Connecting theory and simulation with experiment for the study of diffusion in nanoporous solids

Nanoporous solids are ubiquitous in chemical, energy, and environmental processes, where controlled transport of molecules through the pores plays a crucial role. They are used as sorbents, chromatographic or membrane materials for separations, and as catalysts and catalyst supports. Defined as materials where confinement effects lead to substantial deviations from bulk diffusion, nanoporous materials include crystalline microporous zeotypes and metal–organic frameworks (MOFs), and a number of semi-crystalline and amorphous mesoporous solids, as well as hierarchically structured materials, containing both nanopores and wider meso- or macropores to facilitate transport over macroscopic distances. The ranges of pore sizes, shapes, and topologies spanned by these materials represent a considerable challenge for predicting molecular diffusivities, but fundamental understanding also provides an opportunity to guide the design of new nanoporous materials to increase the performance of transport limited processes. Remarkable progress in synthesis increasingly allows these designs to be put into practice. Molecular simulation techniques have been used in conjunction with experimental measurements to examine in detail the fundamental diffusion processes within nanoporous solids, to provide insight into the free energy landscape navigated by adsorbates, and to better understand nano-confinement effects. Pore network models, discrete particle models and synthesis-mimicking atomistic models allow to tackle diffusion in mesoporous and hierarchically structured porous materials, where multiscale approaches benefit from ever cheaper parallel computing and higher resolution imaging. Here, we discuss synergistic combinations of simulation and experiment to showcase theoretical progress and computational techniques that have been successful in predicting guest diffusion and providing insights. We also outline where new fundamental developments and experimental techniques are needed to enable more accurate predictions for complex systems.

Water-Induced Structural Dynamic Process in Molecular Sieves under Mild Hydrothermal Conditions: Ship-in-a-Bottle Strategy for Acidity Identification and Catalyst Modification

Water is the most important substance in nature. Imitating the formation of natural materials, molecular sieves have been synthesized under hydrothermal conditions and applied in industry. Herein, we reveal an unforeseen observation on a very special water-induced structural dynamic process of these materials. Dynamic and reversible breaking and forming of T-O-T bonds in silicoaluminophosphate (SAPO) occurs through interactions between gaseous water and the molecular-sieve framework under mild hydrothermal conditions and is confirmed by detection of the incorporation of ¹⁷ O from H₂ ¹⁷ O into molecular-sieve framework. Encapsulation of the bulky molecules trimethylphosphine and pyridine (kinetic diameters much larger than the pore size of SAPO-34) into CHA cavities consolidated the water-induced dynamic process. Consequently, new insights into the dynamic features of molecular sieves in water are provided. The ship-in-a-bottle strategy based on these findings also open new fields for fine acidity identification and gives extra boost in shape-selective catalysis.

Carbonate-Promoted Drift of Alkali Cations in Small Pore Zeolites: Ab Initio Molecular Dynamics Study of CO2 in NaKA Zeolite

An effect of deblocking of small size (8R, D8R) pores in zeolites due to cation drift is analyzed by using ab initio molecular dynamics (AIMD) at the PBE-D2/PAW level. The effect of carbonate and hydrocarbonate species on the carbon dioxide uptake in NaKA zeolite is demonstrated. It is shown that a hydrocarbonate or carbonate anion can form strong complexes with K⁺ cation and withdraw it from the 8R window, so that the probability of CO₂ diffusion through 8R increases. For the first time, correlations between cationic and HCO₃^-/CO₃^2- positions are demonstrated in favor of their significant interaction leading to the cationic drift from 8R windows. This phenomenon explains a nonzero CO₂ adsorption in narrow pore zeolites upon high Na/K exchange. In a gas mixture, such deblocking effect reduces the separation factor because of the possible passage of both components through the plane of partly open 8R windows.

