A systematic DFT study of structure and electronic properties of titanium dioxide.

DFT functionals are of paramount importance for an accurate electronic and structural description of transition metal systems. In this work, a systematic analysis using some well-known and commonly used DFT functionals is performed. A comparison of the structural and energetic parameters calculated with the available experimental data is made in order to find the adequate functional for an accurate description of the TiO2 bulk and surface of both anatase and rutile structures. In the absence of experimental data on the surface energy, the theoretical predictions obtained using the high-accuracy HSE06 functional were used as a reference to compare against the surface energy values calculated with the other DFT functionals. A clear improvement in the electronic description of both anatase and rutile was observed by introducing the Hubbard U correction term to PBE, PW91, and OptPBE functionals. The OptPBE-U4 functional was found to offer a good compromise between accurately describing the structural and electronic properties of titania.

Coarse-grained force field for ZIF-8: A study on adsorption, diffusion, and structural properties.

Metal-organic frameworks (MOFs) are revolutionizing a spectrum of industries, from groundbreaking gas storage solutions to transformative biological system applications. The intricate architecture of these materials necessitates the use of advanced computational techniques for a comprehensive understanding of their molecular structure and prediction of their physical properties. Coarse-grained (CG) simulations shine a spotlight on the often-neglected influences of defects, pressure effects, and spatial disorders on the performance of MOFs. These simulations are not just beneficial but indispensable for high-demand applications, such as mixed matrix membranes and intricate biological system interfaces. In this work, we propose an optimized CG force field tailored for ZIF-8. Our work provides a deep dive into sorption isotherms and diffusion coefficients of small molecules. We demonstrate the structural dynamics of ZIF-8, particularly how it responds to pressurization, which affects its crystal structure and leads to local changes in aperture size and area. Emphasizing the game-changing potential of CG simulations, we explore the characteristics of amorphization in ZIF-8. Through computational exploration, we aim to bridge the knowledge gap, enhancing the potential applications of nanoporous materials for various applications.

Phase equilibria molecular simulations of hydrogen hydrates via the direct phase coexistence approach.

We report the three-phase (hydrate-liquid water-vapor) equilibrium conditions of the hydrogen-water binary system calculated with molecular dynamics simulations via the direct phase coexistence approach. A significant improvement of ∼10.5 K is obtained in the current study, over earlier simulation attempts, by using a combination of modifications related to the hydrogen model that include (i) hydrogen Lennard-Jones parameters that are a function of temperature and (ii) the water-guest energy interaction parameters optimized further by using the Lorentz-Berthelot combining rules, based on an improved description of the solubility of hydrogen in water.

Delayed Linker Addition (DLA) Synthesis for Hybrid SOD ZIFs with Unsubstituted Imidazolate Linkers for Propylene/Propane and n-Butane/i-Butane Separations.

We present a novel synthesis strategy termed delayed linker addition (DLA) to synthesize hybrid zeolitic-imidazolate frameworks containing unsubstituted imidazolate linkers (Im) with SOD topology (hereafter termed Im/ZIF-8). Im linker incorporation can create larger voids and apertures, which are important properties for gas storage and separation. To date, there have been only a handful of reports of Im linkers incorporated into ZIF-8 frameworks, typically requiring arduous and complicated post synthesis approaches. DLA, as reported here, is a simple one-step synthesis strategy allowing high incorporation of Im linker into the ZIF-8 framework while still retaining its SOD topology. We fabricated mixed-matrix membranes (MMMs) with 6FDA-DAM polymer and Im/ZIF-8 obtained via DLA as a filler. The Im/ZIF-8-containing MMMs showed excellent performance for both propylene/propane and n-butane/i-butane separation, displaying permeability and ideal selectivity well above the polymer upper bound. Moreover, highly detailed molecular simulations shed light to the aperture size and flexibility response of Im/ZIF-8 and its improved diffusivity as compared to ZIF-8.

Molecular Modeling of Thermodynamic and Transport Properties for CO2 and Aqueous Brines.

