Transport Phenomena in Nanoporous Materials

Diffusion, that is, the irregular movement of atoms and molecules, is a universal phenomenon of mass transfer occurring in all states of matter. It is of equal importance for fundamental research and technological applications. The present review deals with the challenges of the reliable observation of these phenomena in nanoporous materials. Starting with a survey of the different variants of diffusion measurement, it highlights the potentials of “microscopic” techniques, notably the pulsed field gradient (PFG) technique of NMR and the techniques of microimaging by interference microscopy (IFM) and IR microscopy (IRM). Considering ensembles of guest molecules, these techniques are able to directly record mass transfer phenomena over distances of typically micrometers. Their concerted application has given rise to the clarification of long‐standing discrepancies, notably between microscopic equilibrium and macroscopic non‐equilibrium measurements, and to a wealth of new information about molecular transport under confinement, hitherto often inaccessible and sometimes even unimaginable.     

NMR diffusometry with beds of nanoporous host particles: an assessment of mass transfer in compartmented two-phase systems

Molecular diffusion in a bed of zeolite crystallites is mimicked by dynamic Monte Carlo simulation of a particle hopping on a two-dimensional square lattice. The resulting probability distribution of molecular propagation (the "mean propagator") is used for a rigorous determination of the resulting dependencies of diffusion measurement by pulsed field gradient NMR. In the limiting cases of intracrystalline, restricted, and long-range diffusion, these dependencies are found to coincide with the well-known relations resulting from the application of a simplifying exchange model (the "two-region" approximation). The intensity of transport resistances on the boundary between the intra- and intercrystalline spaces, i.e., on the compartment boundaries, is only accessible in the intermediate case, i.e., for observation times comparable with the mean lifetimes within the different compartments. In this case, significant differences between the results of the rigorous treatment and the "two-region" approximation may occur.     

Effect of surface resistances on the diffusion of binary mixtures in the silicalite single crystal membrane

Diffusion of methane and argon mixtures through the silicalite single-crystal membrane is studied using the dual-control volume-grand canonical molecular dynamics method to understand how surface resistances alter selectivity and permeance. Comparison of results from intracrystalline transport and entrance simulations for binary mixtures of CH4 and Ar shows that the selectivity of silicalite membranes toward Ar is enhanced in the presence of the surface resistances. In both cases, however, diffusion of faster Ar molecules was inhibited by slower diffusing CH4 molecules, whereas diffusion of the latter remained unaffected. This behavior was explained by the difference between the magnitudes of surface resistances for two molecules, which is much smaller for Ar because of its smaller permeant-crystal interaction size. We find that selectivity of the membrane at the surface depends strongly on total feed pressure and temperature, whereas this dependence is weak for intracrystalline diffusion. Furthermore, we show that the selectivity at the surface diminishes with crystal thickness until a certain thickness is reached, whereas the intracrystalline selectivity remains constant with increasing thickness. Finally, a study of diffusion of C2H6 and CF4 mixtures shows that the diatomic ethane molecules diffuse faster inside the zeolite channels, but their desorption is hindered to a larger extent than that of a spherical molecule with larger diameter and lower heat of adsorption. This observation indicates that the difference in molecular geometry is also a significant factor to explain the exit effect.     

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 相似文献   

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.     

Unexpectedly low translational mobility of methane and tetrafluoromethane in the large-pore molecular sieve VPI-5

Molecular diffusion of methane and tetrafluoromethane in the microporous material VPI-5 was studied by pulsed field gradient nuclear magnetic resonance (PFG NMR) and NMR exchange experiments. The translational mobility of both molecules in VPI-5 was found to be at least two orders of magnitude smaller than in ZSM-5. This is surprising since the channels in VPI-5 are about two times as wide as those in ZSM-5. The surprisingly small translational mobility in VPI-5 could be caused by a more complete stabilization effect or by single-file diffusion. The intracrystalline mean life time of methane in VPI-5 directly measured in the NMR tracer exchange experiments was found to be in satisfactory agreement with the value estimated on the basis of the PFG NMR data on translational mobility for ordinary intracrystalline diffusion. It must be ruled out, therefore, that molecular transportation over length scales of the order of the crystallite dimensions is controlled by single-file diffusion.     

