New Perspectives for Evaluating the Mass Transport in Porous Catalysts and Unfolding Macro- and Microkinetics

In this article we shed light on newly emerging perspectives to characterize and understand the interplay of diffusive mass transport and surface catalytic processes in pores of gas phase metal catalysts. As a case study, nanoporous gold, as an interesting example exhibiting a well-defined pore structure and a high activity for total and partial oxidation reactions is considered. PFG NMR (pulsed field gradient nuclear magnetic resonance) measurements allowed here for a quantitative evaluation of gas diffusivities within the material. STEM (scanning transmission electron microscopy) tomography furthermore provided additional insight into the structural details of the pore system, helping to judge which of its features are most decisive for slowing down mass transport. Based on the quantitative knowledge about the diffusion coefficients inside a porous catalyst, it becomes possible to disentangle mass transport contributions form the measured reaction kinetics and to determine the kinetic rate constant of the underlying catalytic surface reaction. In addition, predictions can be made for an improved effectiveness of the catalyst, i.e., optimized conversion rates. This approach will be discussed at the example of low-temperature CO oxidation, efficiently catalysed by npAu at 30 °C. The case study shall reveal that novel porous materials exhibiting well-defined micro- and mesoscopic features and sufficient catalytic activity, in combination with modern techniques to evaluate diffusive transport, offer interesting new opportunities for an integral understanding of catalytic processes.

Graphical Abstract

Influence of vanillic acid immobilization in Nafion membranes on intramembrane diffusion and structural properties

Pulsed field gradient (PFG) NMR in combination with quasielastic neutron scattering (QENS) was used to investigate self-diffusion of water and acetone in Nafion membranes with and without immobilized vanillic acid (VA). Complementary characterization of these membranes was performed by small angle X-ray scattering (SAXS) and NMR relaxometry. This study was motivated by the recent data showing that an organic acid, such as VA, in Nafion can preserve its catalytic activity in the presence of water even at high intra-polymer water concentrations corresponding up to 100% ambient relative humidity. However, there is currently no clear understanding of how immobilized organic acid molecules influence the microscopic transport properties and related structural properties of Nafion. Microscopic diffusion data measured by PFG NMR and QENS are compared for Nafion with and without VA. For displacements smaller than the micrometer-sized domains previously reported for Nafion, the VA addition was not observed to lead to any significant changes in the water and/or acetone self-diffusivity measured by each technique inside Nafion. However, the reported PFG NMR data present evidence of a different influence of acetone concentration in the membranes with and without VA on the water permeance of the interfaces between neighboring micrometer-sized domains. The reported diffusion data are correlated with the results of SAXS structural characterization and NMR relaxation data for water and acetone.

Unblocking A Rigid Purine MOF for Kinetic Separation of Xylenes

The separation of xylene isomers still remains an industrially challenging task. Here, porous purine-based metal-organic frameworks (MOFs) have been synthesized and studied for their potential in xylene separations. In particular,...

Transition between Different Diffusion Regimes and Its Relationship with Structural Properties in Nafion by High Field Diffusion NMR in Combination with Small-Angle X-ray and Neutron Scattering

Pulsed field gradient (PFG) NMR at high field was utilized to directly observe a transition between two different diffusion regimes in a Nafion 117 membrane loaded with water and acetone. Although water self-diffusivity at small water loadings was observed to be diffusion time-independent in the limit of small and large diffusion times, it showed a significant decrease with increasing diffusion time at intermediate times corresponding to root mean square displacements on the order of several microns. Under our experimental conditions, no self-diffusivity dependence on diffusion time was found for water at large water loadings and for acetone at all studied acetone loadings. The diffusion time-dependent self-diffusivity at small water concentration is explained by the existence of finite domains of interconnected water channels with sizes in the range of several microns that form in Nafion in the presence of acetone. The domain sizes and permeance of transport barriers separating adjacent domains are estimated based on the measured PFG NMR data. At large water concentrations, the water channels form a fully interconnected network, resulting in time-independent self-diffusivity. The absence of such a percolation-like transition with increasing molecular concentration for acetone is attributed to a difference in the regions available for water and acetone diffusion in Nafion. The diffusion data are correlated with and supported by structural data obtained using small-angle X-ray and neutron scattering techniques. These techniques reveal distinct water channels with radial dimensions in the nanometer range increasing upon water addition, while acetone appears to be in an interfacial perfluoroether region, reducing the size of the radial channel dimension.

