Transport Diffusivity of N2 and CO2 in Silicalite: Coherent Quasielastic Neutron Scattering Measurements and Molecular Dynamics Simulations

Molecular Diffusion in Nanoreactors' Pore Channel System: Measurement Techniques, Structural Regulation, and Catalytic Effects

Nanoreactors, as a new class of materials with highly enriched and ordered pore channel structures, can achieve special catalytic effects by precisely identifying and controlling the molecular diffusion behavior within the ordered pore channel system. Nanoreactors-driven molecular diffusion within the ordered pore channels can be highly dependent on the local microenvironment in the nanoreactors' pore channel system. Although the diffusion process of molecules within the ordered pore channels of nanoreactors is crucial for the regulation of catalytic behaviors, it has not yet been as clearly elucidated as it deserves to be in this study. In this review, fundamental theory and measurement techniques for molecular diffusion in the pore channel system of nanoreactors are presented, structural regulation strategies of pore channel parameters for controlling molecular diffusion are discussed, and the effects of molecular diffusion in the pore channel system on catalytic reactivity and selectivity are further analyzed. This article attempts to further develop the underlying theory of molecular diffusion within the theoretical framework of nanoreactor-driven catalysis, and the proposed perspectives may contribute to the rational design of advanced catalytic materials and the precise control of complex catalytic kinetics.

Measurement of Enthalpies and Entropies of Activation as a Function of Pairwise Distance for the Pairwise Relative Diffusion of SrI2 in Water over Lengthscales from 6 Å to 40 Å

Quasi-elastic neutron scattering (QENS) has been used to provide insight into the motions within solutions for many decades, and coherent QENS (CQENS) determines the motions of one ion relative to...

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.

MOF-Based Membranes for Gas Separations

Metal-organic frameworks (MOFs) represent the largest known class of porous crystalline materials ever synthesized. Their narrow pore windows and nearly unlimited structural and chemical features have made these materials of significant interest for membrane-based gas separations. In this comprehensive review, we discuss opportunities and challenges related to the formation of pure MOF films and mixed-matrix membranes (MMMs). Common and emerging separation applications are identified, and membrane transport theory for MOFs is described and contextualized relative to the governing principles that describe transport in polymers. Additionally, cross-cutting research opportunities using advanced metrologies and computational techniques are reviewed. To quantify membrane performance, we introduce a simple membrane performance score that has been tabulated for all of the literature data compiled in this review. These data are reported on upper bound plots, revealing classes of MOF materials that consistently demonstrate promising separation performance. Recommendations are provided with the intent of identifying the most promising materials and directions for the field in terms of fundamental science and eventual deployment of MOF materials for commercial membrane-based gas separations.

Structure and dynamics of ethane confined in silica nanopores in the presence of CO2

Fundamental understanding of the subcritical/supercritical behavior of key hydrocarbon species inside nano-porous matrices at elevated pressure and temperature is less developed compared to bulk fluids, but this knowledge is of great importance for chemical and energy engineering industries. This study explores in detail the structure and dynamics of ethane (C2H6) fluid confined in silica nanopores, with a focus on the effects of pressure and different ratios of C2H6 and CO2 at non-ambient temperature. Quasi-elastic neutron scattering (QENS) experiments were carried out for the pure C2H6, C2H6:CO2 = 3:1, and 1:3 mixed fluids confined in 4-nm cylindrical silica pores at three different pressures (30 bars, 65 bars, and 100 bars) at 323 K. Two Lorentzian functions were required to fit the spectra, corresponding to fast and slow translational motions. No localized motions (rotations and vibrations) were detected. Higher pressures resulted in hindrances of the diffusivity of C2H6 molecules in all systems investigated. Pore size was found to be an important factor, i.e., the dynamics of confined C2H6 is more restricted in smaller pores compared to the larger pores used in previous studies. Molecular dynamics simulations were performed to complement the QENS experiment at 65 bars, providing supportive structure information and comparable dynamic information. The simulations indicate that CO2 molecules are more strongly attracted to the pore surface compared to C2H6. The C2H6 molecules interacting with or near the pore surface form a dense first layer (L1) close to the pore surface and a second less dense layer (L2) extending into the pore center. Both the experiments and simulations revealed the role that CO2 molecules play in enhancing C2H6 diffusion ("molecular lubrication") at high CO2:C2H6 ratios. The energy scales of the two dynamic components, fast and slow, quantified by both techniques, are in very good agreement. Herein, the simulations identified the fast component as the main contributor to the dynamics. Molecule motions in the L2 region are mostly responsible for the dynamics (fast and slow) that can be detected by the instrument.

