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.

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.

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.

Molecular Modeling of Double Retrograde Vaporization Using Monte Carlo Simulations and Equations of State.

Vapor-liquid equilibria of binary systems consisting of a low-boiling (i.e., more volatile) and a high-boiling compound may exhibit unexpected behavior near the critical point of the low-boiling compound. Near the critical temperature of the low-boiling compound and for compositions rich in the low-boiling compound, increasing the pressure may result in multiple crossings of the dew- and bubble-point curves. This phenomenon is often called double retrograde vaporization (or condensation) and may play a role in oil field operations and gas transport through pipelines, but the microscopic driving forces for the unusual shape of the dew-point curve are not well understood. Monte Carlo simulations in the constant-pressure, constant-temperature Gibbs ensemble using the united-atom version of the TraPPE force field were carried out for the methane/n-butane mixture at temperatures ranging from 0.95 to 1.05 of the reduced (T/Tc) temperature of methane. The simulations predict a wealth of additional thermodynamic data (densities and free energies of transfer) and structural data that are used to provide much needed molecular-level insights into the fluid properties associated with double retrograde vaporization. Simulated thermodynamic data are also compared with calculations using the Peng-Robinson and PC-SAFT equations of state.

Prediction of Adsorption and Diffusion of Shale Gas in Composite Pores Consisting of Kaolinite and Kerogen using Molecular Simulation.

Natural gas production from shale formations is one of the most recent and fast growing developments in the oil and gas industry. The accurate prediction of the adsorption and transport of shale gas is essential for estimating shale gas production capacity and improving existing extractions. To realistically represent heterogeneous shale formations, a composite pore model was built from a kaolinite slit mesopore hosting a kerogen matrix. Moreover, empty slabs (2, 3, and 4 nm) were added between the kerogen matrix and siloxane surface of kaolinite. Using Grand-Canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations, the adsorption and diffusion of pure methane, pure ethane, and a shale gas mixture were computed at various high pressures (100, 150, and 250 atm) and temperature of 298.15 K. The addition of an inner slit pore was found to significantly increase the excess adsorption of methane, as a pure component and in the shale gas mixture. The saturation of the composite pore with methane was observed to be at a higher pressure compared to ethane. The excess adsorption of carbon dioxide was not largely affected by pressure, and the local number density profile showed its strong affinity to kerogen micropores and the hydroxylated gibbsite surface under all conditions and pore widths. Lateral diffusion coefficients were found to increase with increasing the width of the empty slab inside the composite pore. Statistical errors of diffusion coefficients were found to be large for the case of shale gas components present at low composition. A larger composite pore configuration was created to investigate the diffusion of methane in different regions of the composite pore. The calculated diffusion coefficients and mean residence times were found to be indicative of the different adsorption mechanisms occurring inside the pore.

The Contribution of the Ion-Ion and Ion-Solvent Interactions in a Molecular Thermodynamic Treatment of Electrolyte Solutions.

Developing molecular equations of state to treat electrolyte solutions is challenging due to the long-range nature of the Coulombic interactions. Seminal approaches commonly used are the mean spherical approximation (MSA) and the Debye-Hückel (DH) theory to account for ion-ion interactions and, often, the Born theory of solvation for ion-solvent interactions. We investigate the accuracy of the MSA and DH approaches using each to calculate the contribution of the ion-ion interactions to the chemical potential of NaCl in water, comparing these with newly computer-generated simulation data; the ion-ion contribution is isolated by selecting an appropriate primitive model with a Lennard-Jones force field to describe the solvent. A study of mixtures with different concentrations and ionic strengths reveals that the calculations from both MSA and DH theories are of similar accuracy, with the MSA approach resulting in marginally better agreement with the simulation data. We also demonstrate that the Born theory provides a good qualitative description of the contribution of the ion-solvent interactions; we employ an explicitly polar water model in these simulations. Quantitative agreement up to moderate salt concentrations and across the relevant range of temperature is achieved by adjusting the Born radius using simulation data of the free energy of solvation. We compute the radial and orientational distribution functions of the systems, thereby providing further insight on the differences observed between the theory and simulation. We thus provide rigorous benchmarks for use of the MSA, DH, and Born theories as perturbation approaches, which will be of value for improving existing models of electrolyte solutions, especially in the context of equations of state.

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.

Industrial Requirements for Thermodynamic and Transport Properties: 2020.