Transport in Nanoporous Materials Including MOFs: The Applicability of Fick’s Laws

Diffusion in nanoporous host–guest systems is often considered to be too complicated to comply with such “simple” relationships as Fick’s first and second law of diffusion. However, it is shown herein that the microscopic techniques of diffusion measurement, notably the pulsed field gradient (PFG) technique of NMR spectroscopy and microimaging by interference microscopy (IFM) and IR microscopy (IRM), provide direct experimental evidence of the applicability of Fick’s laws to such systems. This remains true in many situations, even when the detailed mechanism is complex. The limitations of the diffusion model are also discussed with reference to the extensive literature on this subject.     

Imaging of transient guest profiles in nanoporous host materials: a new experimental technique to study intra-crystalline diffusion

The application of interference microscopy (IFM) and infrared microscopy (IRM) to monitoring transient concentration profiles during uptake and release of guest molecules in nanoporous materials has opened a novel technique for diffusion studies with adsorbed molecules. For the first time, the coefficients of transport diffusion and the surface permeabilities have become accessible by direct observation under non-equilibrium conditions. The examples presented in this communication include diffusion and permeation measurements with zeolites of the ferrierite type and with metal-organic frameworks (MOFs) of type ZIF-8     

Monitoring molecular mass transfer in cation-free nanoporous host crystals of type AlPO-LTA

Micro-imaging is employed to monitor the evolution of intra-crystalline guest profiles during molecular adsorption and desorption in cation-free zeolites AlPO-LTA. The measurements are shown to provide direct evidence on the rate of intra-crystalline diffusion and surface permeation and their inter-relation. Complemented by PFG NMR and integral IR measurements, a comprehensive overview of the diffusivities of light hydrocarbons in this important type of host materials is provided.     

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.     

Intracrystalline Transport Resistances in Nanoporous Zeolite X

By applying pulsed‐field gradient nuclear magnetic resonance (PFG NMR) in comparison to quasi‐elastic neutron scattering (QENS), we sense by measurement of the diffusion of n‐octane on different length scales, transport resistances in faujasite type X (which is isostructural with type Y and differs by the lower Si/Al ratio only) with mutual distances of less than 300 nm. Direct observation of the real structure of zeolite X by transmission electron microscopy identifies them as stacking faults of mirror‐twin type on (111)‐type planes of the cubic framework. Thus, direct experimental proof is given that, in general, nanoporous host systems such as zeolite crystals cannot be considered as a mere arrangement of cavities. It is rather the presence of structural defects that dominates their properties as soon as transport phenomena with practical relevance, including chemical conversion by heterogeneous catalysis and chemical separation by molecular sieving and selective adsorption, become relevant.     

The nature of surface barriers on nanoporous solids explored by microimaging of transient guest distributions

Nanoporous solids are attractive materials for energetically efficient and environmentally friendly catalytic and adsorption separation processes. Although the performance of such materials is largely dependent on their molecular transport properties, our fundamental understanding of these phenomena is far from complete. This is particularly true for the mechanisms that control the penetration rate through the outer surface of these materials (commonly referred to as surface barriers). Recent detailed sorption rate measurements with Zn(tbip) crystals have greatly enhanced our basic understanding of such processes. Surface resistance in this material has been shown to arise from the complete blockage of most of the pore entrances on the outer surface, while the transport resistance of the remaining open pores is negligibly small. More generally, the revealed correlation between intracrystalline diffusion and surface permeation provides a new view of the nature of transport resistances in nanoporous materials acting in addition to the diffusion resistance of the regular pore network, leading to a rational explanation of the discrepancy which is often observed between microscopic and macroscopic diffusion measurements.     