Structure and Gas Transport at the Polymer-Zeolite Interface: Insights from Molecular Dynamics Simulations

We investigate the structure of polyimide (PI) at the surface of a silicalite zeolite (MFI), as part of a model hybrid organic-inorganic mixed matrix membrane system, through equilibrium molecular dynamics simulations. Furthermore, we report a comparison of the adsorption and transport characteristics of pure components CO₂ and CH₄ in PI, MFI, and PI-MFI composite membranes. It is seen that incorporation of MFI zeolite into PI results in the formation of densified polymer layers (rigidified region) near the surface, having thickness around 1.2 nm, before bulklike behavior of the polymer is attained, contrary to empirical fits suggesting the existence of an approximately 1 μm thick interface between the polymer and filler. This region offers an extra resistance to gas diffusion especially for the gas with a larger kinetic diameter, CH₄, thus improving the CO₂/CH₄ kinetic selectivity in the PI-MFI composite membrane. Furthermore, we find that the kinetic selectivity of CO₂ over CH₄ in the rigidified region increases with temperature and that additivity of transport resistances in MFI, interfacial layer, and bulklike region of the polymer satisfactorily explains transport behavior in the composite sandwich investigated. The gas adsorption isotherms are extracted considering the dynamics and structural transitions in the PI and PI-MFI composite upon gas adsorption, and it is seen that the rigidified layer affects the gas adsorption in the polymer in the PI-MFI hybrid system. A significant increase in CO₂/CH₄ selectivity as well as gas permeability is observed in the PI-MFI composite membrane compared to that in the pure PI polymer membrane, which is correlated with the high selectivity of the rigidified interfacial layer in the polymer. Thus, while enhancing transport resistance, the rigidified layer is beneficial to membrane selectivity, leading to improved performance based on the Robeson upper bound plot for polymers.

CO2 Capture and Separations Using MOFs: Computational and Experimental Studies

This Review focuses on research oriented toward elucidation of the various aspects that determine adsorption of CO₂ in metal-organic frameworks and its separation from gas mixtures found in industrial processes. It includes theoretical, experimental, and combined approaches able to characterize the materials, investigate the adsorption/desorption/reaction properties of the adsorbates inside such environments, screen and design new materials, and analyze additional factors such as material regenerability, stability, effects of impurities, and cost among several factors that influence the effectiveness of the separations. CO₂ adsorption, separations, and membranes are reviewed followed by an analysis of the effects of stability, impurities, and process operation conditions on practical applications.

Molecular dynamics simulations of propane in slit shaped silica nano-pores: direct comparison with quasielastic neutron scattering experiments

MD simulations reveal the origin of anomalous pressure dependence of propane diffusion in silica mesopores.

Probing the hydrogen equilibrium and kinetics in zeolite imidazolate frameworks via molecular dynamics and quasi-elastic neutron scattering experiments

The problem of simulating processes involving equilibria and dynamics of guest sorbates within zeolitic imidazolate frameworks (ZIF) by means of molecular dynamics (MD) computer experiments is of growing importance because of the promising role of ZIFs as molecular "traps" for clean energy applications. A key issue for validating such an atomistic modeling attempt is the possibility of comparing the MD results, with real experiments being able to capture analogous space and time scales to the ones pertained to the computer experiments. In the present study, this prerequisite is fulfilled through the quasi-elastic neutron scattering technique (QENS) for measuring self-diffusivity, by elaborating the incoherent scattering signal of hydrogen nuclei. QENS and MD experiments were performed in parallel to probe the hydrogen motion, for the first time in ZIF members. The predicted and measured dynamics behaviors show considerable concentration variation of the hydrogen self-diffusion coefficient in the two topologically different ZIF pore networks of this study, the ZIF-3 and ZIF-8. Modeling options such as the flexibility of the entire matrix versus a rigid framework version, the mobility of the imidazolate ligand, and the inclusion of quantum mechanical effects in the potential functions were examined in detail for the sorption thermodynamics and kinetics of hydrogen and also of deuterium, by employing MD combined with Widom averaging towards studying phase equilibria. The latter methodology ensures a rigorous and efficient way for post-processing the dynamics trajectory, thereby avoiding stochastic moves via Monte Carlo simulation, over the large number of configurational degrees of freedom a nonrigid framework encompasses.

