Testing Predictions of Macroscopic Binary Diffusion Coefficients Using Lattice Models with Site Heterogeneity

Quantitatively predicting mass transport rates for chemical mixtures in porous materials is important in applications of materials such as adsorbents, membranes, and catalysts. Because directly assessing mixture transport experimentally is challenging, theoretical models that can predict mixture diffusion coefficients using only single-component information would have many uses. One such model was proposed by Skoulidas, Sholl, and Krishna (Langmuir, 2003, 19, 7977), and applications of this model to a variety of chemical mixtures in nanoporous materials have yielded promising results. In this paper, the accuracy of this model for predicting mixture diffusion coefficients in materials that exhibit a heterogeneous distribution of local binding energies is examined. To examine this issue, single-component and binary mixture diffusion coefficients are computed using kinetic Monte Carlo for a two-dimensional lattice model over a wide range of lattice occupancies and compositions. The approach suggested by Skoulidas, Sholl, and Krishna is found to be accurate in situations where the spatial distribution of binding site energies is relatively homogeneous, but is considerably less accurate for strongly heterogeneous energy distributions

Effects of Intrinsic Flexibility on Adsorption Properties of Metal–Organic Frameworks at Dilute and Nondilute Loadings

Molecular simulation of adsorption in nanoporous materials has become a valuable complement to experimental studies of these materials. In almost all cases, these simulations treat the adsorbing material as rigid. We use molecular simulations to examine the validity of this approximation for the adsorption in metal–organic frameworks (MOFs) that have framework flexibility without change in their unit cells because of thermal vibrations. All nanoporous materials are subject to this kind of framework flexibility. We examine the adsorption of nine molecules (CO2, CH4, ethane, ethene, propane, propene, butane, Xe, and Kr) and four molecular mixtures (CO2/CH4, ethane/ethene, propane/propene/butane, and Xe/Kr) in 100 MOFs at dilute and nondilute adsorption conditions. Our results show that single-component adsorption uptakes at nondilute conditions are only weakly affected by framework flexibility, but adsorption selectivities at both dilute and nondilute conditions can be significantly affected by flexibility. The most dramatic impacts of framework flexibility occur for adsorption uptake in the limit of dilute adsorption. These results suggest that the importance of including framework flexibility when attempting to make quantitative predictions of adsorption selectivity in MOFs and similar materials may have been underestimated in the past

Computational Model and Characterization of Stacking Faults in ZIF‑8 Polymorphs

Degradation of metal–organic frameworks (MOFs) in aqueous, humid, and acid gas environments likely begins at defect sites. Until now, however, theoretical studies of MOFs have widely assumed an ideal defect-free structure. Here we present a computational model for low-energy extended defects in bulk zeolitic imidazolate frameworks (ZIFs) that are analogous to stacking faults in zeolites. We demonstrate the thermodynamic accessibility of stacking faults in ZIFs and examine the impact of these defects on pore diffusion and accessible surface area. We identify strong correlations between the defect density of a structure and its X-ray diffraction spectra. By examining a topologically isomorphic ZIF that has been reported experimentally we find characteristic defect-induced peak broadening and splitting in the reported powder patterns, giving strong evidence for the existence for stacking faults in this material

Molecular Simulations of CH₄ and CO₂ Diffusion in Rigid Nanoporous Amorphous Materials

Molecular diffusion in nanoporous materials is important in determining the rate of equilibration of various adsorption processes and plays a pivotal role in kinetic separations and membrane-based separations. Because generating realistic structures of amorphous nanoporous materials is difficult, far less is known about diffusion in amorphous nanoporous materials than in their crystalline counterparts. Here, we present molecular dynamics simulations assessing the room-temperature self-diffusion of CH4 and CO2 in a wide range of rigid amorphous nanoporous materials, including porous carbons, kerogens, polymers of intrinsic microporosity, and hyper-cross-linked polymers. Our results are the largest collection of molecular diffusivities in amorphous nanoporous materials to date. In each material, the diffusivity increases with the adsorbate concentration at low and moderate adsorbate concentrations, reaching a maximum before decreasing due to steric effects at higher concentrations. The observed diffusivities are much slower than that would be expected based on standard descriptions of Knudsen diffusivity. We show that the observed diffusivities are not correlated in a simple way with scalar descriptors of the pore structures such as the pore limiting diameter

Molecular Simulations of CH₄ and CO₂ Diffusion in Rigid Nanoporous Amorphous Materials

Molecular diffusion in nanoporous materials is important in determining the rate of equilibration of various adsorption processes and plays a pivotal role in kinetic separations and membrane-based separations. Because generating realistic structures of amorphous nanoporous materials is difficult, far less is known about diffusion in amorphous nanoporous materials than in their crystalline counterparts. Here, we present molecular dynamics simulations assessing the room-temperature self-diffusion of CH4 and CO2 in a wide range of rigid amorphous nanoporous materials, including porous carbons, kerogens, polymers of intrinsic microporosity, and hyper-cross-linked polymers. Our results are the largest collection of molecular diffusivities in amorphous nanoporous materials to date. In each material, the diffusivity increases with the adsorbate concentration at low and moderate adsorbate concentrations, reaching a maximum before decreasing due to steric effects at higher concentrations. The observed diffusivities are much slower than that would be expected based on standard descriptions of Knudsen diffusivity. We show that the observed diffusivities are not correlated in a simple way with scalar descriptors of the pore structures such as the pore limiting diameter