Molecular simulation techniques using classical force-fields occupy the space between ab initio quantum mechanical methods and phenomenological correlations. In particular, Monte Carlo and molecular dynamics algorithms can be used to provide quantitative predictions of thermodynamic and transport properties of fluids relevant for geologic carbon sequestration at conditions for which experimental data are uncertain or not available. These methods can cover time and length scales far exceeding those of quantum chemical methods, while maintaining transferability and predictive power lacking from phenomenological correlations. The accuracy of predictions depends sensitively on the quality of the molecular models used. Many existing fixed-point-charge models for water and aqueous mixtures fail to represent accurately these fluid properties, especially when descriptions covering broad ranges of thermodynamic conditions are needed. Recent work on development of accurate models for water, CO2, and dissolved salts, as well as their mixtures, is summarized in this Account. Polarizable models that can respond to the different dielectric environments in aqueous versus nonaqueous phases are necessary for predictions of properties over extended ranges of temperatures and pressures. Phase compositions and densities, activity coefficients of the dissolved salts, interfacial tensions, viscosities and diffusivities can be obtained in near-quantitative agreement to available experimental data, using relatively modest computational resources. In some cases, for example, for the composition of the CO2-rich phase in coexistence with an aqueous phase, recent results from molecular simulations have helped discriminate among conflicting experimental data sets. The sensitivity of properties on the quality of the intermolecular interaction model varies significantly. Properties such as the phase compositions or electrolyte activity coefficients are much more sensitive than phase densities, viscosities, or component diffusivities. Strong confinement effects on physical properties in nanoscale media can also be directly obtained from molecular simulations. Future work on molecular modeling for CO2 and aqueous brines is likely to be focused on more systematic generation of interaction models by utilizing quantum chemical as well as direct experimental measurements. New ion models need to be developed for use with the current generation of polarizable water models, including ion-ion interactions that will allow for accurate description of dense, mixed brines. Methods will need to be devised that go beyond the use of effective potentials for incorporation of quantum effects known to be important for water, and reactive force fields developed that can handle bond creation and breaking in systems with carbonate and silicate minerals. Another area of potential future work is the integration of molecular simulation methods in multiscale models for the chemical reactions leading to mineral dissolution and flow within the porous media in underground formations.

Monte Carlo simulations of the separation of a binary gas mixture (CH4 + CO2) using hydrates.

The current study employs Grand Canonical Monte Carlo simulations in order to calculate the process efficiency of separating CH4 + CO2 gas mixtures by utilizing structure sI clathrate hydrates. The temperature and pressure conditions examined in the current study resemble those used in industry. The simulation results are compared with experimental measurements and very good agreement is found. In addition, hydrate cage occupancies are compared with experimental measurements and calculations using a commercial simulator. Excellent agreement is found only for the case of large cages, while for the case of small cages significant disagreement is observed.

Tailoring the gas separation efficiency of metal organic framework ZIF-8 through metal substitution: a computational study.

The influence of a zeolitic imidazolate framework (ZIF)'s metal identity on its gas separation performance is studied extensively through molecular simulations for a variety of gases. ZIF-8 is used as the original framework for alterations of different metal substitutes of the Zn2+ metal. ZIF-8 consists of cages connected by narrow apertures that exhibit flexibility through "swelling", allowing for relatively large penetrants to diffuse. Replacing the central metal atom in the basic tetrahedral unit of ZIF-8 with Cd, Co or Be results in three different structures with increasing bonding stiffness with their neighboring atoms. The metal modification approach offers a way to control the flexibility and the size of the aperture, which constitutes the main energy barrier of the penetrant's hop-like diffusion between the framework's cages. Newly developed force fields are reported and utilized here; the new frameworks are compared to the original one, in terms of the diffusivity of various gas molecules as a function of their size (from He to n-butane). The correlation of the gas diffusivity with the aperture flexibility-molecular size relation is investigated. The results reveal that the aperture flexibility-molecular size relation governs the diffusivity, which shapes a common trend along all modifications. Furthermore, a new generalized method is employed for the screening of the various modifications for specific gas separations. This method is useful to detect optimum separation performance for the various modifications: CdIF-1 (Cd) for n-butane/iso-butane mixture; ZIF-67 (Co) for propylene/n-propane and ethylene/ethane mixtures; BeIF-1 (Be) for CO2/C2H6, CO2/CH4 and CO2/N2 mixtures.

