Pulsed Field Gradient NMR Research Articles

Considerations when determining Counter-diffusion constants in liquid phase catalytic reactions using the Zero Length column (ZLC) method

The confusion with diffusion: In heterogeneous catalysis often, the catalytic material is housed within a porous support structure. It is important therefore to determine whether this support structure exerts limiting behaviors. In this paper, desorption and diffusion effects are separated under reactions conditions, to provide accurate effective diffusion constants in swelling and gate-opening catalysts. • A Zero Length Column (ZLC) method was developed using liquid chromatography. • Diffusion in porous catalyst pellets as small as 5 mg can be directly characterised. • Reactant counter-diffusion coefficients were determined for the Heck reaction. • Clear differences in diffusion rates for reactants versus non-reactant species. A Zero Length Column (ZLC) method was developed using a liquid chromatographic system to calculate reactant counter-diffusion coefficients in porous, solvent swollen catalytic pellets and gate-opening support materials. Reactant diffusivities within these porous materials were determined at the reaction conditions of 80 °C and 0.3–0.75 mL min −1 . For all materials, molecules of a similar size to the pore apertures, or molecules with strong interactions with the material surfaces, catalysts, were observable by the ZLC method, with both micro and macropore diffusion observed. Differences between Pd(II) and Pd(0) forms of the EnCat30 catalyst were examined to determine the effects of catalytic deactivation. The deactivated catalyst showed iodobenzene macroporous diffusion constants similar to the relatively inert toluene molecules. Finally, pulse field gradient NMR was utilised to compare and validate ZLC diffusion measurements for solvent swollen reaction systems. This study presents much needed novel findings on diffusivity data for liquid phase catalytic systems.

Nanoscale Ionic Materials for Nafion Based Nanocomposites Membranes As Single Lithium-Ion Conducting Polymer Electrolytes for Lithium Sulfur Batteries

Currently, rechargeable batteries with the lithium–sulfur (Li–S) chemistry has attracted great interest as one of the most promising candidates for next generation electrochemical energy storage systems. Research into these high energy density devices is critical to the development of thinner, lighter, and lower cost battery systems. One of the biggest obstacles for practical applications of Li-S batteries is caused by the soluble nature of the highly ordered lithium polysulfides (Li2Sn) in the organic electrolytes and induce a so-called “shuttle effect”. A solid-state electrolyte (SPEs) could be a valid alternative in terms of reducing the polysulfides dissolution and shuttle, as well as to protect the lithium metal anode and to minimize dendrite formation, which is beneficial for improving the safety and cycle life of Li−S batteries. SPEs are typically dual-ion conductor systems both cations and anions are mobile and cause a concentration polarization leading to poor performances of batteries. Recently, single lithium-ion conducting solid polymer electrolytes (SLIC-SPEs) have been proposed for polymer electrolytes, where anions are covalently bonded to the polymer, inorganic backbone, or immobilized by anion acceptors and only the Li+ cation will contribute to a permanent flow of charge. They have advantages over conventional dual-ion conducting SPEs such as unity transference number, absence of harmful effect of anion polarization, extremely low rate of Li dendrite growth and immobilization of the lithium polysulfides in the lithium-sulfur (Li-S) batteries. Polymer electrolytes based on ionomers (e.g., Nafion) with easily ionizable groups (e.g., sulfonic groups covalently bonded to the polymer side-chains, −CF2SO3 −) are promising thanks to the high concentration of weakly coordinating anions (counterions). In this work, lithiated Nafion and Nafion-nanocomposites membranes based on Nanoscale Ionic Materials (NIMs) were synthesized, and their ionic conductivity and lithium transference number were investigated in common nonaqueous organic solvents (EC/PC and Glymes).A thorough and systematic study of the lithium-ion transport was conducted by p 1H and 7Li pulsed field gradient (PFG) NMR spectroscopy and electrochemical impedance spectroscopy (EIS), while the mechanical properties of the film electrolytes have been tested by dynamic mechanical analysis (DMA) in a wide temperature range. The electrochemical studies have been conducted both in Li/Li symmetric cell and in secondary Li-S cells. The preliminary results are very interesting, showing ionic conductivities of the order of 5 × 10-4 S/ cm at 25°C satisfactory properties in terms of stability window and stability of the lithium stripping. The lithium transport number is very close to unity thus confirming the complete immobilization of the negative charge carriers.

