Spatial dependence of dispersion

The use of Pulsed Gradient Spin Echo (PGSE) NMR to investigate flow in porous media is well established. Using two pairs of position-encoding pulses in the PGSE experiment gives the possibility of examining velocity fluctuations, by comparing displacements, during the two encoding intervals. This method may be used to measure the asymptotic dispersion coefficient as well as the Velocity Auto-Correlation Function (VACF) in porous media flow. Some examples of two-dimensional maps of density and velocity distributions are accompanied by the first attempt to perform localized measurements of flow dispersion in porous media.     

Applications of controlled-flow laser-polarized xenon gas to porous and granular media study

We report initial NMR studies of continuous flow laser-polarized xenon gas, both in unrestricted tubing, and in a model porous media. The study uses Pulsed Gradient Spin Echo-based techniques in the gas-phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients. Pulsed Gradient Echo studies of continuous flow laser-polarized xenon gas in unrestricted tubing indicate clear diffraction minima resulting from a wide distribution of velocities in the flow field. The maximum velocity experienced in the flow can be calculated from this minimum, and is seen to agree with the information from the complete velocity spectrum, or motion propagator, as well as previously published images. The susceptibility of gas flows to parameters such as gas mixture content, and hence viscosity, are observed in experiments aimed at identifying clear structural features from echo attenuation plots of gas flow in porous media. Gas-phase NMR scattering, or position correlation flow-diffraction, previously clearly seen in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack is not so clear in experiments using a different gas mixture. A propagator analysis shows most gas in the sample remains close to static, while a small portion moves through a presumably near-unimpeded path at high velocities.     

Applications of Nuclear Magnetic Resonance Imaging in Particle Technology

During the past decade, the application of Nuclear Magnetic Resonance (NMR) imaging techniques to problems of relevance to the process industries has been identified. In the context of particle technology, NMR imaging, in addition to the more routinely used techniques of Pulsed Gradient Spin Echo (PGSE) NMR and NMR spectroscopy, offer new methods of characterising pore structure, adsorption and diffusion processes within particles and packed beds of particles, as well as enabling time-resolved in-situ study of processes such as twophase flow, aggregation, polymerisation, crystallisation and phase separation phenomena. This paper reviews recent work in these areas, and also highlights the new insights NMR imaging can give us regarding the characterisation of porous materials, and the influence of the structure of the pore space on the transport processes occuring within a given porous solid.     

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media.

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.     

Magnetic resonance imaging of convection in laser-polarized xenon

We demonstrate nuclear magnetic resonance (NMR) imaging of the flow and diffusion of laser-polarized xenon (129Xe) gas undergoing convection above evaporating laser-polarized liquid xenon. The large xenon NMR signal provided by the laser-polarization technique allows more rapid imaging than one can achieve with thermally polarized gas-liquid systems, permitting shorter time-scale events such as rapid gas flow and gas-liquid dynamics to be observed. Two-dimensional velocity-encoded imaging shows convective gas flow above the evaporating liquid xenon, and also permits the measurement of enhanced gas diffusion near regions of large velocity variation.     

Time domain analysis: an alternative way to interpret PGSE experiment.

We report a theoretical development which aims at interpreting Pulsed Gradient Spin Echo data for diffusing fluids in saturated porous media. It consists in analyzing the time dependence of PGSE amplitudes for each single gradient strength, and introduces a new diffusion coefficient D(q) as being continuously dependent on the length scale in the material. Both experimental measurements on water saturated bead packings and simulated experiments in 2D and 3D model systems are interpreted with this approach. D(q) is shown to give a new insight in the micro-macro transition. Its evolution vs. the length scale is non trivial, and can be sensitive to local slow kinetic effects.     