Statistical Mechanical Model for Adsorption Coupled with SAFT-VR Mie Equation of State.

We extend the SAFT-VR Mie equation of state to calculate adsorption isotherms by considering explicitly the residual energy due to the confinement effect. Assuming a square-well potential for the fluid-solid interactions, the structure imposed by the fluid-solid interface is calculated using two different approaches: an empirical expression proposed by Travalloni et al. ( Chem. Eng. Sci. 65 , 3088 - 3099 , 2010 ), and a new theoretical expression derived by applying the mean value theorem. Adopting the SAFT-VR Mie ( Lafitte et al. J. Chem. Phys. , 139 , 154504 , 2013 ) equation of state to describe the fluid-fluid interactions, and solving the phase equilibrium criteria, we calculate adsorption isotherms for light hydrocarbons adsorbed in a carbon molecular sieve and for carbon dioxide, nitrogen, and water adsorbed in a zeolite. Good results are obtained from the model using either approach. Nonetheless, the theoretical expression seems to correlate better the experimental data than the empirical one, possibly implying that a more reliable way to describe the structure ensures a better description of the thermodynamic behavior.

Two-body perturbation theory versus first order perturbation theory: A comparison based on the square-well fluid.

We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.

Molecular simulations of imidazolium-based tricyanomethanide ionic liquids using an optimized classical force field.

Imidazolium-based ionic liquids (ILs) incorporating the tricyanomethanide ([TCM(-)]) anion are studied using an optimized classical force field. These ILs are very promising candidates for use in a wide range of cutting-edge technologies and, to our knowledge, it is the first time that this IL family is subject to a molecular simulation study with the use of a classical atomistic force field. The [C4mim(+)][TCM(-)] ionic liquid at 298.15 K and at atmospheric pressure was used as the basis for force field optimization which primarily involved the determination of the Lennard-Jones parameters of [TCM(-)] and the implementation of three quantum mechanical schemes for the calculation of the partial charge distribution and the identification of the appropriate scaling factor for the reduction of the total ionic charge. The optimized force field was validated by performing simulations of the 1-alkyl-3-methylimidazolium tricyanomethanide ([Cnmim(+)][TCM(-)], n = 2, 4, 6, and 8) IL family at various temperatures. The results for density, self-diffusivity and viscosity are in very good agreement with the available experimental data for all ILs verifying that the force field reliably reproduces the behaviour of the imidazolium-based [TCM(-)] IL family in a wide temperature range. Furthermore, a detailed analysis of the microscopic structure and the complex dynamic behaviour of the ILs under study was performed.

Direct phase coexistence molecular dynamics study of the phase equilibria of the ternary methane-carbon dioxide-water hydrate system.

Molecular dynamics simulation is used to predict the phase equilibrium conditions of a ternary hydrate system. In particular, the direct phase coexistence methodology is implemented for the determination of the three-phase coexistence temperature of the methane-carbon dioxide-water hydrate system at elevated pressures. The TIP4P/ice, TraPPE-UA and OPLS-UA forcefields for water, carbon dioxide and methane respectively are used, in line with our previous studies of the phase equilibria of the corresponding binary hydrate systems. The solubility in the aqueous phase of the guest molecules of the respective binary and ternary systems is examined under hydrate-forming conditions, providing insight into the predictive capability of the methodology as well as the combination of these forcefields to accurately describe the phase behavior of the ternary system. The three-phase coexistence temperature is calculated at 400, 1000 and 2000 bar for two compositions of the methane-carbon dioxide mixture. The predicted values are compared with available calculations with satisfactory agreement. An estimation is also provided for the fraction of the guest molecules in the mixed hydrate phase under the conditions examined.