Automated Multiscale Approach To Predict Self-Diffusion from a Potential Energy Field

For large-scale screening studies there is a need to estimate the diffusion of gas molecules in nanoporous materials more efficiently than (brute force) molecular dynamics. In particular for systems with low diffusion coefficients molecular dynamics can be prohibitively expensive. An alternative is to compute the hopping rates between adsorption sites using transition state theory. For large-scale screening this requires the automatic detection of the transition states between the adsorption sites along the different diffusion paths. Here an algorithm is presented that analyzes energy grids for the moving particles. It detects the energies at which diffusion paths are formed, together with their directions. This allows for easy identification of nondiffusive systems. For diffusive systems, it partitions the grid coordinates assigned to energy basins and transitions states, permitting a transition state theory based analysis of the diffusion. We test our method on CH₄ diffusion in zeolites, using a standard kinetic Monte Carlo simulation based on the output of our grid analysis. We find that it is accurate, fast, and rigorous without limitations to the geometries of the diffusion tunnels or transition states.

Assessing the Impact of Point Defects on Molecular Diffusion in ZIF-8 Using Molecular Simulations

Because defects are ubiquitous in materials, they may play an important role in affecting the performance of materials in practical applications. Here, we investigate the influence of point defects on the diffusion of molecules including water, hydrocarbons, and acid gases in zeolitic imidazolate framework-8 (ZIF-8) using molecular simulations. To make these simulations possible, we introduce a force field that extends previous descriptions of pristine ZIF-8 to include experimentally relevant point defects. In general, the point defects we examined increase the local hopping rate for molecular diffusion, suggesting that low concentrations of these defects will not dominate long-range molecular diffusion in ZIF-8.

Zeolite Adsorption Free Energies from ab Initio Potentials of Mean Force

The ability of metal-exchanged zeolites to chemisorb small gas molecules is key to their performance as heterogeneous catalysts and gas-separating agents. Here, we propose and evaluate an ab initio potential of mean force (PMF) method for computing adsorption free energies of representative small molecules to Cu-exchanged sites in SSZ-13 zeolite. We show that Cu ions are mobilized by adsorbates and, as a result, computed free energies are significantly more negative than those obtained from a conventional harmonic oscillator model. PMF-derived free energies are consistent with available experiment and, in many cases, with a dynamics-based quasi-harmonic analysis (QHA). The PMF approach avoids the artificial partitioning of degrees of freedom intrinsic to the QHA. On the basis of the PMF results, we propose a simple correlation to estimate free energies from computed adsorption energies and gas-phase entropies.

Thermodynamic evidence of flexibility in H2O and CO2 absorption of transition metal ion exchanged zeolite LTA

Absorption thermodynamics on the framework flexibility of TMI-exchanged zeolite LTA driven by water/CO₂ molecules.

Hybrid films with excellent oxygen and water vapor barrier properties as efficient anticorrosive coatings

A hydrophobic film is fabricated by spin-coating of Tween 80 modified layered double hydroxide and polydimethylsiloxane alternately, which displays enhanced oxygen/water vapor barrier properties and anti-corrosion behavior toward metal substrates.

Ab initio molecular dynamics determination of competitive O₂ vs. N₂ adsorption at open metal sites of M₂(dobdc)

The separation of oxygen from nitrogen using metal-organic frameworks (MOFs) is of great interest for potential pressure-swing adsorption processes for the generation of purified O2 on industrial scales. This study uses ab initio molecular dynamics (AIMD) simulations to examine for the first time the pure-gas and competitive gas adsorption of O2 and N2 in the M2(dobdc) (M = Cr, Mn, Fe) MOF series with coordinatively unsaturated metal centers. Effects of metal, temperature, and gas composition are explored. This unique application of AIMD allows us to study in detail the adsorption/desorption processes and to visualize the process of multiple guests competitively binding to coordinatively unsaturated metal sites of a MOF.

Highly selective uptake of carbon dioxide on the zeolite |Na10.2KCs0.8|-LTA – a possible sorbent for biogas upgrading

Zeolite |Na_10.2KCs_0.8|-LTA was found to be a promising adsorbent for applications such as biogas upgrading. The CO₂-over-CH₄ selectivity was very high (over 1500).