Pore-Structure Determinations of Silica Aerogels byXe NMR Spectroscopy and Imaging

Silica aerogels represent a new class of open-pore materials with pore dimensions on a scale of tens of nanometers, and are thus classified as mesoporous materials. In this work, we show that the combination of NMR spectroscopy and chemical-shift selective magnetic resonance imaging (MRI) can resolve some of the important aspects of the structure of silica aerogels. The use of xenon as a gaseous probe in combination with spatially resolved NMR techniques is demonstrated to be a powerful, new approach for characterizing the average pore structure and steady-state spatial distributions of xenon atoms in different physicochemical environments. Furthermore, dynamic NMR magnetization transfer experiments and pulsed-field gradient (PFG) measurements have been used to characterize exchange processes and diffusive motion of xenon in samples at equilibrium. In particular, this new NMR approach offers unique information and insights into the nanoscopic pore structure and microscopic morphology of aerogels and the dynamical behavior of occluded adsorbates. MRI provides spatially resolved information on the nature of the flaw regions found in these materials. Pseudo-first-order rate constants for magnetization transfer among the bulk and occluded xenon phases indicate xenon-exchange rate constants on the order of 1 s⁻¹for specimens having volumes of 0.03 cm³. PFG diffusion measurements show evidence of anisotropic diffusion for xenon occluded within aerogels, with nominal self-diffusivity coefficients on the order ofD= 10⁻³cm²/s.     

Time-dependent velocities in porous media dispersive flow.

Pulsed Gradient Spin Echo (PGSE) NMR methods may be used to measure the asymptotic dispersion coefficient as well as the velocity autocorrelation function (VACF) in porous media flow. The VACF can be measured in the frequency domain using repetitive gradient pulse trains, and in the time domain using double PGSE encoding. The one dimensional double PGSE method, and the two dimensional velocity exchange experiment (VEXSY) are briefly outlined and their application to flow in monodisperse 0.5 mm diameter beads packs described, both axial and transverse VACFs being examined. The measured correlation times are shown to agree well with calculated values. The asymptotic dispersion coefficients agree with literature values in the case of transverse flow while in axial flow it is shown that asymptotic conditions are not achieved, even for observation times longer than the correlation time for flow around a bead.     

High Temperature Diffusion of 6Li Adsorbed on a Ru(001) Single Crystal Surface as Seen by Pulse NMR

Diffusion measurements on lithium atoms adsorbed on a ruthenium single crystal were performed in the high temperature regime (1100–1200 K). Pulsed NMR techniques were utilized to produce and observe the decay of magnetization patterns from which the diffusion coefficient was extracted. The observed temperature dependence could be described by D = (10 ± 7) cm²/s · exp (−(0.46 ± 0.07) eV/kT). The extremely high diffusion coefficient and prefactor are understood by a gas like adsorbate behavior. The electric field gradient has been measured with ⁷Li: V _zz = −5.0 ± 0.1 10¹⁵ V/cm² with an inhomogeneity of less then 1% as judged by the width of the satellite transitions.     

Measurement of diffusion coefficients in polystyrene using xenon-129 NMR

A sample of polystyrene beads, 18 μm in diameter, has been sealed in an NMR tube under 10 atm of xenon gas. Two dimensional,¹²⁹Xe NMR spectra show cross peaks between the resonances corresponding to xenon in the free gas and the sorbed state, indicating that appreciable exchange occurs during the mixing time of the NMR experiment. Selective saturation of the free gas resonance attenuates the integrated intensity of the sorbed xenon resonance as a function of saturation time, thus allowing the accurate measurement of the exchange rates between the gas and the sorbed states. A model has been developed using a slightly modified form of Crank’s treatment of diffusion in a sphere which allows for the accurate determination of the diffusion coefficient for xenon in the sorbed state. The diffusion coefficient for xenon in polystyrene at 25°C is determined to be 2.9·10^?9 cm²/s.     