Relationship between Ethane and Ethylene Diffusion inside ZIF-11 Crystals Confined in Polymers to Form Mixed-Matrix Membranes

Self-diffusivities of ethane were measured by multinuclear pulsed field gradient (PFG) NMR inside zeolitic imidazolate framework-11 (ZIF-11) crystals dispersed in several selected polymers to form mixed-matrix membranes (MMMs). These diffusivities were compared with the corresponding intracrystalline self-diffusivities in ZIF-11 crystal beds. It was observed that the confinement of ZIF-11 crystals in ZIF-11 / Torlon MMM can lead to a decrease in the ethane intracrystalline self-diffusivity. Such diffusivity decrease was observed at different temperatures used in this work. PFG NMR measurements of the temperature dependence of the intracrystalline self-diffusivity of ethylene in the same ZIF-11 / Torlon MMM revealed similar diffusivity decrease as well as an increase in the diffusion activation energy in comparison to those in unconfined ZIF-11 crystals in a crystal bed. These observations for ethane and ethylene were attributed to the reduction of the flexibility of the ZIF-11 framework due to the confinement in Torlon leading to a smaller effective aperture size of ZIF-11 crystals. Surprisingly, the intra-ZIF diffusion selectivity for ethane and ethylene was not changed appreciably by the confinement of ZIF-11 crystals in Torlon in comparison to the selectivity in a bed of ZIF-11 crystals. No ZIF-11 confinement effects leading to a reduction in the intracrystalline self-diffusivity of ethane and ethylene were observed for the other two studied MMM systems: ZIF-11 / Matrimid and ZIF-11 / 6FDA-DAM. The absence of the confinement effect in the latter MMMs can be related to the lower values of the polymer bulk modulus in these MMMs in comparison to that in ZIF-11 / Torlon MMM. In addition, there may be a contribution from possible differences in the ZIF-11/polymer adhesion in different MMM types.

Self-diffusion of pure and mixed gases in mixed-linker zeolitic imidazolate framework-7-8 by high field diffusion NMR

Self-diffusion of pure gases including carbon dioxide, methane, ethylene, ethane, and xenon as well as selected two-component mixtures was studied in hybrid zeolitic imidazolate framework-7-8 (ZIF-7-8) crystals using pulsed field gradient (PFG) NMR. This material was formed by mixing 2-methylimidazolate (ZIF-8 linker) and bulkier benzimidazolate (ZIF-7 linker) in the same framework. The intracrystalline diffusion data measured in mixed-linker ZIF-7-8 was compared with the corresponding data in the parent ZIF-8 material. It was found that under the same or comparable experimental conditions the intracrystalline gas diffusion was always slower in ZIF-7-8 than in ZIF-8. This observation is consistent with the expected lower pore aperture size in ZIF-7-8 than in ZIF-8. At the same time, the ethane/ethylene diffusion selectivity was found to be similar in both ZIFs. It was also observed that for the pure studied gases larger than carbon dioxide the diffusivity ratios in ZIF-8 and ZIF-7-8 do not increase with increasing gas size at all loading pressures used. All these data are attributed to greater framework flexibility effects in ZIF-7-8 than ZIF-8. Such effects manifest themselves in a distortion and/or increase in the aperture size in the presence of large sorbates due to linker flexibility.

Single-crystal-to-single-crystal guest exchange in columnar assembled brominated triphenylamine bis-urea macrocycles

Crystals of brominated triphenylamine bis-urea macrocycles are robust materials which can undergo single-crystal-to-single-crystal guest exchange inside 1-dimensional columns.