Thermophysical properties of imidazolium tricyanomethanide ionic liquids: experiments and molecular simulation.

The low-viscous tricyanomethanide ([TCM](-))-based ionic liquids (ILs) are gaining increasing interest as attractive fluids for a variety of industrial applications. The thermophysical properties (density, viscosity, surface tension, electrical conductivity and self-diffusion coefficient) of the 1-alkyl-3-methylimidazolium tricyanomethanide [Cnmim][TCM] (n = 2, 4 and 6-8) IL series were experimentally measured over the temperature range from 288 to 363 K. Moreover, a classical force field optimized for the imidazolium-based [TCM](-) ILs was used to calculate their thermodynamic, structural and transport properties (density, surface tension, self-diffusion coefficients, viscosity) in the temperature range from 300 to 366 K. The predictions were directly compared against the experimental measurements. The effects of anion and alkyl chain length on the structure and thermophysical properties have been evaluated. In cyano-based ILs, the density decreases with increasing molar mass, in contrast to the behavior of the fluorinated anions, being in agreement with the literature. The contribution per -CH2- group to the increase of the viscosity presents the following sequence: [PF6](-) > [BF4](-) > [Tf2N](-) > [DCA](-) > [TCB](-) > [TCM](-). [TCM](-)-based ILs show lower viscosity than dicyanamide ([DCA](-))- and tetracyanoborate ([TCB](-))-based ILs, while the latter two exhibit a crossover which depends both on temperature and the alkyl chain length of the cation. The surface tension of the investigated ILs decreases with increasing alkyl chain length. [C2mim][TCM] shows an outlier behavior compared to other members of the homologous series. The surface enthalpies and surface entropies for all the studied systems have been calculated based on the experimentally determined surface tensions. The relationship between molar conductivity and viscosity was analyzed using the Walden rule. The experimentally determined self-diffusion coefficients of the cations are in good agreement with the molecular simulation predictions, in which a decrease of the self-diffusion of the cations with increasing alkyl chain length is observed with a simultaneous increase in viscosity and for the longer alkyl lengths the anion becomes more mobile than the cation.

Anisotropic parallel self-diffusion coefficients near the calcite surface: A molecular dynamics study.

Applying classical molecular dynamics simulations, we calculate the parallel self-diffusion coefficients of different fluids (methane, nitrogen, and carbon dioxide) confined between two {101̄4} calcite crystal planes. We have observed that the molecules close to the calcite surface diffuse differently in distinct directions. This anisotropic behavior of the self-diffusion coefficient is investigated for different temperatures and pore sizes. The ion arrangement in the calcite crystal and the strong interactions between the fluid particles and the calcite surface may explain the anisotropy in this transport property.

System-size corrections for self-diffusion coefficients calculated from molecular dynamics simulations: The case of CO2, n-alkanes, and poly(ethylene glycol) dimethyl ethers.

Molecular dynamics simulations were carried out to study the self-diffusion coefficients of CO2, methane, propane, n-hexane, n-hexadecane, and various poly(ethylene glycol) dimethyl ethers (glymes in short, CH3O-(CH2CH2O)n-CH3 with n = 1, 2, 3, and 4, labeled as G1, G2, G3, and G4, respectively) at different conditions. Various system sizes were examined. The widely used Yeh and Hummer [J. Phys. Chem. B 108, 15873 (2004)] correction for the prediction of diffusion coefficient at the thermodynamic limit was applied and shown to be accurate in all cases compared to extrapolated values at infinite system size. The magnitude of correction, in all cases examined, is significant, with the smallest systems examined giving for some cases a self-diffusion coefficient approximately 15% lower than the infinite system-size extrapolated value. The results suggest that finite size corrections to computed self-diffusivities must be used in order to obtain accurate results.

