Quantitating Diffusion Enhancement in Pore Hierarchies.

A microporous continuum traversed by a set of mutually perpendicular channels is considered to be a model for a hierarchically porous system of the mesoporous zeolite type. Transient profiles of molecular uptake as determined by kinetic Monte Carlo (kMC) simulation are found to be in excellent agreement with the result attained by the application of the two-region model (the Kärger model) of molecular diffusion. In particular, it is found that, in the two limiting cases referred to as fast exchange and slow exchange, there exist two simple analytical expressions for the rate of molecular uptake and hence for the quantification of transport enhancement in comparison with the purely microporous adsorbent. In the general case, transport enhancement is simply recognized by the reciprocal addition of the expressions in the two limiting cases.

Determination of the adsorption isotherms and transport diffusivities of gases in mixtures inside zeolitic crystals using Infra-Red Micro-imaging.

Different regions of Infra-Red (IR) light absorption by guest molecules inside a zeolitic crystal are measured and quantified to determine binary adsorption isotherms and transport diffusivities. This has been achieved using a vacuum capable setup which includes an Infra-Red Microscope (IRM) and Fourier Transform Infra-Red (FTIR) Spectrometer. By utilizing IR light and FTIR spectroscopy, this method can be used to describe the behavior of low concentrations of relatively fast molecules inside zeolitic crystals as an alternative to chromatographic pulse methods. To demonstrate the capabilities of this method, binary adsorption isotherms and transport diffusivities of CO2 in mixtures composed of CO2 and N2 inside silicalite have been determined. From the fundamental measurements determined using this method, complex gas separation processes such as swing adsorption and multi stage membrane systems can be designed for novel zeolite materials. This method can also be used to develop models for complex adsorption and diffusion systems, and validate sophisticated molecular simulation models.•IR microimaging with static gas dosing system for measuring transient uptake, diffusion and chemical reactions of gases and their mixtures in individual crystals or particles of nanoporous materials•Using giant crystals the setup allows to study adsorption and transport of single components and mixtures in nanoporous materials also for fast diffusing guest molecules.

Tracing compartment exchange by NMR diffusometry: Water in lithium-exchanged low-silica X zeolites.

The two-region model for analyzing signal attenuation in pulsed field gradient (PFG) NMR diffusion studies with molecules in compartmented media implies that, on their trajectory, molecules get from one region (one type of compartment) into the other one with a constant (i.e. a time-invariant) probability. This pattern has proved to serve as a good approach for considering guest diffusion in beds of nanoporous host materials, with the two regions ("compartments") identified as the intra- and intercrystalline pore spaces. It is obvious, however, that the requirements of the application of the two-region model are not strictly fulfilled given the correlation between the covered diffusion path lengths in the intracrystalline pore space and the probability of molecular "escape" from the individual crystallites. On considering water diffusion in lithium-exchanged low-silica X zeolite, we are now assuming a different position since this type of material is known to offer "traps" in the trajectories of the water molecules. Now, on attributing the water molecules in the traps and outside of the traps to these two types of regions, we perfectly comply with the requirements of the two-region model. We do, moreover, benefit from the option of high-resolution measurements owing to the combination of magic angle spinning (MAS) with PFG NMR. Data analysis via the two-region model under inclusion of the influence of nuclear magnetic relaxation yields satisfactory agreement between experimental evidence and theoretical estimates. Limitations in accuracy are shown to result from the fact that mass transfer outside of the traps is too complicated for being adequately reflected by simple Fick's laws with but one diffusivity.

Diffusion in hierarchical mesoporous materials: applicability and generalization of the fast-exchange diffusion model.

Transport properties of cyclohexane confined to a silica material with an ordered, bimodal pore structure have been studied by means of pulsed field gradient nuclear magnetic resonance. A particular organization of the well-defined pore structure, composed of a collection of spatially ordered, spherical mesopores interconnected via narrow worm-like pores, allowed for a quantitative analysis of the diffusion process in a medium with spatially ordered distribution of the fluid density for a broad range of the gas-liquid equilibria. The measured diffusion data were interpreted in terms of effective diffusivities, which were determined within a microscopic model considering long-range molecular trajectories constructed by assembling the alternating pieces of displacement in the two constituting pore spaces. It has further been found that for the system under study, in particular, and for mesoporous materials with multiple porosities, in general, this generalized model simplifies to the conventional fast-exchange model used in the literature. Thus, not only was justification of the applicability of the fast-exchange model to a diversity of mesoporous materials provided, but the diffusion parameters entering the fast-exchange model were also exactly defined. The equation resulting in this way was found to nicely reproduce the experimentally determined diffusivities, establishing a methodology for targeted fine-tuning of transport properties of fluids in hierarchical materials with multiple porosities.

Micro-imaging of transient guest profiles in nanochannels.