Ethane diffusion in mixed linker zeolitic imidazolate framework-7-8 by pulsed field gradient NMR in combination with single crystal IR microscopy

Pulsed field gradient (PFG) NMR was used in combination with single crystal IR microscopy (IRM) to study diffusion of ethane inside crystals of a mixed linker zeolitic imidazolate framework (ZIF) of the type ZIF-7-8 under comparable experimental conditions. These crystals contain 2-methylimidazolate (ZIF-8 linker) and benzimidazolate (ZIF-7 linker). It was observed that the PFG NMR attenuation curves measured for ethane in ZIF-7-8 exhibit deviations from the monoexponential behaviour, thereby indicating that the ethane self-diffusivity in different crystals of a crystal bed can be different. Measurements of the ethane uptake curves performed by IRM under the same conditions in different ZIF-7-8 crystals of the bed yield different transport diffusivities thus confirming that the rate of ethane diffusion is different in different ZIF-7-8 crystals. The IRM observation that the fractions of ZIF-8 and ZIF-7 linkers are different in different ZIF-7-8 crystals allowed attributing the observed heterogeneity in diffusivities to the heterogeneity in the linker fraction. The quantitative comparison of the average ethane self-diffusivities measured by PFG NMR in ZIF-7-8 with the corresponding data on corrected diffusivities from IRM measurements revealed a good agreement between the results obtained by the two techniques. In agreement with the expectation of smaller aperture sizes in ZIF-7-8 than in ZIF-8, the average ethane self-diffusivities in ZIF-7-8 were found to be significantly lower than the corresponding self-diffusivities in ZIF-8.

Strongly Bound Sodium Dodecyl Sulfate Surrounding Single-Wall Carbon Nanotubes

NMR techniques have been widely used to infer molecular structure, including surfactant aggregation. A combination of optical spectroscopy, proton NMR spectroscopy, and pulsed field gradient NMR (PFG NMR) is used to study the adsorption number for sodium dodecyl sulfate (SDS) with single-wall carbon nanotubes (SWCNTs). Distinct transitions in the NMR chemical shift of SDS are observed in the presence of SWCNTs. These transitions demonstrate that micelle formation is delayed by SWCNTs due to the adsorption of SDS on the nanotube surface. Once the nanotube surface is saturated, the free SDS concentration increases until micelle formation is observed. Therefore, the adsorption number of SDS on SWCNTs can be determined by the changes to the apparent critical micelle concentration (CMC). PFG NMR found that SDS remains strongly bound onto the nanotube. Quantitative analysis of the diffusivity of SDS allowed calculation of the adsorption number of strongly bound SDS on SWCNTs. The adsorption numbers from these techniques give the same values within experimental error, indicating that a significant fraction of the SDS interacting with nanotubes remains strongly bound for as long as 0.5 s, which is the maximum diffusion time used in the PFG NMR measurements.

Relationship between single-file diffusion of mixed and pure gases in dipeptide nanochannels by high field diffusion NMR

Under single-file confinement, the relationship between diffusion rates of mixed and pure gases is studied experimentally for the first time and observed to differ from that for normal diffusion.

The origin of a large apparent tortuosity factor for the Knudsen diffusion inside monoliths of a samaria–alumina aerogel catalyst: a diffusion NMR study

The contribution from surface diffusion into the apparent tortuosity factor can be separated for light gases in a porous catalyst.

Relationship between Diffusion and Chemical Exchange in Mixtures of Carbon Dioxide and an Amine-Functionalized Ionic Liquid by High Field NMR and Kinetic Monte Carlo Simulations

NMR exchange spectroscopy (EXSY) and NMR diffusion spectroscopy (PFG NMR) were applied in combination with kinetic Monte Carlo (MC) simulations to investigate self-diffusion in a mixture of carbon dioxide and an amine-functionalized ionic liquid under conditions of an exchange of carbon dioxide molecules between the reacted and unreacted states in the mixture. EXSY studies enabled residence times of carbon dioxide molecules to be obtained in the two states, whereas PFG NMR revealed time-dependent effective diffusivities for diffusion times comparable with and larger than the residence times. Analytical treatment of the PFG NMR attenuation curves as well as fitting of the PFG NMR effective diffusivities by KMC simulations enabled determination of diffusivities of carbon dioxide in the reacted and unreacted states. In contrast to carbon dioxide, the ion diffusivities were found to be diffusion time independent.