Sorption Kinetics and Intracrystalline Diffusion of Methanol in Ferrierite: An Example of Disguised Kinetics

Sorption kinetics of methanol in large crystals of ferrierite have been studied in detail by interference microscopy (IFM) and infra-red microscopy (IRM). The IFM measurements yield the transient concentration profiles, thus providing a direct measurement of both the surface resistance to mass transfer and the internal diffusion resistance. It is shown that, for this system, the uptake rate is controlled by the combined effects of surface resistance and diffusion through the 8-ring channels (in the y-direction). Transport through the 10-ring channels (in the z-direction) appears to be blocked by surface resistance. Although the overall uptake curves conform well to the “root t law” the diffusivity values derived from the uptake curves vary widely depending on the assumed direction of diffusion. Even if the correct direction of diffusion is assumed, the diffusivity values derived from the uptake curves are seriously in error as a result of the intrusion of surface resistance. The existence of transport resistances at the crystal surface is clearly apparent from the transient concentration profiles but is not obvious from the uptake curves.     

Measurement of Diffusion in Zeolites—A Never Ending Challenge?

A review is given on the main problems associated with the determination and interpretation of molecular diffusion in zeolites. It is shown that the diffusivities may most decisively depend on the relevant space and time scales of observation, as well as on the physical state under which the measurements are carried out. Special emphasis is given to the microscopic techniques and their most recent evidence on the existence of transport resistances distributed over the intracrystalline space.     

The Potentials of Pulsed Field Gradient NMR for Investigation of Porous Media

PFG NMR self-diffusion studies provide information on the translational mobility of fluid molecules. Since in porous media the diffusion path of fluid molecules in the pore space is affected by interaction with the pore wall, PFG NMR measurements are sensitive to structural peculiarities of the confining porous medium. The pore space properties which can be investigated depend on length scales set by the PFG NMR experiment in respect to the typical size of the structural feature studied. Based upon these length scales, an interpretation pattern for PFG NMR self-diffusion studies in porous media is given. PFG NMR self-diffusion studies in macro- and microporous systems such as sedimentary rocks and zeolite crystallites, respectively, are reviewed.     

Tracing pore-space heterogeneities in X-type zeolites by diffusion studies

Pore-space homogeneity of zeolite NaX was probed by pulsed field gradient (PFG) NMR diffusion studies with n-butane as a guest molecule. At a loading of 0.75 molecules per supercage, a wide spectrum of diffusivities was observed. Guest molecules in the (well-shaped) zeolite crystallites were thus found to experience pore spaces of quite different properties. After loading enhancement to 3 molecules per supercage, however, molecular propagation ideally followed the laws of normal diffusion in homogeneous media. At sufficiently high guest concentrations, sample heterogeneity was thus found to be of no perceptible influence on the guest mobilities anymore.     

Solvent Effect and Reactivity Trend in the Aerobic Oxidation of 1,3‐Propanediols over Gold Supported on Titania: NMR Diffusion and Relaxation Studies

In recent work, it was reported that changes in solvent composition, precisely the addition of water, significantly inhibits the catalytic activity of Au/TiO₂ catalyst in the aerobic oxidation of 1,4‐butanediol in methanol due to changes in diffusion and adsorption properties of the reactant. In order to understand whether the inhibition mechanism of water on diol oxidation in methanol is generally valid, the solvent effect on the aerobic catalytic oxidation of 1,3‐propanediol and its two methyl‐substituted homologues, 2‐methyl‐1,3‐propanediol and 2,2‐dimethyl‐1,3‐propanediol, over a Au/TiO₂ catalyst has been studied here using conventional catalytic reaction monitoring in combination with pulsed‐field gradient nuclear magnetic resonance (PFG‐NMR) diffusion and NMR relaxation time measurements. Diol conversion is significantly lower when water is present in the initial diol/methanol mixture. A reactivity trend within the group of diols was also observed. Combined NMR diffusion and relaxation time measurements suggest that molecular diffusion and, in particular, the relative strength of diol adsorption, are important factors in determining the conversion. These results highlight NMR diffusion and relaxation techniques as novel, non‐invasive characterisation tools for catalytic materials, which complement conventional reaction data.     