Lattice constants of pure methane and carbon dioxide hydrates at low temperatures. Implementing quantum corrections to classical molecular dynamics studies.

We introduce a simple correction to the calculation of the lattice constants of fully occupied structure sI methane or carbon dioxide pure hydrates that are obtained from classical molecular dynamics simulations using the TIP4PQ/2005 water force field. The obtained corrected lattice constants are subsequently used in order to obtain isobaric thermal expansion coefficients of the pure gas hydrates that exhibit a trend that is significantly closer to the experimental behavior than previously reported classical molecular dynamics studies.

Prediction of the phase equilibria of methane hydrates using the direct phase coexistence methodology.

The direct phase coexistence method is used for the determination of the three-phase coexistence line of sI methane hydrates. Molecular dynamics (MD) simulations are carried out in the isothermal-isobaric ensemble in order to determine the coexistence temperature (T3) at four different pressures, namely, 40, 100, 400, and 600 bar. Methane bubble formation that results in supersaturation of water with methane is generally avoided. The observed stochasticity of the hydrate growth and dissociation processes, which can be misleading in the determination of T3, is treated with long simulations in the range of 1000-4000 ns and a relatively large number of independent runs. Statistical averaging of 25 runs per pressure results in T3 predictions that are found to deviate systematically by approximately 3.5 K from the experimental values. This is in good agreement with the deviation of 3.15 K between the prediction of TIP4P/Ice water force field used and the experimental melting temperature of ice Ih. The current results offer the most consistent and accurate predictions from MD simulation for the determination of T3 of methane hydrates. Methane solubility values are also calculated at the predicted equilibrium conditions and are found in good agreement with continuum-scale models.

The role of intermolecular interactions in the prediction of the phase equilibria of carbon dioxide hydrates.

The direct phase coexistence methodology was used to predict the three-phase equilibrium conditions of carbon dioxide hydrates. Molecular dynamics simulations were performed in the isobaric-isothermal ensemble for the determination of the three-phase coexistence temperature (T3) of the carbon dioxide-water system, at pressures in the range of 200-5000 bar. The relative importance of the water-water and water-guest interactions in the prediction of T3 is investigated. The water-water interactions were modeled through the use of TIP4P/Ice and TIP4P/2005 force fields. The TraPPE force field was used for carbon dioxide, and the water-guest interactions were probed through the modification of the cross-interaction Lennard-Jones energy parameter between the oxygens of the unlike molecules. It was found that when using the classic Lorentz-Berthelot combining rules, both models fail to predict T3 accurately. In order to rectify this problem, the water-guest interaction parameters were optimized, based on the solubility of carbon dioxide in water. In this case, it is shown that the prediction of T3 is limited only by the accuracy of the water model in predicting the melting temperature of ice.

Molecular simulation of thermodynamic and transport properties for the H2O+NaCl system.

Molecular dynamics and Monte Carlo simulations have been carried out to obtain thermodynamic and transport properties of the binary mixture H2O+NaCl at temperatures from T = 298 to 473 K. In particular, vapor pressures, liquid densities, viscosities, and vapor-liquid interfacial tensions have been obtained as functions of pressure and salt concentration. Several previously proposed fixed-point-charge models that include either Lennard-Jones (LJ) 12-6 or exponential-6 (Exp6) functional forms to describe non-Coulombic interactions were studied. In particular, for water we used the SPC and SPC/E (LJ) models in their rigid forms, a semiflexible version of the SPC/E (LJ) model, and the Errington-Panagiotopoulos Exp6 model; for NaCl, we used the Smith-Dang and Joung-Cheatham (LJ) parameterizations as well as the Tosi-Fumi (Exp6) model. While none of the model combinations are able to reproduce simultaneously all target properties, vapor pressures are well represented using the SPC plus Joung-Cheathem model combination, and all LJ models do well for the liquid density, with the semiflexible SPC/E plus Joung-Cheatham combination being the most accurate. For viscosities, the combination of rigid SPC/E plus Smith-Dang is the best alternative. For interfacial tensions, the combination of the semiflexible SPC/E plus Smith-Dang or Joung-Cheatham gives the best results. Inclusion of water flexibility improves the mixture densities and interfacial tensions, at the cost of larger deviations for the vapor pressures and viscosities. The Exp6 water plus Tosi-Fumi salt model combination was found to perform poorly for most of the properties of interest, in particular being unable to describe the experimental trend for the vapor pressure as a function of salt concentration.