Mobility of water molecules in Li+, Na+ and Cs+ ionic forms of Nafion membrane studied by NMR

Correlation times and diffusion coefficients of water molecules were measured for the first time by 1H spin relaxation and pulsed field gradient NMR in Li+, Na+ and Cs+ ionic forms of Nafion 117 membrane. Hydration numbers of Li+, Na+ and Cs+ cations were calculated. It was shown that at high humidity macroscopic transfer is controlled by the local translational motion of water molecules.

Diffusion mechanisms of DNA in agarose gels: NMR studies and Monte Carlo simulations.

We report on the diffusion mechanism of short, single-stranded DNA molecules with up to 100 nucleobases in agarose gels with concentrations of up to 2.0% with the aim to characterize the DNA-agarose interaction. The diffusion coefficients were measured directly, i.e., without any model assumptions, by pulsed field gradient nuclear magnetic resonance (PFG-NMR). We find that the diffusion coefficient decreases, as expected, with an increase in both DNA strand length and gel concentration. In addition, we performed Monte Carlo simulations of particle diffusion in a model network of polymer chains, considering our experimental conditions. Together, the Monte Carlo simulations and the PFG-NMR results show that the decrease in diffusion coefficients in the presence of the agarose gel is due to a temporary adhesion of the DNA molecules to the surface of gel fibers. The average adhesion time to a given gel fiber increases with the length of the DNA strands but is independent of the number of gel fibers. The corresponding magnitude of the binding enthalpies of DNA strands to gel fibers indicates that a mixture of van der Waals interactions and hydrogen bonding contributes to the decreased diffusion of DNA in agarose gels.

Charge Transport and Glassy Dynamics in Blends Based on 1-Butyl-3-vinylbenzylimidazolium Bis(trifluoromethanesulfonyl)imide Ionic Liquid and the Corresponding Polymer.

Charge transport, diffusion properties, and glassy dynamics of blends of imidazolium-based ionic liquid (IL) and the corresponding polymer (polyIL) were examined by Pulsed-Field-Gradient Nuclear Magnetic Resonance (PFG-NMR) and rheology coupled with broadband dielectric spectroscopy (rheo-BDS). We found that the mechanical storage modulus increases with an increasing amount of polyIL and is a factor of 10,000 higher for the polyIL compared to the monomer (= Pa at 100 rad s−1 and 298 K). Furthermore, the ionic conductivity of the IL is a factor higher than its value for the polymerized monomer with S cm−1 at K. Additionally, we found the Haven Ratio ( obtained through PFG-NMR and BDS measurements to be constant around a value of for the IL and blends with 30 wt% and 70 wt% polyIL. These results show that blending of the components does not have a strong impact on the charge transport compared to the charge transport in the pure IL at room temperature, but blending results in substantial modifications of the mechanical properties. Furthermore, it is highlighted that the increase in might be attributed to the addition of a more mobile phase, which also possibly reduces ion-ion correlations in the polyIL.

