Jörg Kärger

The propagator representation of molecular transport in microporous crystallites

Abstract NMR diffusion data may easily be represented by the propagator, that is, by the probability that after a time interval Δ a molecule, initially at position z = 0, will be found at position z. Such a propagator representation is used for visualizing the mean features of molecular diffusion in biporous systems as, e.g., a powder sample of zeolite crystallites. As an example, propagator representations for ethane in NaX and NaCaA zeolites in dependence on the temperature and on the crystallite radii are given. The observed diffusion characteristics are in satisfactory agreement with theoretical estimates of the influence of inter- and intracrystalline transport on the overall diffusion behavior.

N.m.r. self-diffusion studies in zeolite science and technology

Abstract A review is given on the uses of nuclear magnetic resonance (n.m.r.) spectroscopy to investigate molecular migration in zeolitic adsorbate-adsorbent systems. The main parameters determining the transport properties of these systems are (a) the coefficients of intracrystalline and long-range self-diffusion, and (b) the molecular intercrystalline exchange rates. It is shown that these quantities may be determined directly by the n.m.r. pulsed field gradient technique in combination with the n.m.r. tracer desorption technique, thus allowing a complete description of the processes of molecular transport (‘diffusion analysis’). The variety of conditions to which molecular migration is subjected in the interior of the different types of zeolites gives rise to characteristic concentration dependences of intracrystalline self-diffusion. The n.m.r. studies yield at least five different patterns of concentration dependence. Being sensitive to the resonating nuclei (generally protons) of the adsorbed molecules, n.m.r. spectroscopy provides favourable conditions for self-diffusion measurements in multicomponent adsorption. Examples of diffusion studies on the mutual influence of co-adsorbed molecules, as well as on the influence of a carrier gas, are given. Under the conditions of technical application, the deposition of reaction products as well as changes in the structure of the zeolite crystallites and the whole zeolite granule may significantly affect the transport properties. As an example, the influence of a hydrothermal pretreatment on zeolite NaCaA, and the influence of a hydrocarbon atmosphere at elevated temperatures on zeolites NaCaA and HZSM-5 are studied. In all cases considered, changes in the overall transport properties may be correlated with corresponding changes in the elementary processes of molecular migration, caused by structural changes of the adsorbent.

NMR Studies of Single-File Diffusion in Unidimensional Channel Zeolites

Single-file diffusion is the restricted propagation of particles that cannot pass each other. The occurrence of this phenomenon should be reflected by a change in the time dependence of the mean particle displacement in comparison with ordinary diffusion. Although this process is considered to be the rate-controlling mechanism in a large variety of processes, so far no direct evidence of this phenomenon has been provided. Diffusion measurements made with pulsed field gradient nuclear magnetic resonance (NMR) in unidimensional pore systems (zeolites AlPO4-5 and Theta-1) reflect the expected time dependence of single-file diffusion.

Exploration of molecular dynamics during transient sorption of fluids in mesoporous materials

In recent years, considerable progress has been made in the development of novel porous materials with controlled architectures and pore sizes in the mesoporous range. An important feature of these materials is the phenomenon of adsorption hysteresis: for certain ranges of applied pressure, the amount of a molecular species adsorbed by the mesoporous host is higher on desorption than on adsorption, indicating a failure of the system to equilibrate. Although this phenomenon has been known for over a century, the underlying internal dynamics responsible for the hysteresis remain poorly understood. Here we present a combined experimental and theoretical study in which microscopic and macroscopic aspects of the relaxation dynamics associated with hysteresis are quantified by direct measurement and computer simulations of molecular models. Using nuclear magnetic resonance techniques and Vycor porous glass as a model mesoporous system, we have explored the relationship between molecular self-diffusion and global uptake dynamics. For states outside the hysteresis region, the relaxation process is found to be essentially diffusive in character; within the hysteresis region, the dynamics slow down dramatically and, at long times, are dominated by activated rearrangement of the adsorbate density within the host material.