Unexpectedly High Propylene/Propane Separation Performance of Asymmetric Mixed-Matrix Membranes through Additive-Assisted In Situ ZIF-8 Filler Formation: Experimental and Computational Studies.

Zeolitic-imidazolate framework-8 (ZIF-8), composed of a zinc center tetrahedrally coordinated with 2-methylimidazolate linkers, has garnered extensive attention as a selective filler for propylene-selective mixed-matrix membranes (MMMs). Recently, we reported an innovative and scalable MMM fabrication approach, termed "phase-inversion in sync with in situ MOF formation" (PIMOF), aimed at addressing the prevailing challenges in MMM processing. In this study, we intend to investigate the effect of additives, specifically sodium formate and 1,4-butanediol, on the modification of ZIF-8 filler formation within the polymer matrix in order to further improve the separation performance of the asymmetric MMMs prepared by the PIMOF. Remarkably, MMMs prepared with sodium formate as an additive in the coagulation bath exhibited an unprecedented C3H6/C3H8 separation factor of 222.5 ± 1.8 with a C3H6 permeance of 10.1 ± 0.3 GPU, surpassing that of MMMs prepared without additives (a C3 separation factor of 57.7 ± 11.2 with a C3 permeance of 22.5 ± 4.5 GPU). Our computational work complements the experimental investigation by studying the effect of ZIF-8 nanoparticle size on the specific surface interaction energy and apertures of ZIF-8. Calculations indicate that by having smaller ZIF-8 nanoparticles, stronger interactions are present with the polymer affecting the aperture of ZIF-8 nanoparticles. This reduction in aperture size is expected to improve selectivity toward propylene by reducing the permeability of propylene. These results represent a significant advancement, surpassing the performance of all previously reported propylene-selective MMMs and most high-quality polycrystalline ZIF-8 membranes. The notably enhanced separation performance primarily arises from the formation of exceedingly small ZIF-8-like particles with an amorphous or poorly crystalline structure, corroborated by our computational work.

Mixed Solvent Electrolyte Solutions: A Review and Calculations with the eSAFT-VR Mie Equation of State.

In this work, mixed-solvent mean ionic activity coefficients (MIAC), vapor-liquid equilibrium (VLE), and liquid-liquid equilibrium (LLE) of electrolyte solutions have been addressed. An extended literature review of existing electrolyte activity coefficient models (eGE) and electrolyte equations of state (eEoS) for modeling mixed solvent electrolyte systems is first presented, focusing on the details of the models in terms of physical and electrolyte terms, relative static permittivity, and parameterization. The analysis of this literature reveals that the property predictions can be ranked, from the easiest to the most difficult, in the following order: VLE, MIAC, and LLE. We have then used our previously developed eSAFT-VR Mie model to predict MIAC, VLE, and LLE in mixed solvents without fitting any new adjustable parameters. The model was parameterized on MIAC of aqueous electrolyte solutions and successfully extended to nonaqueous, single solvent electrolyte solutions without any new adjustable parameters by using a salt-dependent expression for the relative static permittivity. Our approach yields excellent results for MIAC and VLE of mixed solvent electrolyte solutions, while being fully predictive. LLE is significantly more challenging, and an accurate model for the salt-free solution is crucial for accurate calculations. When the compositions of the two phases in the binary salt-free system are accurately captured, then the electrolyte extension of our model shows a lot of potential and is currently among the best eEoS for LLE prediction in the literature.