Solvent Effects in the Homogeneous Catalytic Reduction of Propionaldehyde with Aluminium Isopropoxide Catalyst: New Insights from PFG NMR and NMR Relaxation Studies

Solvent effects in homogeneous catalysis are known to affect catalytic activity. Whilst these effects are often described using qualitative features, such as Kamlet-Taft parameters, experimental tools able to quantify and reveal in more depth such effects have remained unexplored. In this work, PFG NMR diffusion and T₁ relaxation measurements have been carried out to probe solvent effects in the homogeneous catalytic reduction of propionaldehyde to 1-propanol in the presence of aluminium isopropoxide catalyst. Using data on diffusion coefficients it was possible to estimate trends in aggregation of different solvents. The results show that solvents with a high hydrogen-bond accepting ability, such as ethers, tend to form larger aggregates, which slow down the molecular dynamics of aldehyde molecules, as also suggested by T₁ measurements, and preventing their access to the catalytic sites, which results in the observed decrease of catalytic activity. Conversely, weakly interacting solvents, such as alkanes, do not lead to the formation of such aggregates, hence allowing easy access of the aldehyde molecules to the catalytic sites, resulting in higher catalytic activity. The work reported here is a clear example on how combining traditional catalyst screening in homogeneous catalysis with NMR diffusion and relaxation time measurements can lead to new physico-chemical insights into such systems by providing data able to quantify aggregation phenomena and molecular dynamics.     

How to compare diffusion processes assessed by single-particle tracking and pulsed field gradient nuclear magnetic resonance

Heterogeneous diffusion processes occur in many different fields such as transport in living cells or diffusion in porous media. A characterization of the transport parameters of such processes can be achieved by ensemble-based methods, such as pulsed field gradient nuclear magnetic resonance (PFG NMR), or by trajectory-based methods obtained from single-particle tracking (SPT) experiments. In this paper, we study the general relationship between both methods and its application to heterogeneous systems. We derive analytical expressions for the distribution of diffusivities from SPT and further relate it to NMR spin-echo diffusion attenuation functions. To exemplify the applicability of this approach, we employ a well-established two-region exchange model, which has widely been used in the context of PFG NMR studies of multiphase systems subjected to interphase molecular exchange processes. This type of systems, which can also describe a layered liquid with layer-dependent self-diffusion coefficients, has also recently gained attention in SPT experiments. We reformulate the results of the two-region exchange model in terms of SPT-observables and compare its predictions to that obtained using the exact transformation which we derived.     

Pivotal steps towards quantification of molecular diffusion coefficients by NMR.

Using nuclear magnetic resonance (NMR) spectroscopy with a pair of pulsed field gradients (PFGs), Stajeskal and Tanner successfully measured molecular diffusion coefficients in solution in 1965. This method has since been used extensively in various applications, especially after the PFG was implemented in commercial NMR probes. Due to the nonuniformity of the PFG and radio frequency (RF) fields, molecules distributed throughout the sample experience different PFG and RF fields and contribute unevenly to the measured diffusion coefficients, resulting in considerable errors in conventional NMR diffusion experiments. By selective excitation of a central sample region with an offset-independent adiabatic inversion pulse and a PFG, a uniform RF field can be assumed, and the PFG can be represented as a linear approximation. Under these conditions, the molecules diffuse as if they were all experiencing the same effective gradient g(e), leading to a Gaussian signal decay as a function of the PFG strength. Quantitative measurement of molecular diffusion coefficients is therefore made possible. From the diffusion coefficient of a 90 % H(2)O/10 % D(2)O sample, it is convenient to calibrate g(e) with a Java program. In a similar way the nonlinearity of the PFG can be corrected.