Self-diffusion of carbon dioxide in samaria/alumina aerogel catalyst using high field NMR diffusometry

Pulsed field gradient (PFG) NMR was used to investigate the self-diffusion of carbon dioxide in alumina stabilized samaria aerogel catalyst, a promising porous catalyst for gas-phase reactions featuring high porosity and high surface area. For diffusion studies, the catalyst was prepared in two sample packing types, macroscopic monoliths (i.e., macroscopic cylindrical particles) and powder beds with particle sizes around 200 μm that are considered for catalytic applications. Studies of diffusion in these samples revealed how macroscopic packing influences the catalyst transport properties. Application of a high magnetic field of 17.6 T in the reported PFG NMR studies enabled diffusion measurements for relatively low carbon dioxide densities in the catalyst samples corresponding to a gas loading pressure of around 0.1 atm. As a result, it was possible to perform diffusion measurements for a large range of carbon dioxide loading pressures between 0.1 and 10 atm. The measured carbon dioxide diffusivities in the beds of catalyst particles are interpreted in the context of a simple diffusion-mediated exchange model previously used for zeolites and other porous materials.

Diffusion of methane and carbon dioxide in carbon molecular sieve membranes by multinuclear pulsed field gradient NMR

Carbon molecular sieve (CMS) membranes are promising materials for energy efficient separations of light gases. In this work, we report a detailed microscopic study of carbon dioxide and methane self-diffusion in three CMS membrane derived from 6FDA/BPDA(1:1)-DAM and Matrimid polymers. In addition to diffusion of one-component sorbates, diffusion of a carbon dioxide/methane mixture was investigated. Self-diffusion studies were performed by the multinuclear (i.e., (1)H and (13)C) pulsed field gradient (PFG) NMR technique which combines the advantages of high field (17.6 T) NMR and high magnetic field gradients (up to 30 T/m). Diffusion measurements were carried out at different temperatures and for a broad range of the root-mean-square displacements of gas molecules inside the membranes. The diffusion data obtained from PFG NMR are compared with the corresponding results of membrane permeation measurements reported previously for the same membrane types. The observed differences between the transport diffusivities and self-diffusion coefficients of carbon dioxide and methane are discussed.

Influence of water on diffusion in imidazolium-based ionic liquids: a pulsed field gradient NMR study

In this work, we applied a novel pulsed field gradient (PFG) NMR option, which combines advantages of high-field (17.6 T) NMR and high magnetic field gradients (up to 30 T/m), to study diffusion of anions, cations and water in two 1-ethyl-3-methylimidazolium-based ionic liquids. Application of high field allows for an easy recording of an NMR signal from small amounts of water added to the ionic liquids. Using high gradients is advantageous because under conditions of such gradients any susceptibility-induced inhomogeneities in the local magnetic field are expected to be negligibly small in comparison with the applied gradients. PFG NMR studies have been performed in a broad range of temperatures and for different diffusion times. The effect of water addition on the diffusion behavior of the anions and cations is discussed in the context of the presence of polar and nonpolar domains in the ionic liquids. A partial screening of the electrostatic interaction between the cations and anions in the polar domains by water is believed to be responsible for the following changes in the diffusion behavior, which were observed experimentally: (i) increase in the ion diffusivities with increasing water concentration, and (ii) decrease in the difference between the diffusion coefficient of the cation and that of the anion as water concentration increases.

