Restricted self-diffusion of adsorbed water in MIL-100(Al)

An extended two-site exchange model is presented, which is used to evaluate pulsed field gradient (PFG) nuclear magnetic resonance (NMR) measurements of water in the nanoporous metal-organic framework MIL-100(Al). Here the water molecules exchange between the inter- and the intracrystalline space during the observation time, but are also restricted in their movement by the crystal surface. The evaluation of temperature and loading dependent PFG NMR data yields information about the intracrystalline diffusion process, the radius of the restricting geometry and the time constants of the exchange process. The intracrystalline mean residence time is found to decrease with increasing temperature, which allows an estimate of the heat of adsorption under the equilibrium conditions of the NMR measurements.

Development and application of an exchange model for anisotropic water diffusion in the microporous MOF aluminum fumarate

Diffusion of water in aluminum fumarate was studied by means of pulsed field gradient (PFG) nuclear magnetic resonance (NMR). Due to water molecules exchanging between the intracrystalline anisotropic pore space and the isotropic intercrystalline void space the model of intracrystalline anisotropic diffusion fails to describe the experimental PFG NMR data at high observation times. Therefore, the two-site exchange model developed by Kärger is extended to the case of exchange between an anisotropic and an isotropic site. This extended exchange model is solved by numerical integration. It describes the experimental data very well and yields values for the intracrystalline diffusion coefficient and the mean residence times of the respective sites. Further PFG NMR studies were performed with coatings consisting of small aluminum fumarate crystals, which are used in adsorptive heat transformation applications. The diffusion coefficients of water in the small crystal coating are compared to the values expected from the extended two-site exchange model and from the model of long-range diffusion.

High-pressure low-field 1H NMR relaxometry in nanoporous materials

A low-field NMR sensor with NdFeB permanent magnets (B0=118 mT) and a pressure cell made of PEEK (4 cm outer diameter) were designed for (1)H relaxation time studies of adsorbed molecules at pressures of up to 300 bar. The system was used to investigate methane uptake of microporous metal-organic frameworks and nanoporous activated carbon. T2 relaxation time distribution of pure methane and of methane under co-adsorption of carbon dioxide show that the host-guest interaction lead to a relaxation time contrasts, which may be used to distinguish between the gas phase and the different adsorbed phases of methane. Adsorption isotherms, exchange of methane between adsorbent particles and the surrounding gas phase, successive displacement of methane from adsorption sites by co-adsorption of carbon dioxide and CO2/CH4 adsorption separation factors were determined from the observed NMR relaxation time distributions.

Self-Diffusion of Chain Molecules in the Metal-Organic Framework IRMOF-1: Simulation and Experiment

Metal-organic frameworks (MOFs) possess characteristics, such as tunable pore size and chemical functionality, that make them attractive candidates for separations, catalysis, gas storage, and sensing applications. The rate of diffusion of guest molecules in the pores is an important property for all of these potential applications. In this work, the self-diffusion of hydrocarbons in IRMOF-1 was studied as a function of chain length with a combination of molecular dynamics simulations and pulsed field gradient NMR experiments. Excellent agreement is seen between the experiments and simulations, and the self-diffusion coefficients in IRMOF-1 are on the same order as those in the bulk liquid. Additionally, the effect of concentration on diffusivity was found to be very small for low to moderate loadings. Molecular dynamics simulations also provided insights about the preferential diffusion pathways of these guests in IRMOF-1.