Spectrophotometric Determination of Ammonia in Estuarine Waters by Hybrid Reagent‐Injection Gas‐Diffusion Flow Analysis

Abstract

A flow‐injection gas‐diffusion technique is described for the online determination of ammonia in estuarine waters covering a salinity range of S=0 to 36. The flow analysis system, which is a hybrid of reagent injection and conventional sample‐injection flow systems, avoids the need for a rotary injection valve. Whereas gas‐diffusion techniques have been widely applied in conventional sample‐injection flow analysis, reagent‐injection flow analysis involving gas diffusion has been little used because it is susceptible to interference from dissolved gaseous species such as carbon dioxide coexisting with ammonia in the sample. This source of interference has been overcome by online adjustment of sample to pH 8.4 prior to the injection of the base that initiates gas diffusion of ammonia. The pore sizes of hydrophobic membranes used in gas diffusion were characterized by a bubble‐point test prior to use in the flow analysis system. These showed wide variation in pore size, and grading and careful selection was necessary in order to obtain reliable gas diffusion measurements of ammonia. The proposed flow‐injection system can be operated in a continuous flow mode, at a sample throughput of 135 measurements hr^?1 with a typical limit of detection (LOD) of 9 µg N L^?1, or in stopped‐flow mode at 60 measurements hr^?1 with a LOD of 3 µg N L^?1. The technique was validated using water samples containing a wide range of dissolved carbon dioxide concentrations, salinity, and pH. Excellent agreement (r=0.999) was observed between results obtained using the reagent‐injection system and an approved reference method.     

Intravascular delivery of hyperpolarized129Xenon forin vivo MRI

The nuclear polarization of¹²⁹Xe and³He can be enhanced by several orders of magnitude by using optical pumping techniques, thus allowing NMR detection of xenon and helium in very low concentrations. The benefits of optically enhanced magnetic resonance (MR) are already exploited in MR imaging of the lungs using optically polarized³He. The high solubility of xenon in blood and lipids suggests a variety ofin vivo MR applications, for instance perfusion measurements or functional MR studies. This article reviews some current work directed towards delivery of optically polarized xenon forin vivo MR applications.     

Novel MRI applications of laser-polarized noble gases

Gas-phase nuclear magnetic resonance (NMR) has great potential as a probe for a variety of interesting physical and biomedical problems that are not amenable to study by water or similar liquid. However, NMR of gases was largely neglected due to the low signal obtained from the thermally polarized gases with very low sample density. The advent of optical pumping techniques for enhancing the polarization of the noble gases³He and¹²⁹Xe has bought new life to this field, especially in medical imaging where³He lung inhalation imaging is approaching a clinical application. However, there are numerous applications in materials science that also benefit from the use of these gases. We review primarily nonmedical applications of laser-polarized noble gases for both NMR imaging and spectroscopy and highlight progress with examples from our laboratory including high-resolution imaging at millitesla applied field strength and velocity imaging of convective flow. Porous media microstucture has been probed with both thermal and laser-polarized xenon, as xenon is an ideal probe due to low surface interaction with the grains of the porous media.     

Production of nitrogen-free, hyperpolarized 129Xe gas

129 Xe with a nuclear polarization far above the thermal equilibrium value (hyperpolarized) is used in NMR studies to increase sensitivity. Gaseous, adsorbed, or dissolved xenon is utilized in physical, chemical, and medical applications. With the aim in mind to study single-crystal surfaces by NMR of adsorbed hyperpolarized ¹²⁹Xe, three problems have to be solved. The reliable production of ¹²⁹Xe with highest nuclear polarization possible, the separation of the xenon gas from the necessary quench gas nitrogen without polarization loss, and the dosing/delivery of small amounts of polarized xenon gas to a sample surface. Here we describe an optical pumping setup that regularly produces xenon gas with a ¹²⁹Xe nuclear polarization of 0.7(±0.07). We show that a freeze–pump–thaw separation of xenon and nitrogen is feasible without a significant loss in xenon polarization. The nitrogen partial pressure can be suppressed by a factor of 400 in a single separation cycle. Dosing is achieved by using the low vapor pressure of a frozen hyperpolarized xenon sample. Received: 12 June 1998     

Neutron electric dipole moment measurement with a buffer gas comagnetometer

A neutron EDM measurement with a comagnetometer is discussed. For magnetometry, polarized xenon atoms are injected into a cylindrical cell where a cylindrically symmetric magnetic field and an electric field are applied for the EDM measurement. The geometric phase effect (GPE), which originates from particle motion in a magnetic field gradient, is analyzed in terms of the Dyson series. The motion of the xenon atom is largely suppressed because of a small mean free path. The field gradient is controlled by means of NMR measurements, where the false effect of Earth?s rotation is removed. As a result, the GPE is reduced below 10⁻²⁸e cm${10}^{-28}e\text{cm}$.     