On the comparison between macroscopic and n.m.r. measurements of intracrystalline diffusion in zeolites

The extensive intracrystalline diffusivity data that have been obtained by both macroscopic and microscopic (principally n.m.r.) methods for a wide range of zeolitic systems are reviewed. Further experimental evidence for the self-consistency of the n.m.r. diffusion data has been obtained by applying both 1H and 19F resonances to study the self-diffusion of CHF2Cl in NaX zeolite and by varying the intensity of the external magnetic field. For relatively immobile systems, there is, in general, good agreement between the diffusivity values derived from both classes of experiment, but for the more mobile systems, the n.m.r. diffusivity values are substantially higher than are the values derived from sorption rate or membrane transport measurements. For several such systems (e.g., propane-silicalite, xylenes-NaX), both the microscopic and macroscopic measurements have been confirmed by different experimental methods, in different laboratories. In such cases, it seems unlikely that the discrepancy can be explained by mere shortcomings of the individual techniques (e.g., the intrusion of extracrystalline rate processes), and we are forced to conclude that both classes of experiment measure intracrystalline migration but on different time scales. Such behaviour is consistent with a slow equilibration between mobile and immobile intracrystalline states. Tentative evidence to support such a hypothesis is provided by frequency response measurements carried out over a wide range of time scales, but this is not confirmed by the evidence from the intensity of the n.m.r. pulsed-field gradient signals.

Single-file diffusion and reaction in zeolites

Mass transfer and chemical reaction in channels in which the individual molecules cannot pass each other (single-file systems) are studied by Monte Carlo simulations. Applying a simple jump model for the elementary steps of diffusion, macroscopically observable phenomena like molecular adsorption and desorption, tracer exchange, and counterdiffusion are considered. In the case of chemical reaction, the simulation results are used for a generalization of the Thiele concept to single-file systems.

Mass transfer in mesoporous materials: the benefit of microscopic diffusion measurement

We introduce the various options of experimentally observing mass transfer in mesoporous materials. It shall be demonstrated that the exploration of the underlying mechanisms is excessively complicated by the complexity of the phenomena contributing to molecular transport in such systems and their mutual interdependence. Microscopic diffusion measurement by the pulsed field gradient (PFG) technique of NMR offers the unique option to measure both the relative amount of molecules adsorbed and the probability distribution of their displacements over space scales relevant to fundamental adsorption science just as for technological application. These advantages are shown to have cared for a recent breakthrough in our understanding. The examples presented include the measurement of diffusion in purely mesoporous materials and the rationalization of the complex concentration patterns revealed by such studies on the basis of suitably chosen micro-kinetic models. As an interesting feature, transition into the supercritical state is shown to become directly observable by monitoring a jump in the diffusivities during temperature enhancement, occurring at temperatures notably below the bulk critical temperature. PFG NMR studies with hierarchical materials are shown to permit selective diffusion measurement with each of the involved subspaces, in parallel with the measurement of the overall diffusivity as the key parameter for the technological exploitation of such materials. We refer to the occurrence of diffusion hysteresis as a novel phenomenon, found to accompany phase transitions quite in general. Though further complicating the measuring procedure and the correlation between experimental observation and the underlying mechanisms, diffusion hysteresis is doubtlessly among the new options provided by diffusion studies for gaining deeper insight into the structure and dynamics of complex porous systems.

NMR self-diffusion studies in heterogeneous systems

Abstract The principles and main limitations of the application of the NMR field gradient technique to self-diffusion measurements are discussed. Due to their higher sensitivity for small diffusion coefficients and due to several advantages with the analytical treatment of the experimental data, the pulsed gradient methods are of special importance for the investigation of heterogeneous systems. Examples of the application of these techniques to diffusion studies in multicomponent systems and bounded media are given.

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.

Microdynamics of methane, ethane and propane in ZSM-5 type zeolites

The n.m.r. pulsed field-gradient technique has been used to study systematically the intracrystalline self-diffusion of methane, ethane and propane in ZSM-5. In conjunction with the information obtained from nuclear magnetic relaxation studies the elementary steps of diffusion are found to be activated jumps between the channel intersections. Only for sorbate concentrations > 2.5 molecules per intersection is a decrease in the jump lengths observed. The results are compared with alkane self-diffusion measurements in zeolites A and X, as well as with the self-diffusion of water in ZSM-5 and zeolites A and X.