Paramagnetic relaxation enhancement (PRE) as a tool for probing diffusion in environmentally relevant porous media

The transport diffusivity of the paramagnetic molecule 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) was measured by monitoring its influence on the NMR transverse relaxation time (T₂) on surrounding water protons - also known as paramagnetic relaxation enhancement (PRE). Due to the nature of the PRE effect, few paramagnetic molecules are able to simultaneously reduce the T₂ of many NMR active nuclei, which represents a significant gain in sensitivity. In an aqueous solution, the minimal detectable TEMPO concentration was around 70 ppm. The value of the diffusivity was estimated by fitting the relaxation data, collected as a function of time, with the appropriate solutions of the second Fick's law in respect to the corresponding sample geometry and dimensions. Considering the experimentally determined TEMPO relaxivity in water ("TEMPO-water relaxivity"; R(TEMPO) = (1.05 ± 0.12) × 10⁻³ ppm⁻¹ s⁻¹), the obtained diffusion coefficients (D) of TEMPO in homogeneous solution and in a water saturated sand column (D(bulk) = (6.7 ± 0.4) × 10⁻¹⁰ m² s⁻¹ and D(sand) = (1.4 ± 0.5) × 10⁻¹⁰ m² s⁻¹, respectively) are in good agreement with the expected values (literature values: D(bulk) = 6.6 × 10⁻¹⁰ m² s⁻¹, 1.3 × 10⁻¹⁰ m² s⁻¹ < D(sand) < 2.3 × 10⁻¹⁰ m² s⁻¹). This new approach enables one to determine the diffusivity of paramagnetic molecules in homogeneous (aqueous solution) and porous media with basic NMR equipment, at low concentrations and in a noninvasive manner.

Combining macroscopic and microscopic diffusion studies in zeolites using NMR techniques

In this study the zero length column (ZLC) technique is extended to the case where the decay of the adsorbed phase concentration is observed directly by nuclear magnetic resonance (NMR). An adsorption-desorption apparatus compatible with a 400-MHz NMR spectrometer was developed. It operates with nitrogen or helium as the inert purge gas. The column of the adsorbent material is placed in the sensitive region of the superconducting magnet and the rf coil of the NMR spectrometer. The time scales of the adsorption and desorption processes depend on concentration, temperature and crystal shape and are found to be in the range of 1-10 min. From the desorption branch, the non-equilibrium ZLC-NMR measurements yield intracrystalline diffusion coefficients in the range of 10(-13) to 10(-11) m2/s for different alkanes in silicalite-1. These values are always found to be smaller than the values measured by pulsed field gradient NMR under equilibrium condition indicating that there must be additional transport resistance at the external surface of these silicalite-1 zeolite crystals.

Proton dynamics in the perchloric acid clathrate hydrate HClO4⋅5.5H2O

In the perchloric acid clathrate hydrate HClO4.5.5H2O, the perchlorate anions are contained inside an aqueous host crystalline matrix, positively charged because of the presence of delocalized acidic protons. Our experimental results demonstrate that the microscopic mechanisms of proton conductivity in this system are effective on a time scale ranging from nanosecond to picosecond. In the present paper, we discuss more specifically on the relaxation processes occurring on a nanosecond time scale by combining high-resolution quasielastic neutron scattering and 1H pulse-field-gradient nuclear magnetic resonance experiments. The combination of these two techniques allows us to probe proton dynamics in both space and time domains. The existence of two types of proton dynamical processes has been identified. The slowest one is associated to long-range translational diffusion of protons between crystallographic oxygen sites and has been precisely characterized with a self-diffusion coefficient of 3.5 x 10(-8) cm2/s at 220 K and an activation energy of 29.2+/-1.4 kJ/mol. The fastest dynamical process is due to water molecules' reorientations occurring every 0.7 ns at 220 K with an activation energy of 17.4+/-1.5 kJ/mol. This powerful multitechnique approach provides important information required to understand the microscopic origin of proton transport in an ionic clathrate hydrate.

Direct investigation of the fate of NAPL contaminations in a hydrating cement matrix by means of magnetic resonance techniques

The behavior of nonwatery solvent phases in hydrating cement pastes is of great interest in the context of solidification of wastes containing such phases. In a recent study, the influence of various solvents on the hydration kinetics of cement was studied. In this paper, we present results on the changes in the behavior of the solvent phases themselves during setting of the cement pastes. The methods used in the studies were NMR relaxometry and pulsed field gradient (PFG) NMR diffusometry. To study selectively the behavior of the non-aqueous-phase liquid (NAPL) phases, heavy water was used in the preparation of the cement pastes. The experimental results are in good agreement with the observations from earlier studies concerning the behavior of toluene in hydrating cement. For aliphatic solvents (cyclooctane, n-hexanol), indications for surprisingly large networks of connected droplets in the cement matrices are found.

Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios

By evaluating the spin echo attenuation for a generalized 13-interval PFG NMR sequence consisting of pulsed field gradients with four different effective intensities (F(p/r) and G(p/r)), magic pulsed field gradient (MPFG) ratios for the prepare (G(p)/F(p)) and the read (G(r)/F(r)) interval are derived, which suppress the cross term between background field gradients and the pulsed field gradients even in the cases where the background field gradients may change during the z-store interval of the pulse sequence. These MPFG ratios depend only on the timing of the pulsed gradients in the pulse sequence and allow a convenient experimental approach to background gradient suppression in NMR diffusion studies with heterogeneous systems, where the local properties of the (internal) background gradients are often unknown. If the pulsed field gradients are centered in the tau-intervals between the pi and pi/2 rf pulses, these two MPFG ratios coincide to eta=G(p/r)/F(p/r)=1-8/[1+(1/3)(delta/tau)(2)]. Since the width of the pulsed field gradients (delta) is bounded by 0< or =delta< or =tau, eta can only be in the range of 5< or =-eta< or =7. The predicted suppression of the unwanted cross terms is demonstrated experimentally using time-dependent external gradients which are controlled in the NMR experiment as well as spatially dependent internal background gradients generated by the magnetic properties of the sample itself. The theoretical and experimental results confirm and extend the approach of Sun et al. (J. Magn. Reson. 161 (2003) 168), who recently introduced a 13-interval type PFG NMR sequence with two asymmetric pulsed magnetic field gradients suitable to suppress unwanted cross terms with spatially dependent background field gradients.

Boundary effects of molecular diffusion in nanoporous materials: A pulsed field gradient nuclear magnetic resonance study

The boundary conditions of intraparticle diffusion in nanoporous materials may be chosen to approach the limiting cases of either absorbing or reflecting boundaries, depending on the host-guest system under study and the temperature of measurement. Pulsed field gradient nuclear magnetic resonance is applied to monitor molecular diffusion of n-hexane and of an n-hexane-tetrafluoromethane mixture adsorbed in zeolite crystallites of type NaX under either of these limiting conditions. Taking advantage of the thus-established peculiarities of mass transfer at the interface between the zeolite bulk phase and the surrounding atmosphere, three independent routes for probing the crystal size are compared. These techniques are based on (i) the measurement of the effective diffusivity under complete confinement, (ii) the application of the so-called NMR tracer desorption technique, and (iii) an analysis of the time dependence of the effective diffusivity in the short-time limit where, by an appropriate variation of the adsorbate and the measuring conditions, the limiting cases of reflecting and adsorbing boundaries could be considered. All these techniques are found to yield coinciding results, which are in excellent agreement with the crystal sizes determined by microscopy.

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.

Structure-mobility relations of molecular diffusion in nanoporous materials

Depending on the measuring conditions, pulsed field gradient (PFG) NMR measurements of molecular diffusion in beds of nanoporous particles may provide information about the propagation rate of guest molecules in both the intra- and interparticle spaces, as well as through the interface between them. Recent progress in both PFG NMR instrumentation and computational techniques have initiated studies of novel aspects in each of these areas, which are reviewed in this communication. They concern the possibility of multicomponent diffusion measurements with ultra-high pulsed field gradients, the peculiarities of molecular diffusion in channel networks, the determination of the surface-to-volume ratio of nanoporous particles and the dependence of the tortuosity factor of long-range diffusion on the diffusion mode in the intercrystalline space.