Assessment of a Metal−Organic Framework Membrane for Gas Separations Using Atomically Detailed Calculations: CO₂, CH₄, N₂, H₂ Mixtures in MOF-5

Metal−organic frameworks (MOFs) have emerged as a fascinating alternative to more traditional nanoporous materials. Although hundreds of different MOF structures have been synthesized in powder form, little is currently known about the potential performance of MOFs for membrane-based separations. We have used atomistic calculations to predict the performance of a MOF membrane for separation of various gas mixtures in order to provide information for material selection in membrane design. Specifically, we investigated the performance of MOF-5 as a membrane for separation of CO2/CH4, CO2/H2, CO2/N2, CH4/H2, N2/H2, and N2/CH4 mixtures at room temperature. In every case, mixture effects play a crucial role in determining the membrane performance. Although the membrane selectivities predicted for MOF-5 are not large for the mixtures we studied, our result suggest that atomistic simulations will be a useful tool for considering the large number of MOF crystal structures that are known in order to seek membrane materials with more desirable characteristics

Effects of Intrinsic Flexibility on Adsorption Properties of Metal–Organic Frameworks at Dilute and Nondilute Loadings

Molecular simulation of adsorption in nanoporous materials has become a valuable complement to experimental studies of these materials. In almost all cases, these simulations treat the adsorbing material as rigid. We use molecular simulations to examine the validity of this approximation for the adsorption in metal–organic frameworks (MOFs) that have framework flexibility without change in their unit cells because of thermal vibrations. All nanoporous materials are subject to this kind of framework flexibility. We examine the adsorption of nine molecules (CO2, CH4, ethane, ethene, propane, propene, butane, Xe, and Kr) and four molecular mixtures (CO2/CH4, ethane/ethene, propane/propene/butane, and Xe/Kr) in 100 MOFs at dilute and nondilute adsorption conditions. Our results show that single-component adsorption uptakes at nondilute conditions are only weakly affected by framework flexibility, but adsorption selectivities at both dilute and nondilute conditions can be significantly affected by flexibility. The most dramatic impacts of framework flexibility occur for adsorption uptake in the limit of dilute adsorption. These results suggest that the importance of including framework flexibility when attempting to make quantitative predictions of adsorption selectivity in MOFs and similar materials may have been underestimated in the past

Rapid Diffusion of CH₄/H₂ Mixtures in Single-Walled Carbon Nanotubes

Equilibrium molecular dynamics (EMD) are used to examine the self-diffusion and macroscopic diffusion of CH4/H2 mixtures adsorbed inside a (10,10) single-walled carbon nanotube. EMD can be used to determine the macroscopic diffusion coefficients of adsorbed mixtures by evaluating the matrix of Onsager transport coefficients. Earlier studies have indicated the diffusion of light gases adsorbed as single components in carbon nanotubes is extremely rapid compared to that in other known nanoporous materials. The results presented here indicate that extremely rapid diffusion can also occur for mixtures of adsorbed molecules. The rapid diffusion of adsorbed molecules and the strong coupling between the fluxes of the adsorbed species in a mixture have interesting implications for uses of carbon nanotubes in membrane-based applications

Comprehensive Assessment of the Accuracy of the Ideal Adsorbed Solution Theory for Predicting Binary Adsorption of Gas Mixtures in Porous Materials

Quantifying the adsorption of chemical mixtures in porous adsorbents is critical to developing these materials for useful separation applications. The ideal adsorbed solution theory (IAST) is the most widely applied mixing theory for predicting mixture adsorption using single-component adsorption data, but a perceived lack of experimental data has limited previous efforts to explore the accuracy of IAST in a systematic way. In this paper, we take advantage of a large collection of binary experimental data for gas adsorption that became available recently (Cai. X et al., Ind. Eng. Chem. Res. 2021, 60; 639) to tackle this issue. We identify more than 400 examples in which binary adsorption data and single-component data are available in the same publication and apply IAST to all these examples. This analysis includes experimental data from 63 gas mixtures of 37 different molecular species and 174 different adsorbents. In addition to being the most systematic evaluation to date of the accuracy of IAST for gas adsorption, these data will be valuable for future efforts to test or develop mixing theories that improve upon IAST

Comprehensive Assessment of the Accuracy of the Ideal Adsorbed Solution Theory for Predicting Binary Adsorption of Gas Mixtures in Porous Materials

Quantifying the adsorption of chemical mixtures in porous adsorbents is critical to developing these materials for useful separation applications. The ideal adsorbed solution theory (IAST) is the most widely applied mixing theory for predicting mixture adsorption using single-component adsorption data, but a perceived lack of experimental data has limited previous efforts to explore the accuracy of IAST in a systematic way. In this paper, we take advantage of a large collection of binary experimental data for gas adsorption that became available recently (Cai. X et al., Ind. Eng. Chem. Res. 2021, 60; 639) to tackle this issue. We identify more than 400 examples in which binary adsorption data and single-component data are available in the same publication and apply IAST to all these examples. This analysis includes experimental data from 63 gas mixtures of 37 different molecular species and 174 different adsorbents. In addition to being the most systematic evaluation to date of the accuracy of IAST for gas adsorption, these data will be valuable for future efforts to test or develop mixing theories that improve upon IAST