This paper reports the results of an investigation of industrial requirements for thermodynamic and transport properties carried out during the years 2019-2020. It is a follow-up of a similar investigation performed and published 10 years ago by the Working Party (WP) of Thermodynamics and Transport Properties of European Federation of Chemical Engineering (EFCE).1 The main goal was to investigate the advances in this area over the past 10 years, to identify the limitations that still exist, and to propose future R&D directions that will address the industrial needs. An updated questionnaire, with two new categories, namely, digitalization and comparison to previous survey/changes over the past 10 years, was sent to a broad number of experts in companies with a diverse activity spectrum, in oil and gas, chemicals, pharmaceuticals/biotechnology, food, chemical/mechanical engineering, consultancy, and power generation, among others, and in software suppliers and contract research laboratories. Very comprehensive answers were received by 37 companies, mostly from Europe (operating globally), but answers were also provided by companies in the USA and Japan. The response rate was about 60%, compared to 47% in the year 2010. The paper is written in such a way that both the majority and minority points of view are presented, and although the discussion is focused on needs and challenges, the benefits of thermodynamics and success stories are also reported. The results of the survey are thematically structured and cover changes, challenges, and further needs for a number of areas of interest such as data, models, systems, properties, and computational aspects (molecular simulation, algorithms and standards, and digitalization). Education and collaboration are discussed and recommendations on the future research activities are also outlined. In addition, a few initiatives, books, and reviews published in the past decade are briefly discussed. It is a long paper and, to provide the reader with a more complete understanding of the survey, many (anonymous) quotations (indicated with "..." and italics) from the industrial colleagues who have participated in the survey are provided. To help disseminate the specific information of interest only to particular industrial sectors, the paper has been written in such a way that the individual sections can also be read independently of each other.

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.

Characterization of Long Linear and Branched Alkanes and Alcohols for Temperatures up to 573.15 K by Surface Light Scattering and Molecular Dynamics Simulations.

This work contributes to the characterization of long linear and branched alkanes and alcohols via the determination of their thermophysical properties up to temperatures of 573.15 K. For this, experimental techniques including surface light scattering (SLS) and molecular dynamics (MD) simulations were used under equilibrium conditions to analyze the influences of chain length, branching, and hydroxylation on liquid density, liquid viscosity, and surface tension. For probing these effects, 12 pure model systems given by the linear alkanes n-dodecane, n-hexadecane, n-octacosane, n-triacontane, and n-tetracontane, the linear alcohols 1-dodecanol, 1-hexadecanol, and 1,12-dodecanediol, the branched alkanes 2,2,4,4,6,8,8-heptamethylnonane (HMN) and 2,6,10,15,19,23-hexamethyltetracosane (squalane), and the branched alcohols 2-butyl-1-octanol and 2-hexyl-1-decanol were investigated at or close to saturation conditions at temperatures between 298.15 and 573.15 K. Based on the experimental results for the liquid densities, liquid viscosities, and surface tensions with average expanded uncertainties (k = 2) of 0.061, 2.1, and 2.6%, respectively, the performance of the three commonly employed force fields (FFs) TraPPE, MARTINI, and L-OPLS was assessed in MD simulations. To improve the simulation results for the best-performing all-atom L-OPLS FF at larger temperatures, a modified version was suggested. This incorporates a temperature dependence for the energy parameters of the Lennard-Jones potential obtained by calibrating only against the experimental liquid density data of n-dodecane. By transferring this approach to all other systems studied, the modified L-OPLS FF shows now a distinctly better representation of the equilibrium and transport properties of the long alkanes and alcohols, especially at high temperatures.

Kirkwood-Buff Integrals Using Molecular Simulation: Estimation of Surface Effects.

Kirkwood-Buff (KB) integrals provide a connection between microscopic properties and thermodynamic properties of multicomponent fluids. The estimation of KB integrals using molecular simulations of finite systems requires accounting for finite size effects. In the small system method, properties of finite subvolumes with different sizes embedded in a larger volume can be used to extrapolate to macroscopic thermodynamic properties. KB integrals computed from small subvolumes scale with the inverse size of the system. This scaling was used to find KB integrals in the thermodynamic limit. To reduce numerical inaccuracies that arise from this extrapolation, alternative approaches were considered in this work. Three methods for computing KB integrals in the thermodynamic limit from information of radial distribution functions (RDFs) of finite systems were compared. These methods allowed for the computation of surface effects. KB integrals and surface terms in the thermodynamic limit were computed for Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) fluids. It was found that all three methods converge to the same value. The main differentiating factor was the speed of convergence with system size L. The method that required the smallest size was the one which exploited the scaling of the finite volume KB integral multiplied by L. The relationship between KB integrals and surface effects was studied for a range of densities.