Application of pulsed field gradient NMR with high gradient strength for studies of self-diffusion in lipid membranes on the nanoscale

This work demonstrates the feasibility of noninvasive studies of lipid self-diffusion in model lipid membranes on the nanoscale using proton pulsed field gradient (PFG) NMR spectroscopy with high (up to 35 T/m) gradient amplitudes. Application of high gradients affords for the use of sufficiently small diffusion times under the conditions when the width of the gradient pulses is much smaller than the diffusion time. As a result, PFG NMR studies of partially restricted or anomalous diffusion in lipid bilayers become possible over length scales as small as 100 nm. This length scale is important because it is comparable to the size of membrane domains, or lipid rafts, which are believed to exist in biomembranes. In this work, high-gradient PFG NMR has been applied to study lipid self-diffusion in three-component planar-supported multibilayers (1,2-dioleoyl- sn-glycerol-3-phosphocholine/sphingomyelin/cholesterol). The degree of lipid orientation in the bilayers was determined with (31)P NMR. A special insert was designed to mechanically align the multibilayer stack at the magic angle with respect to the direction of the constant magnetic field to address the detrimental effects of proton dipole-dipole interactions on the NMR signal. This insert is an alternative to the conventional method of magic angle orientation of lipid membranes, the goniometer probe, which is not compatible with commercial high-gradient coils because of the lack of space in the magnet bore. Macroscopic orientation of the multibilayer stacks using the insert was confirmed with (1)H NMR spectroscopic studies and the comparison of results obtained from identical experiments using a goniometer probe for orientation. Diffusion studies were carried out at three different constant magnetic field strengths ( B 0) over a range of temperatures and diffusion times. The measured diffusivities were found to be in agreement with the data obtained previously by techniques that are limited to much larger length scales of diffusion observation than high-gradient PFG NMR.

Heterogeneity of polyelectrolyte diffusion in polyelectrolyte-protein coacervates: a 1H pulsed field gradient NMR study

Proton pulsed field gradient (PFG) NMR was used to study the diffusion of poly(diallyldimethylammonium chloride) (PDADMAC) in coacervates formed from this polycation and the protein bovine serum albumin (BSA). Application of high (up to 30 T/m) magnetic field gradients in PFG NMR measurements allowed probing the diffusion of PDADMAC on a length scale of displacements as small as 100 nm in coacervates formed at different pH's and ionic strengths, i.e., conditions of varying protein-polycation interaction energy. Studies were carried out for a broad range of diffusion times and corresponding values of the mean square displacements. Several ensembles of PDADMAC polycations with different diffusivities were observed in the measured range of diffusion times. The existence of these ensembles and the pattern of their changes with increasing diffusion time support the hypothesis about the microscopic heterogeneity of PDADMAC-BSA coacervates and also provide evidence for the dynamic disintegration and reformation of dense domains.

Toward observation of single-file diffusion using the tracer zero-length column method

The tracer zero-length column (ZLC) method has been employed to study the diffusion of toluene in one-dimensional ZSM-12 and SAPO-5 zeolites. A significant deviation in the shape of the measured tracer exchange curves from monoexponential behavior was observed for toluene diffusion in both adsorbents in the limit of long-time asymptotes. In contrast, water/ZSM-12 and acetylene/SAPO-5 systems exhibit tracer exchange curves that are close to monoexponential behavior. Monoexponential curves are usually observed for systems obeying normal (Fickian) diffusion. Such diffusion is expected for the latter two systems because the diameters of both sorbates are less than the radii of their corresponding host channels. The differences in the shape of the tracer exchange curves for large and small sorbates can be explained by assuming the occurrence of anomalous, single-file diffusion for large sorbates in narrow, one-dimensional channels.

Probing lateral diffusion in lipid membranes on nanoscale by PFG NMR with high gradient strength

This work demonstrates the feasibility of noninvasive studies of diffusion on a submicrometer length scale in aligned model lipid membranes using pulsed field gradient nuclear magnetic resonance with ultrahigh (up to 35 T/m) gradient strength. Application of such gradients allows the use of sufficiently small diffusion times under conditions of narrow-pulse approximation. As a result, monitoring anomalous or restricted diffusion in lipid membranes on a length scale in the range of 100 nm becomes possible. The ability to study diffusion in lipid membranes on this length scale is very important because it is comparable with the size of biologically relevant domains (i.e., rafts), which are believed to exist in biomembranes.