Influence of adsorption thermodynamics on guest diffusivities in nanoporous crystalline materials

Published experimental data, underpinned by molecular simulations, are used to highlight the strong influence of adsorption thermodynamics on diffusivities of guest molecules inside ordered nanoporous crystalline materials such as zeolites, metal-organic frameworks (MOFs), and zeolitic imidazolate frameworks (ZIFs). For cage-type structures (e.g. LTA, CHA, DDR, and ZIF-8), the variation of the free energy barrier for inter-cage hopping across the narrow windows, -δFi, provides a rationalization of the observed strong influence of pore concentrations, ci, on diffusivities. In open structures with large pore volumes (e.g. FAU, IRMOF-1, CuBTC) and within channels (MFI, BEA, MgMOF-74, MIL-47, MIL-53), the pore concentration (ci) dependence of the self- (Di,self), Maxwell-Stefan (Đi), and Fick (Di) diffusivities are often strongly dictated by the inverse thermodynamic correction factor, 1/Γi≡∂ln ci/∂ln pi; the magnitudes of the diffusivities are dictated by the binding energies for adsorption. For many guest-host combinations Đi-ci dependence is directly related to the 1/Γivs. ci variation. When molecular clustering occurs, we get 1/Γi > 1, causing unusual Đivs. ci dependencies. The match, or mis-match, between the periodicity of the pore landscape and the conformations of adsorbed chain molecules often leads to non-monotonic variation of diffusivities with chain lengths.

Sorbents for CO(2) capture from flue gas--aspects from materials and theoretical chemistry

Predictions of future climate change have triggered a search for ways to reduce the release of greenhouse gases into the atmosphere. Carbon capture and storage (CCS) assists this goal by reducing carbon dioxide emissions, and CO(2) adsorbents in particular can reduce the costs of CO(2) capture. Here, we review the nanoscale sorbent materials that have been developed and the theoretical basis for their function in CO(2) separation, particularly from N(2)-rich flue gases.

Self and transport diffusivity of CO2 in the metal-organic framework MIL-47(V) explored by quasi-elastic neutron scattering experiments and molecular dynamics simulations

Quasi-elastic neutron scattering measurements are combined with molecular dynamics simulations to determine the self-diffusivity, corrected diffusivity, and transport diffusivity of CO(2) in the metal-organic framework MIL-47(V) (MIL = Materials Institut Lavoisier) over a wide range of loading. The force field used for describing the host/guest interactions is first validated on the thermodynamics of the MIL-47(V)/CO(2) system, prior to being transferred to the investigations of the dynamics. A decreasing profile is then deduced for D(s) and D(o) whereas D(t) presents a non monotonous evolution with a slight decrease at low loading followed by a sharp increase at higher loading. Such decrease of D(t) which has never been evidenced in any microporous systems comes from the atypical evolution of the thermodynamic correction factor that reaches values below 1 at low loading. This implies that, due to intermolecular interactions, the CO(2) molecules in MIL-47(V) do not behave like an ideal gas. Further, molecular simulations enabled us to elucidate unambiguously a 3D diffusion mechanism within the pores of MIL-47(V).

Assessing guest diffusivities in porous hosts from transient concentration profiles

Using the short-chain-length alkanes from ethane to n-butane as guest molecules, transient concentration profiles during uptake or release (via interference microscopy) and tracer exchange (via IR microimaging) in Zn(tbip), a particularly stable representative of a novel family of nanoporous materials (the metal organic frameworks), were recorded. Analyzing the spatiotemporal dependence of the profiles provides immediate access to the transport diffusivities and self-diffusivities, yielding a data basis of unprecedented reliability for mass transfer in nanoporous materials. As a particular feature of the system, self- and transport diffusivities may be combined to estimate the rate of mutual passages of the guest molecules in the chains of pore segments, thus quantifying departure from a genuine single-file system.

