodynamic contributions to Fick diffusion coefficients and the presence of microscopic heterogeneities caused by hydrogen bonding. Experimental work alone cannot explain these mechanisms, while present simulations on the molecular level indicate structural changes and uniform intermolecular interactions between benzene and acetone molecules in the three ternary mixtures. The main diffusion coefficients of these ternary mixtures exhibit similarities with their binary subsystems. Analyses of radial distribution functions and hydrogen bonding statistics quantitatively evidence alcohol self-association and cluster formation, as well as component segregation. Furthermore, the excess volume of the mixtures is analyzed in the light of intermolecular interactions, further demonstrating the benefits of the simultaneous use of experiment and simulation. The proposed framework for studying diffusion coefficients of a set of ternary mixtures, where only one component varies, opens the way for further investigations and a better understanding of multicomponent diffusion. The presented numerical results may also give an impulse to the development of predictive approaches for multicomponent diffusion.