Exploring the surface permeability of nanoporous particles by pulsed field gradient NMR

A new method to determine the surface permeability of nanoporous particles is proposed. It is based on the comparison of experimental data on tracer exchange and intracrystalline molecular mean square displacements as obtained by the PFG NMR tracer desorption technique with the corresponding solutions of the diffusion equation via dynamical Monte Carlo simulations. The method is found to be particularly sensitive in the "intermediate" regime, when the influence of intracrystalline diffusion and surface resistances of the nanoporous crystal on molecular transport are comparable and the conventional method fails. As an example, the surface permeabilities of two samples of zeolite NaCaA with different crystal sizes are determined with methane, as a probe molecule, at room temperature.

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.

Internal Concentration Gradients of Guest Molecules in Nanoporous Host Materials: Measurement and Microscopic Analysis

Evolution of internal concentration profiles of methanol in 2-D pore structure of ferrierite crystal was measured in the pressure range of 0 to 80 mbar with the help of the recently developed interference microscopy technique. The measured profiles showed that both a surface barrier and internal diffusion controlled the kinetics of adsorption/desorption. Furthermore, they indicated that in the main part of the crystal, the z-directional 10-ring channels were not accessible to methanol and that the transport of methanol mainly occurred via 8-ring y-directional channels. The roof-like part of the crystal was almost instantaneously filled/emptied during adsorption/desorption, indicating accessible 10-ring channels in this section. The measured profiles were analyzed microscopically with the direct application of Fick's second law, and the transport diffusivity of methanol in ferrierite was determined as a function of adsorbed phase concentration. The transport diffusivity varied by more than 2 orders of magnitude over the investigated pressure range. Transport diffusivities, calculated from measured profiles from small and large pressure step changes, were all found to be consistent. Simulated concentration profiles obtained from the solution of Fick's second law with the calculated functional dependence of diffusivities on concentration compared very well with the measured concentration profiles, indicating validity and consistency of the measured data and the calculated diffusivities. The results indicate the importance of measuring the evolution of concentration profiles as this information is vital in determining (1) the direction of internal transport, (2) the presence of internal structural defects, and (3) surface/internal transport barriers. Such detailed information is available neither from common macroscopic methods since, they measure changes in macroscopic properties and use model assumptions to predict the concentration profiles inside, nor from microscopic methods, since they only provide information on average displacement of diffusing molecules.

Single-file diffusion near channel boundaries

Molecular transport under the conditions of single-file diffusion was investigated near the channel boundaries by using dynamic Monte Carlo and molecular dynamics simulations of tracer exchange between single-file channels and their surroundings. The boundary effect reported in our recent papers (Vasenkov S.; Kärger, J. Phys. Rev. E 2002, 66, 052601. Schüring, A.; Vasenkov S.; Fritzsche, S. J. Phys. Chem. B 2005, 109, 16711) was studied in detail. This boundary effect is characterized by deviations of the intrachannel concentration profiles of tracer molecules observed in the case of single-file diffusion near the channel boundaries from the corresponding profiles typical for normal diffusion. It has been shown in our previous studies that these deviations occur under the conditions when the potential-energy difference inside and outside of single-file channels was both comparable and much larger than the activation energy of intrachannel diffusion. Here, we report a quantitative model describing the boundary effect. According to this model, an occurrence of the boundary effect is related to a complex character of diffusion in finite single-file systems. Such diffusion can be described by the following two types of movements occurring in parallel: (i) correlated displacements of all molecules in any particular channel and (ii) fast displacements of single molecules, which are uncorrelated with the displacements of all other molecules in the same channel. The latter displacements are restricted to a certain length interval that depends on the channel length and the channel occupancy. This length interval is shown to determine the extensions of the channel margins where the boundary effect is observed.

The Role of Mesopores in Intracrystalline Transport in USY Zeolite: PFG NMR Diffusion Study on Various Length Scales

PFG NMR has been applied to study intracrystalline diffusion in USY zeolite as well as in the parent ammonium-ion exchanged zeolite Y used to produce the USY by zeolite steaming. The diffusion studies have been performed for a broad range of molecular displacements and with two different types of probe molecules (n-octane and 1,3,5-triisopropylbenzene) having critical molecular diameters smaller and larger than the openings of the zeolite micropores. Our experimental data unambiguously show that, in contrast to what is usually assumed in the literature, the intracrystalline mesopores do not significantly affect intracrystalline diffusion in USY. This result indicates that the intracrystalline mesopores of USY zeolite do not form a connected network, which would allow diffusion through crystals only via mesopores.