Zeolites of type ferrierite are exploited as a host system for monitoring the evolution of guest concentration (methanol) in nanoporous host materials upon adsorption. Additional transport resistances at the crystal surface have been removed so that uptake is exclusively controlled by the diffusion resistance of the pore space. Since the crystal shape deviates from a simple parallelepiped, the primary imaging data do not immediately reflect true local concentrations. A simple algorithm is developed which overcomes this complication. The determined transient concentration profiles ideally comply with the requirements for the application of the Boltzmann-Matano integration method for determining diffusivities. The resulting diffusivities (along the direction of the "10-ring channels") are found to exceed those along the 8-ring channels by three orders of magnitude.

Self-diffusion of poly(propylene glycol) in nanoporous glasses studied by pulsed field gradient NMR: A study of molecular dynamics and surface interactions.

Pulsed field gradient NMR is applied to investigate the self-diffusion of poly(proypylene glycol) in nanoporous glasses (nominal pore sizes of 2.5-7.5 nm). In general, the diffusion is slowed down by the confinement compared to the bulk. For native pore surfaces covered by hydroxyl groups the spin echo attenuation Ψ displays a bimodal behavior versus q(2)t (q-norm of a generalized scattering vector). This was explained assuming spatial regions of different diffusivities in a two-phase model. The slow component is assigned to segments forming a surface layer close to the pore walls in which the segments have a lower mobility than those located in the center of the pores. By variation of observation time it was concluded that time constant for the dynamic exchange of segments between these two regions is around 100 ms at room temperature. For silanized pores, the bimodal behavior in the spin echo attenuation Ψ shows a stretched exponential decay versus q(2)t. The estimated diffusion coefficients decrease strongly with decreasing pore size. The temperature dependence of the diffusion coefficient can be approximated by an Arrhenius law where the activation energy increases with decreasing pore size. The observed pore size dependence for the diffusion of poly(propylene glycol) in silanized nanoporous glasses can be discussed assuming interaction and confining size effects.

Discriminating the molecular pathways during uptake and release on nanoporous host systems.

The use of optical techniques, such as interference microscopy, has enabled the observation of transient concentration profiles generated by intracrystalline transport diffusion in nanoporous host materials. In this way, the relevant transport parameters become directly accessible by experiment. We demonstrate that this novel type of information allows one to determine the fraction of molecules which, during molecular uptake (or release), are entering (or leaving) the host crystal through its different faces. By means of numerical calculations of a large amount of different uptake processes, the fraction of the respective fluxes is found to be reasonably calculated by means of the analytical solution for constant (i.e., mean) transport parameters. A more straightforward procedure, based on the assumption that the fraction of the flux is inversely proportional to the time constant calculated with the mean transport parameters, also yields reasonable results. It is shown that even for anisotropic mass transfer with strong concentration dependencies, the divergence from the actual results is generally less than 8%. In most cases such deviations would be below the limits of the accuracy of the determined transport parameters.

Charge transport and glassy dynamics in imidazole-based liquids.

Broadband dielectric spectroscopy, differential scanning calorimetry, rheology, and pulsed field gradient-nuclear magnetic resonance (PFG NMR) are combined to study glassy dynamics and charge transport in a homologous series of imidazole-based liquids with systematic variation of the alkyl chain length. The dielectric spectra are interpreted in terms of dipolar relaxation and a conductivity contribution. By applying the Einstein, Einstein-Smoluchowski, and Stokes-Einstein relations, translational diffusion coefficients--in quantitative agreement with PFG NMR measurements--are obtained. With increasing alkyl chain length, it is observed that the viscosity increases, whereas the structural alpha-relaxation rate decreases, in accordance with Maxwell's relation. Between the rate omega(e) of electrical relaxation and the rate omega(alpha) of the structural alpha-relaxation, scaling is observed over more than six decades with a decoupling index of about 2.

Charge transport and mass transport in imidazolium-based ionic liquids.

The mechanism of charge transport in the imidazolium-based ionic liquid 1,3-dimethylimidazolium dimethylphosphate is analyzed by combining broadband dielectric spectroscopy (BDS) and pulsed field gradient nuclear magnetic resonance (PFG NMR). The dielectric spectra are dominated-on the low-frequency side-by electrode polarization effects while, for higher frequencies, charge transport in a disordered matrix is the underlying physical mechanism. Using the Einstein and Einstein-Smoluchowski equations enables one to determine-in excellent agreement with direct measurements by PFG NMR-the diffusion coefficient of the charge carriers. By that, it becomes possible to extract from the dielectric spectra separately the number density and the mobilities of the charge carriers and the type of their thermal activation. It is shown that the observed Vogel-Fulcher-Tammann (VFT) dependence of the dc conductivity can be traced back to a similar temperature dependence of the mobility while for the number density an Arrhenius-type thermal activation is found. Extrapolating the latter to room temperature indicates that nearly all charge carriers are participating in the conduction process.

Electrical conductivity and translational diffusion in the 1-butyl-3-methylimidazolium tetrafluoroborate ionic liquid.