Diffusion and separation of CO2 and CH4 in silicalite, C168 schwarzite, and IRMOF-1: a comparative study from molecular dynamics simulation

Recently we have investigated the storage and adsorption selectivity of CO(2) and CH(4) in three different classes of nanoporous materialssilicalite, IRMOF-1, and C(168) schwarzite through Monte Carlo simulation (Babarao, R.; Hu, Z.; Jiang, J. Langmuir, 2007, 23, 659). In this work, the self-, corrected, and transport diffusivities of CO(2) and CH(4) in these materials are examined using molecular dynamics simulation. The activation energies at infinite dilution are evaluated from the Arrhenius fits to the diffusivities at various temperatures. As loading increases, the self-diffusivities in the three frameworks decrease as a result of the steric hindrance; the corrected diffusivities remain nearly constant or decrease approximately linearly depending on the adsorbate and framework; and the transport diffusivities generally increase except for CO(2) in IRMOF-1. The correlation effects are identified to reduce from MFI, C(168) to IRMOF-1, in accordance with the porosity increasing in the three frameworks. Predictions of self-, corrected, and transport diffusivities for pure CO(2) and CH(4) from the Maxwell-Stefan formulation match the simulation results well. In a CO(2)/CH(4) mixture, the self-diffusivities decreases with loading, and good agreement is found between simulated and predicted results. On the basis of the adsorption and self-diffusivity in the mixture, the permselectivity is found to be marginal in IRMOF-1, slightly enhanced in MFI, and greatest in C(168) schwarzite. Although IRMOF-1 has the largest storage capacity for CH(4) and CO(2), its selectivity is not satisfactory.

Kinetics of molecular transport in a nanoporous crystal studied by confocal Raman microspectrometry: single-file diffusion in a densely filled tunnel

Confocal Raman microspectrometry has been used as an in situ probe of the transport of guest molecules along the one-dimensional tunnels in a crystalline urea inclusion compound, under conditions of guest exchange in which "new" guest molecules (pentadecane) are introduced at one end of the tunnel and displace the "original" guest molecules (1,8-dibromooctane). The Raman spectra, recorded as a function of position along the tunnel direction and as a function of time, have been used to establish details of the kinetics of the guest transport process. In particular, the transport of the new pentadecane guest molecules along the tunnel is found to exhibit a linear dependence on time, with the rate of the process in the region of 70-100 nm s-1. Mechanistic aspects relating to the guest transport process are discussed.

Intracrystalline Diffusivities and Surface Permeabilities Deduced from Transient Concentration Profiles: Methanol in MOF Manganese Formate

The intracrystalline concentration profiles during molecular uptake of methanol by an initially empty, single crystal of microporous manganese(II) formate (Mn(HCO2)2), representing an ionic inorganic-organic hybrid within the MOF family, are monitored by interference microscopy. Within these profiles, a crystal section could be detected where over the total of its extension ( approximately 2 microm x 50 microm x 30 microm) molecular uptake ideally followed the pattern of one-dimensional diffusion. Analysis of the evolution of intracrystalline concentration in this section directly yields the permeability of the crystal surface and the intracrystalline diffusivity as a function of the concentration of the total range of 0 <or= theta <or= 0.57 covered in the experiments. Within this range, the surface permeability is found to increase by 1 order of magnitude, while, within the limits of accuracy (+/-30%), the transport diffusivity remains constant, thus reflecting the properties of the lattice gas model.

Mesoscopic simulations of the diffusivity of ethane in beds of NaX zeolite crystals: Comparison with pulsed field gradient NMR measurements

Mesoscopic kinetic Monte Carlo simulations and pulsed field gradient nuclear magnetic resonance (PFG NMR) measurements are compared in order to investigate the transport of ethane in a bed of NaX crystals. A novel molecular mechanics particle-based reconstruction method is employed for the digital representation of the bed, enabling for the first time a parallel study of the real system and of a computer model tailored to reproduce the void fraction, particle shape and average size of the real system. Simulation of the long-range diffusion of ethane in the bed over the Knudsen, transient, and molecular diffusion regimes is consistent with the PFG NMR measurements in yielding tortuosity factors which depend upon the regime of diffusion; more specifically, tortuosity factors defined in the conventional way are higher in the Knudsen than in the molecular diffusion regime. Detailed statistical analysis of the computed molecular trajectories reveals that this difference arises in a nonexponential distribution of the lengths and in a correlation between the directions of path segments traversed between collisions with the solid in the Knudsen regime. When the Knudsen tortuosity is corrected to account for these features, a single, regime-independent value is obtained within the error of the calculations.