Observation of micropores in hard-carbon using Xe NMR porosimetry

The existence of micropores and the change of surface structure in pitch-based hard-carbon in xenon atmosphere were demonstrated using ¹²⁹Xe NMR. For high-pressure (4.0 MPa) ¹²⁹Xe NMR measurements, the hard-carbon samples in Xe gas showed three peaks at 27, 34 and 210 ppm. The last was attributed to the xenon in micropores (<1 nm) in hard-carbon particles. The NMR spectrum of a sample evacuated at 773 K and exposed to 0.1 MPa Xe gas at 773 K for 24 h showed two peaks at 29 and 128 ppm, which were attributed, respectively, to the xenon atoms adsorbed in the large pores (probably mesopores) and micropores of hard-carbon. With increasing annealing time in Xe gas at 773 K, both peaks shifted and merged into one peak at 50 ppm. The diffusion of adsorbed xenon atoms is very slow, probably because the transfer of molecules or atoms among micropores in hard-carbon does not occur readily. Many micropores are isolated from the outer surface. For that reason, xenon atoms are thought to be adsorbed only by micropores near the surface, which are easily accessible from the surrounding space.     

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Padé approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Padé interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Padé length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter.     

Probing porous media with gas diffusion NMR.

We show that gas diffusion nuclear magnetic resonance (GD-NMR) provides a powerful technique for probing the structure of porous media. In random packs of glass beads, using both laser-polarized and thermally polarized xenon gas, we find that GD-NMR can accurately measure the pore space surface-area-to-volume ratio, S/V rho, and the tortuosity, alpha (the latter quantity being directly related to the system's transport properties). We also show that GD-NMR provides a good measure of the tortuosity of sandstone and complex carbonate rocks.     

A PFG NMR experiment for translational diffusion measurements in low-viscosity solvents containing multiple resonances

Pulsed gradient simulated-echo (PGSE) NMR diffusion measurements provide a facile and accurate means for determining the self-diffusion coefficients for molecules over a wide range of sizes and conditions. The measurement of diffusion in solvents of low intrinsic viscosity is particularly challenging, due to the persistent presence of convection. Although convection can occur in most solvent systems at elevated temperatures, in lower viscosity solvents (e.g., short chain alkanes), convection may manifest itself even at ambient laboratory temperatures. In most circumstances, solvent suppression will also be required, and for solvents that have multiple resonances, effective suppression can likewise represent a substantial challenge. In this article, we report an NMR experiment that combines a double-stimulated echo PFG approach with a WET-based solvent suppression scheme that effectively and simultaneously address the issues of dynamic range and the deleterious effects of convection. The experiment described will be of general benefit to studies aimed at the characterization of diffusion of single molecules directly dissolved in low-viscosity solvents, and should also be of substantial utility in studies of supramolecular assemblies such as reverse-micelles dissolved in apolar solvents.     

Xenon NMR measurements of permeability and tortuosity in reservoir rocks

In this work we present measurements of permeability, effective porosity and tortuosity on a variety of rock samples using NMR/MRI of thermal and laser-polarized gas. Permeability and effective porosity are measured simultaneously using MRI to monitor the inflow of laser-polarized xenon into the rock core. Tortuosity is determined from measurements of the time-dependent diffusion coefficient using thermal xenon in sealed samples. The initial results from a limited number of rocks indicate inverse correlations between tortuosity and both effective porosity and permeability. Further studies to widen the number of types of rocks studied may eventually aid in explaining the poorly understood connection between permeability and tortuosity of rock cores.