Chemical reduction of the elastic properties of zeolites: a comparison of the formation of carbonate species versus dealumination

The decrease in elastic moduli (Young's, bulk, and shear modulus), the variations in their asymmetries, the Poisson's ratio and the linear compressibility due to carbonate formation in NaX, have been compared to those produced by dealumination of the zeolite HY framework, from the Al-Si-Al fragment positioned in joined 4R rings. All these systems have been considered at the density functional theory (DFT) level using periodic boundary conditions. The representativeness of the models has been checked by comparison of the calculated IR spectra of carbonate and hydrocarbonate species in NaX and of hydroxyl groups in HY with the experimental equivalents. The correlation between the destabilization energy of the systems and the displacement of Na or K cations coordinated to the carbonate or hydrocarbonate species, expressed in terms of Me-O bond elongation, has been confirmed for either one or two carbonate and hydrocarbonate species per unit cell (UC). Finally, a similar reduction in elasticity in FAU zeolites has been observed, due either to carbonate/bicarbonate formation in NaX or as a step in HY dealumination.

K+ exchanged zeolite ZK-4 as a highly selective sorbent for CO2

Adsorbents with high capacity and selectivity for adsorption of CO2 are currently being investigated for applications in adsorption-driven separation of CO2 from flue gas. An adsorbent with a particularly high CO2-over-N2 selectivity and high capacity was tested here. Zeolite ZK-4 (Si:Al ∼ 1.3:1), which had the same structure as zeolite A (LTA), showed a high CO2 capacity of 4.85 mmol/g (273 K, 101 kPa) in its Na(+) form. When approximately 26 at. % of the extraframework cations were exchanged for K(+) (NaK-ZK-4), the material still adsorbed a large amount of CO2 (4.35 mmol/g, 273 K, 101 kPa), but the N2 uptake became negligible (<0.03 mmol/g, 273 K, 101 kPa). The majority of the CO2 was physisorbed on zeolite ZK-4 as quantified by consecutive volumetric adsorption measurements. The rate of physisorption of CO2 was fast, even for the highly selective sample. The molecular details of the sorption of CO2 were revealed as well. Computer modeling (Monte Carlo, molecular dynamics simulations, and quantum chemical calculations) allowed us to partly predict the behavior of fully K(+) exchanged zeolite K-ZK-4 upon adsorption of CO2 and N2 for Si:Al ratios up to 4:1. Zeolite K-ZK-4 with Si:Al ratios below 2.5:1 restricted the diffusion of CO2 and N2 across the cages. These simulations could not probe the delicate details of the molecular sieving of CO2 over N2. Still, this study indicates that zeolites NaK-ZK-4 and K-ZK-4 could be appealing adsorbents with high CO2 uptake (∼4 mmol/g, 101 kPa, 273 K) and a kinetically enhanced CO2-over-N2 selectivity.

Effect of Anharmonicity on Adsorption Thermodynamics

The effect of anharmonic corrections to the vibrational energies of extended systems is explored. Particular attention is paid to the thermodynamics of adsorption of small molecules on catalytically relevant systems typically affected by anharmonicity. The implemented scheme obtains one-dimensional anharmonic model potentials by distorting the equilibrium structure along the normal modes using both rectilinear (Cartesian) or curvilinear (internal) representations. Only in the latter case, the modes are decoupled also at higher order of the potential and the thermodynamic functions change in the expected directions. The method is applied to calculate ab initio enthalpies, entropies, and Gibbs free energies for the adsorption of methane in acidic chabazite (H-CHA) and on MgO(001) surface. The values obtained for the adsorption of methane in H-CHA (273.15 K, 0.1 MPa, θ = 0.5) are ΔH = -19.3, -TΔS = 11.9, and ΔG = -7.5 kJ/mol. For methane on the MgO(001) (47 K, 1.3 × 10(-14) MPa, θ = 1) ΔH = -14.4, -TΔS = 16.6, and ΔG = 2.1 kJ/mol are obtained. The calculated desorption temperature is 44 K, and the desorption prefactor is 4.26 × 10(12) s(-1). All calculated results agree within chemical accuracy limits with experimental data.

Zeolites and related sorbents with narrow pores for CO2 separation from flue gas

Adsorbents with small pores are especially relevant for capturing carbon dioxide at large emission sources.