Broadband dielectric and terahertz spectroscopy (10(-2)-10(+12) Hz) are combined with pulsed field gradient nuclear magnetic resonance (PFG-NMR) to explore charge transport and translational diffusion in the 1-butyl-3-methylimidazolium tetrafluoroborate ionic liquid. The dielectric spectra are interpreted as superposition of high-frequency relaxation processes associated with dipolar librations and a conductivity contribution. The latter originates from hopping of charge carriers on a random spatially varying potential landscape and quantitatively fits the observed frequency and temperature dependence of the spectra. A further analysis delivers the hopping rate and enables one to deduce--using the Einstein-Smoluchowski equation--the translational diffusion coefficient of the charge carriers in quantitative agreement with PFG-NMR measurements. By that, the mobility is determined and separated from the charge carrier density; for the former, a Vogel-Fulcher-Tammann and for the latter, an Arrhenius temperature dependence is obtained. There is no indication of a mode arising from the reorientation of stable ion pairs.

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.

Isotropic concentration profiles during diffusion-limited desorption from anisotropic media.

Imaging of the concentration profiles of the diffusants during molecular adsorption on and desorption from porous media is developing to become an important, very specific tool of monitoring the structure of these media. With the present study we refer to the remarkable phenomenon that even in the case of anisotropic porous media the concentration profiles recorded under desorption may attain isotropic patterns, irrespective of the fact that desorption is limited by anisotropic diffusion. The presentation is based on both dynamic Monte Carlo simulations and analytical considerations.

Exchange dynamics at the interface of nanoporous materials with their surroundings.

The evolution of transient concentration profiles in nanoporous materials is shown to provide direct information about the rate of molecular exchange at the interface of these materials with the surrounding atmosphere. This includes the quantitation of a surface permeability and, related with each other, of the sticking factor, i.e., of the probability that a molecule colliding with the external surface from the outside atmosphere, will in fact enter the genuine pore system of the material under study. Owing to the recent introduction of interference microscopy to this type of systems, the relevant experimental evidence has become directly accessible and is applied to two model systems which are found to differ notably in their interface dynamics.

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.

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.

Molecular traffic control in single-file networks with fast catalysts.

As a model for molecular traffic control we investigate the diffusion of hard core particles in crossed single-file systems. We consider a square lattice of single-files being connected to external reservoirs. The (vertical) alpha channels, carrying only A particles, are connected to reservoirs with constant density rho(A). B particles move along the (horizontal) beta channels, which are connected to reservoirs of density rho(B). We allow the irreversible transition A-->B at intersections. We are interested in the stationary density profile in the alpha and beta channels, which is the distribution of the occupation probabilities over the lattice. We calculate the stationary currents of the system and show that for sufficiently long channels the currents (as a function of the reservoir densities) show in the limit of large transition rates nonanalytic behavior. The results obtained by direct solution of the master equation are verified by kinetic Monte Carlo simulations.

The gel-forming behaviour of dextran in the presence of KCl: a quantitative 13C and pulsed field gradient (PFG) NMR study.

Although the gel forming ability of certain polysaccharides in the presence of ions is a well-known phenomenon, detailed physicochemical mechanisms of such processes are still unknown. In this investigation high resolution 13C NMR as well as 1H pulsed field gradient (PFG) NMR were used to investigate the mobility of dextran in the sol and in the gel state. Gel-formation of dextran can be easily induced by the addition of large amounts of potassium chloride. No major differences in the T(1) relaxation times of dextran in the sol and in the gel state could be observed. Accordingly, the analysis of the 13C NMR spectroscopic data did not provide any indication of an observable line-broadening upon gel-formation. However, a KCl concentration dependent decrease of signal intensity in comparison to an internal standard was detected. On the other hand, the PFG NMR studies clearly indicated a gradual diminution of the self-diffusion coefficient of the dextran with increasing molecular weight as well as in the presence of potassium chloride. These measurements revealed in agreement with spectroscopic data that at least one potassium ion per monomer subunit (i.e. one glycopyranose residue) is necessary for gel formation.

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.

NMR studies of water diffusion and relaxation in hydrating slag-based construction materials.

The NMR relaxation properties of hydrating blast-furnace slag cements have recently been shown to be dominated by the effect of water self-diffusion in internal magnetic field gradients in the pastes. While this was suggested on the basis of NMR relaxometry and magnetic susceptibility data, we report here the results from first direct studies of the water self-diffusion in the hydrating paste using a specialized PFG sequence and very intensive magnetic field gradient pulses.

Determination of genuine diffusivities in heterogeneous media using stimulated echo pulsed field gradient NMR.

Pulsed field gradient (PFG) NMR diffusion measurements in heterogeneous media may lead to erroneous results due to the disturbing influence of internal magnetic field gradients. Here, we present a simple theoretical model which allows one to interpret data obtained by stimulated spin echo PFG NMR in the presence of spatially varying internal field gradients. Using the results of this theory, the genuine self-diffusion coefficients in heterogeneous media may be extrapolated from the dependence of the apparent diffusivities on the dephasing time of the simulated echo PFG NMR sequence. Experimental evidence that such extrapolation yields satisfactory results for self-diffusion of hexadecane in natural sediments (sand) and of n-octanol in doped MgO pastes is provided.