Self-diffusion of polymers in cartilage as studied by pulsed field gradient NMR

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) was used to investigate the self-diffusion behaviour of polymers in cartilage. Polyethylene glycol and dextran with different molecular weights and in different concentrations were used as model compounds to mimic the diffusion behaviour of metabolites of cartilage. The polymer self-diffusion depends extremely on the observation time: The short-time self-diffusion coefficients (diffusion time Delta approximately 15 ms) are subjected to a rather non-specific obstruction effect that depends mainly on the molecular weights of the applied polymers as well as on the water content of the cartilage. The observed self-diffusion coefficients decrease with increasing molecular weights of the polymers and with a decreasing water content of the cartilage. In contrast, the long-time self-diffusion coefficients of the polymers in cartilage (diffusion time Delta approximately 600 ms) reflect the structural properties of the tissue. Measurements at different water contents, different molecular weights of the polymers and varying observation times suggest that primarily the collagenous network of cartilage but also the entanglements of the polymer chains themselves are responsible for the observed restricted diffusion. Additionally, anomalous restricted diffusion was shown to occur already in concentrated polymer solutions.

Fractal geometry of surface areas of sand grains probed by pulsed field gradient NMR

Pulsed field gradient NMR self-diffusion studies of water were used to determine surface-to-volume ratios and specific surface areas of the grains forming a glacial sand deposit. Both quantities exhibit a noninteger power-law dependence as a function of the diameters of the grains. The associated fractal dimensions of the surface area ( D(s)) and of the pore volume ( D(v)) are found to be D(s)-D(v) = -0.70+/-0.05 and D(s) = 2.20+/-0.05. The results demonstrate that NMR studies with native pore fluids are suitable to investigate the fractal nature of natural, unconsolidated porous materials.

Cation diffusion in cartilage measured by pulsed field gradient NMR

In this study, the pulsed field gradient (PFG) nuclear magnetic resonance (NMR) technique was used for the investigation of (1) concentration and compression effects on cation self-diffusion, and (2) restricted diffusion of cations in cartilage. Since physiologically relevant cations like Na+ are difficult to investigate owing to their very short relaxation times, the cations tetramethylammonium (TMA) and tetraethylammonium (TEA) were employed for diffusion studies in samples of explanted cartilage. Results indicated that the diffusion of monovalent cations shows strong similarities to observations already made in studies of the diffusion of water in cartilage: with increasing compression, i.e. decreasing water content, the diffusion coefficient of the cation decreases concomitantly. The diffusion coefficients also showed a decrease with increasing cation concentrations, basically reflecting the corresponding decrease in the water content. Both results could be explained by the well-established model of Mackie and Meares. This, together with the similarity of the diffusion coefficient D in cartilage relative to free solution (about 50%) for both cations, is consistent with the view that the water content and not the charge is the most important determinant of the intratissue diffusivity of monovalent cations. Diffusion studies with increasing observation times showed strong evidence of restricted diffusion, allowing the estimation of the geometry of barriers within cartilage.

NMR response of non-reservoir fluids in sandstone and chalk

Transverse (T2) NMR relaxation time at 2 MHz proton resonance frequency was measured on core plug samples from two different lithologies, sandstone and chalk, before and after exposure to selected drilling fluids. The results show that NMR signal response was significantly altered after displacing 50% of the original pore fluids, crude oil and water, by drilling fluid filtrate. Relaxation spectra of the rock samples invaded by water-based filtrate shift to significantly shorter T2-values. This shift yields an underestimation of the free-fluid volumes when selecting cut-off values of 33 ms and 100 ms for sandstone and chalk, respectively. In opposite, rock samples affected by oil-based filtrate respond with a signal indicating significantly larger free-fluid volumes than present before exposure. NMR-permeability calculated based on the Timur-Coates Free Fluid model altered in some cases by one order of magnitude.

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.

PFG NMR tracer exchange measurements of xenon in zeolites

Understanding mass transport phenomena in zeolites at a molecular level is of prime importance to the study of zeolite catalysis. Among the techniques applicable, PFG NMR has been shown to provide vital information about diffusion of hydrocarbons in zeolites. Here this technique is used to study xenon as a probe molecule, because of its chemical inertness and the large differences in chemical shift of the xenon atoms in the sorbed and gas phase.