Loading dependence of the diffusion coefficient of methane in nanoporous materials

In this work, we use molecular simulations to study the loading dependence of the self-and collective diffusion coefficients of methane in various zeolite structures. To arrive at a microscopic interpretation of the loading dependence, we interpret the diffusion behavior in terms of hopping rates over a free-energy barrier. These free-energy barriers are computed directly from a molecular simulation. We show that these free-energy profiles are a convenient starting point to explain a particular loading dependence of the diffusion coefficient. On the basis of these observations, we present a classification of zeolite structures for the diffusion of methane as a function of loading: three-dimensional cagelike structures, one-dimensional channels, and intersecting channels. Structures in each of these classes have their loading dependence of the free-energy profiles in common. An important conclusion of this work is that diffusion in nanoporous materials can never be described by one single effect so that we need to distinguish different loading regimes to describe the diffusion over the entire loading range.

Transport diffusion of gases is rapid in flexible carbon nanotubes

Molecular dynamics simulations of rigid, defect-free single-walled carbon nanotubes have previously suggested that the transport diffusivity of gases adsorbed in these materials can be orders of magnitude higher than any other nanoporous material (A. I. Skoulidas et al., Phys. Rev. Lett. 2002, 89, 185901). These simulations must overestimate the molecular diffusion coefficients because they neglect energy exchange between the diffusing molecules and the nanotube. Recently, Jakobtorweihen et al. have reported careful simulations of molecular self-diffusion that allow nanotube flexibility (Phys. Rev. Lett. 2005, 95, 044501). We have used the efficient thermostat developed by Jakobtorweihen et al. to examine the influence of nanotube flexibility on the transport diffusion of CH4 in (20,0) and (15,0) nanotubes. The inclusion of nanotube flexibility reduces the transport diffusion relative to the rigid nanotube by roughly an order of magnitude close to zero pressure, but at pressures above about 1 bar the transport diffusivities for flexible and rigid nanotubes are very similar, differing by less than a factor or two on average. Hence, the transport diffusivities are still extremely large compared to other known materials when flexibility is taken into account.

Influence of isotherm inflection on the loading dependence of the diffusivities of n-hexane and n-heptane in MFI zeolite. Quasi-elastic neutron scattering experiments supplemented by molecular simulations

Quasi-Elastic Neutron Scattering (QENS) experiments were carried out to determine (a) Fick diffusivity, D (b) self-diffusivity, Dself, and (c) 1/Gamma, the inverse of the thermodynamic correction factor, for n-hexane (nC6) and n-heptane (nC7) in MFI zeolite (all silica silicalite-1) at 300 K for a variety of loadings. These experimental results are compared with configurational-bias Monte Carlo (CBMC) and molecular dynamics (MD) simulations of, respectively, the adsorption isotherms and diffusivities. For n-hexane, the CBMC simulated isotherm shows a slight inflection at a loading=4 molecules per unit cell; this inflection manifests, also, in the loading dependence of 1/Gamma, obtained from QENS. The trend in the loading dependence of the Fick D and Dself of nC6 obtained from QENS matches the MD simulation results. For nC7 the CBMC simulated isotherm shows a strong inflection at a loading=4 molecules per unit cell. At this loading=4, 1/Gamma tends to zero and there is a very good match between QENS and molecular simulations for the loading dependence of 1/Gamma. Both MD simulations and QENS data on the Fick diffusivity shows a sharp maximum at a loading in the region of=4. For both nC6 and nC7 the simulated values of diffusivity are about an order of magnitude higher than those determined from QENS.

Modeling the Concentration Dependence of the Methanol Self-Diffusivity in Faujasite Systems: Comparison with the Liquid Phase

Molecular dynamics simulations were performed to understand further the concentration dependence of the self-diffusion of methanol in the faujasite zeolite systems. The evolution of the self-diffusivity was investigated as a function of coverage for DAY and NaY systems to study the effect of both the pore confinement and the presence of the extraframework cations within the supercage. It was found that the self-diffusivity decreases with loading for DAY, whereas for NaY it passes through a maximum at intermediate coverage, in agreement with pulse-field gradient NMR and quasi elastic neutron scattering data reported in similar systems. The activation energies of the methanol diffusion corresponding to a combination of both intra- and intercage motions were evaluated as a function of the coverage. The simulated trends are interpreted on the basis of the predominant interactions which take place in both systems. Finally, the preferential arrangement of the adsorbate molecules are provided and compared with those simulated in the liquid phase. For the fully loaded materials, it was seen that the methanol molecules form a one-dimensional hydrogen-bonded chain along the channels in DAY whereas only dimers are present in NaY.