Defining New Limits in Gas Separations Using Modified ZIF Systems.

Zeolitic-imidazolate frameworks (ZIFs) are candidate materials for the next generation of membranes for cheaper, "greener" separations. More than a decade after ZIF introduction, the high propylene/propane selectivity of ZIF-8 and ZIF-67 is the only example of ZIF membranes with remarkable selectivity efficiency despite their numerous advantages over other families of materials. Herein, we demonstrate the effectiveness of molecular-scale modification in the design of new ZIF materials useful for the separation of important and highly challenging mixtures such as He/CH4, H2/CH4, O2/N2, CO2/CH4, and CO2/N2. Via computational methods, metal and linker substitutions are employed to produce new ZIF-8 variants with a finely discretized range of aperture sizes, as these govern the kinetic-based selectivity of the material. The permeability and selectivity through the ZIF-8 variants of the gases under study are estimated, and their performance is compared with an extensive number of polymeric, metal-organic framework, covalent-organic framework, and mixed-matrix membranes. The comparison shows that some of the ZIF-8 analogues can be used as membranes of unprecedented high separation performance. The scope of this work is to highlight the effectiveness of the molecular level design as means of membrane development to address the global need for cheaper separation methods and CO2 emission reduction.

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.

Molecular Dynamics Simulation of Pure n-Alkanes and Their Mixtures at Elevated Temperatures Using Atomistic and Coarse-Grained Force Fields.

The properties of higher n-alkanes and their mixtures is a topic of significant interest for the oil and chemical industry. However, the experimental data at high temperatures are scarce. The present study focuses on simulating n-dodecane, n-octacosane, their binary mixture at a n-dodecane mole fraction of 0.3, and a model mixture of the commercially available hydrocarbon wax SX-70 to evaluate the performance of several force fields on the reproduction of properties such as liquid densities, surface tension, and viscosities. Molecular dynamics simulations over a broad temperature range from 323.15 to 573.15 K were employed in examining a broad set of atomistic molecular models assessed for the reproduction of experimental data. The well-established united atom TraPPE (TraPPE-UA) was compared against the all atom optimized potentials for liquid simulations (OPLS) reparametrization for long n-alkanes, L-OPLS, as well as Lipid14 and MARTINI force fields. All models qualitatively reproduce the temperature dependence of the aforementioned properties, but TraPPE-UA was found to reproduce liquid densities most accurately and consistently over the entire temperature range. TraPPE-UA and MARTINI were very successful in reproducing surface tensions, and L-OPLS was found to be the most accurate in reproducing the measured viscosities as compared to the other models. Our simulations show that these widely used force fields originating from the world of biomolecular simulations are suitable candidates in the study of n-alkane properties, both in the pure and mixture states.

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.

On the Efficient Separation of Gas Mixtures with the Mixed-Linker Zeolitic-Imidazolate Framework-7-8.

A recently reported modification of the zeolitic-imidazolate framework-8 (ZIF-8) with partial replacement of the 2-methylimidazolate (mIm) linker with benzimidazolate (bIm), namely ZIF-7-8, is investigated with molecular simulations using a first-time reported force field. The size of the ZIF-7-8 aperture, which governs the gas-separation efficiency of this material and which has not been estimated before for this modification, is smaller than that of the original ZIF-8. The diffusivities of CO2, N2, and CH4 estimated through transition state theory calculations result in remarkably high diffusion selectivities for CO2/CH4 and CO2/N2 mixtures. This performance enhancement is investigated in terms of structural flexibility in the form of the aperture motion through extensive estimation of the effective diameter, the total effective area, and the motion of the aperture linkers, of both ZIF-8 and ZIF-7-8. Both apertures exhibit an oscillation through the rotation of the linkers, which are adjusted according to the size of the penetrant molecules the moment they pass through it. Finally, a subsequent analysis reveals that there is strong dependency of the separation performance on the bIm-to-mIm ratio: below 33% bIm incorporation, the appearance of ZIF-8-alike wide apertures decreases dramatically the size-based selectivity of the mixtures in ZIF-7-8.

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.

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.