Eutectic Electrolytes Composed of LiN(SO2F)2 and Sulfones for Li-Ion Batteries

Sulfones are polar molecules that can be used as thermally stable electrolyte solvents for Li-ion batteries (LIBs). Li salts form stoichiometric solvates with sulfones in the electrolytes. The melting points of the solvates tend to be higher than room temperature, thereby limiting the operating temperature range of the batteries. In this study, the applicability of ternary eutectic mixtures of LiN(SO2F)2 (LiFSA), sulfolane (SL), and dimethyl sulfone (DMS) as LIB electrolytes was assessed. Relative to the binary LiFSA–sulfone electrolytes, the ternary eutectic electrolytes remained liquid over a wide temperature range due to the increased entropy of mixing. Sulfone-bridged Li+–sulfone–Li+ and anion-bridged Li+–FSA––Li+ network structures were formed in the eutectic electrolyte with a composition of [LiFSA]/[SL]/[DMS] = 1/1.5/1.5. Pulsed-field gradient NMR measurements revealed that the Li+ ion dynamically exchanges sulfones and anions and diffuses more rapidly than these ligands, resulting in the relatively high Li+ transference number of the electrolyte. Highly reversible charge–discharge processes of the LiCoO2 and graphite electrodes were attained using the ternary eutectic electrolyte. The rate capability of the Li/LiCoO2 cell in the eutectic electrolyte was comparable to that of the cell in the conventional 1 M LiPF6 in an ethylene carbonate/dimethyl carbonate solution despite its lower ionic conductivity.

Investigation of dynamical properties of free water in hydroxypropyl cellulose–water mixture by PFG-NMR

The dynamical behavior of water molecules in hydroxypropyl cellulose (HPC)–water mixtures was observed by the pulse field gradient (PFG) NMR method. For a decay curve of the spin-echo signal intensity of a water proton peak, a contribution of the diffusional motion of free water is observed. The water content dependence of the NMR relaxation time and diffusion coefficient of free water shows characteristic behavior reflecting the isotropic-cholesteric phase transition of HPC. These parameters of free water obtained by PFG-NMR correlate strongly with the fast dynamics of free water observed in the GHz region, and this correlation is explained by dynamics of water constrained by the geometrical self-similarity formed by the HPC molecules.

Self-diffusion of mixed xylene isomers in ZIF-71 crystals dispersed in a polymer to form a hybrid membrane

13C pulsed field gradient (PFG) NMR was used to quantify self-diffusion of a p-xylene/o-xylene mixture inside zeolitic imidazolate framework-71 (ZIF-71) crystals dispersed in a Torlon polymer to form a ZIF-71/Torlon mixed-matrix membrane (MMM). The corresponding reference PFG NMR measurements with a bed of a loosely packed bed of ZIF-71 crystals were also performed. This study is motivated by a demonstrated potential of ZIF-based MMMs for liquid separations. Selective 13C isotopic labelling of each xylene isomer was used to ensure that the self-diffusivity of each isomer in the mixture is measured independently and correctly. The diffusion measurements were performed at different diffusion times at 296 K. The observed dependencies of intra-ZIF self-diffusivities in ZIF-71/Torlon MMMs and the corresponding ZIF-71 crystal beds on diffusion time were explained by an influence of the external crystal surface on the studied diffusion process. Analysis of the time dependencies of the self-diffusivities measured for each xylene isomer allowed obtaining intra-ZIF self-diffusivities not perturbed by crystal surface effects as well as the corresponding diffusion selectivity for the studied sorbate mixture. The reported selectivity of around 4 demonstrates promising separation behavior of the considered membrane type.

Microsized Pore Structure Determination in EPDM Rubbers Using High-Pressure 129Xe NMR Techniques.

Microsized pore parameters, such as pore size and distance between pores in a series of model EPDM rubbers, were determined in situ under the pressure of 500 psi using 129Xe nuclear magnetic resonance (NMR) techniques: spin-lattice (T1) and spin-spin (T2) relaxation measurements, pulsed-field gradient (PFG) NMR, and two-dimensional exchange spectroscopy (2D EXSY). The T1/T2 (≫1) ratio for the xenon confined in the pores is larger than that for nonconfined free xenon. This suggests that almost the entire pore surface interacts with xenon atoms like a closed pore. While these pores still connect each other through very narrow diffusion/exchange channels, it is possible to observe the echo decay in PFG-NMR and cross-peaks in 2D EXSY. The results show that both diffusion (Dpore ≈ 2.1 × 10-10 m2/s) and exchange (exchange rate, τexch = a few tens of milliseconds) of xenon between a pore within the material and outer surface are prolonged. The exchange distances (l), which correspond to the xenon gas penetration depth, were estimated to be 70-100 μm based on the measured diffusion coefficients and exchange rate (1/τexch). NMR diffraction analysis reveals that pore size (a) and pore distance (b) are on the order of magnitude of micrometers and tens of micrometers, while the diffusion coefficients of xenon gas in the diffusion channels (Deff) are about 10-8 m2/s. Overall, this study suggests that the pores with a few micrometers connected through very narrow flowing channels with the length of several tens of micrometers are developed 70 to 100 μm below the rubber surface. Furthermore, the overall steady-state diffusion of xenon is slower, approximately 2 orders of magnitudes, than the diffusion in the channel between the pores. The pore and exchange distances correlated with the composition of rubbers showed that the properties of EPDM rubber as a high-pressure gas barrier could be improved by reducing the size of cracks and the depth of gas penetration by the addition of both carbon black and silica fillers.