Influence of Boundaries of Nanoporous Crystals on Molecular Exchange under the Conditions of Single-File Diffusion

We study the tracer exchange of molecules between the phase adsorbed in one-dimensional channels and the surrounding gas phase by molecular dynamics simulations. Under the conditions of single-file diffusion, a novel boundary effect is observed. The shape of the tracer-exchange concentration profiles deviates from those obtained under the conditions of normal diffusion. Compared to the profiles for normal diffusion, which correspond to the same degree of exchange, the equilibrium concentration is reached faster at the boundaries and slower in the middle part of the channel in the case of single-file diffusion. This boundary effect is observed for the system neopentane in AlPO4-5 (which was chosen as a reference system), as well as for modified systems. The effect can be understood considering two diffusion mechanisms which occur in parallel. First, the diffusion of the whole chain of particles, that is, the center-of-mass diffusion, obeying the laws of normal diffusion. Second, the individual movement of the particles relative to the center of mass of the chain. The second mechanism admits additional displacements which, on average, lead to an accelerated exchange of the marginal particles.

Sticking Probability on Zeolites

The sticking coefficient, i.e., the probability that, on hitting the surface of a nanoporous particle (zeolite), a molecule shall be able to enter the intracrystalline space, is a key quantity for the application of such materials in heterogeneous catalysis and molecular sieving. On the basis of pulsed field gradient NMR diffusion measurements and molecular dynamics simulations, typical values of this probability are found to be close to one. They exceed previous estimates on the basis of IR uptake measurements by many orders of magnitude.

Pulsed-field gradient nuclear magnetic resonance study of transport properties of fluid catalytic cracking catalysts

Pulsed-field gradient nuclear magnetic resonance (PFG NMR) has been applied to study molecular diffusion in industrial fluid catalytic cracking (FCC) catalysts and in USY zeolite for a broad range of molecular displacements and temperatures. The results of this study have been used to elucidate the relevance of molecular transport on various displacements for the rate of molecular exchange between catalyst particles and their surroundings. It turned out that this rate, which may determine the overall rate and selectivity of FCC process, is primarily related to the diffusion mode associated with displacements larger than the size of zeolite crystals located in the particles but smaller than the size of the particles. This conclusion has been confirmed by comparative studies of the catalytic performance of different FCC catalysts.

Long-range diffusion in beds of nanoporous particles: pitfalls and potentials

Owing to the recent progress in the area of hardware and software of the pulsed field gradient NMR technique, molecular transport in real-life zeolite systems, such as zeolite beds and particles of formulated fluid catalytic cracking (FCC) catalysts, can be investigated in detail. These studies have revealed a number of important features of molecular transport in zeolites, which are reviewed in the present paper. In particular, the anomalous character of intracrystalline diffusion in MFI-type zeolites, dependence of the tortuosity factor in zeolite beds on diffusion regime and the role of various modes of diffusion in transport limitations arising for catalytic reactions in FCC catalysts will be discussed.

Gas diffusion in zeolite beds: PFG NMR evidence for different tortuosity factors in the Knudsen and bulk regimes

Self-diffusion of ethane in beds of zeolite NaX is studied using Pulsed Field Gradient (PFG) NMR. The ethane diffusivities were measured for displacements, which are orders of magnitude larger than the size of individual crystals. These diffusivities were compared with those, calculated using simple gas kinetic theory. The results of the comparison indicate that for the same bed of NaX crystals the apparent tortuosity factor in the Knudsen regime ( i.e. when molecule-solid collisions dominate) is significantly larger than that in the bulk regime ( i.e. when molecule-molecule collisions dominate). This finding is attributed to the more pronounced geometrical trapping by the pore structure of the zeolite bed in the Knudsen than in the bulk regime.