Ceramic-glass pellet thickness and Li diffusion in NASICON-type LAGP (Li1.5Al0.5Ge1.5(PO4)3) studied by pulsed field gradient NMR spectroscopy

LAGP (Li1.5Al0.5Ge1.5(PO4)3) is one of inorganic solid electrolytes (ISEs) and is relatively stable against atmospheric CO2 and H2O. Five LAGP pellet samples with thicknesses ranging from 0.5 to 4 mm (10−3 m) were investigated by pulsed field gradient (PFG) 7Li NMR spectroscopy. PFG was applied in the thickness direction and the Li diffusion in the same direction was observed. The apparent diffusion coefficients (Dapparent) of Li were determined over the observation time (Δ) ranging from 5 to 100 × 10−3 s and the distances from 0.1 to 1 × 10−6 m. The Dapparent of LAGP samples was 10−11 to 10−13 m2s−1 at 28 °C. The results showed that the Li diffusion phenomenon was thickness dependent. When Δ was short, diffusion of Li was slower for thinner samples, suggesting that the Li pathway was made to avoid surface boundaries. The Li ions were found to diffuse through preferential and longer paths of the pellet samples. As Δ became longer, the diffusion process of Li averaged out and the diffusion coefficient converged to a constant value regardless of the thickness. The PFG-NMR observes a diffusion coefficient of 7Li species which are marked by the first PFG and detected by the second PFG after Δ. Impedance spectroscopy, on the other hand, measures the ionic conductivity for continuous charge transfer between electrodes under electric field, and higher ionic conductivities have been reported for thinner samples.

Polymer Electrolytes for Lithium-Ion Batteries Studied by NMR Techniques

This review is devoted to different types of novel polymer electrolytes for lithium power sources developed during the last decade. In the first part, the compositions and conductivity of various polymer electrolytes are considered. The second part contains NMR applications to the ion transport mechanism. Polymer electrolytes prevail over liquid electrolytes because of their exploitation safety and wider working temperature ranges. The gel electrolytes are mainly attractive. The systems based on polyethylene oxide, poly(vinylidene fluoride-co-hexafluoropropylene), poly(ethylene glycol) diacrylate, etc., modified by nanoparticle (TiO2, SiO2, etc.) additives and ionic liquids are considered in detail. NMR techniques such as high-resolution NMR, solid-state NMR, magic angle spinning (MAS) NMR, NMR relaxation, and pulsed-field gradient NMR applications are discussed. 1H, 7Li, and 19F NMR methods applied to polymer electrolytes are considered. Primary attention is given to the revelation of the ion transport mechanism. A nanochannel structure, compositions of ion complexes, and mobilities of cations and anions studied by NMR, quantum-chemical, and ionic conductivity methods are discussed.

At-line and inline prediction of droplet size in mayonnaise with near-infrared spectroscopy

A novel use of near-infrared (NIR) spectroscopy and chemometrics is presented for non-invasive prediction of droplet-size of mayonnaise. Both at-line and inline monitoring capabilities were explored. At first during the offline experimentation, two different batches of mayonnaise were prepared under pilot plant manufacturing conditions. The mayonnaise was manufactured with different fat content levels and different milling speeds to induce differences in the droplet size during the process. The reference droplet-sizes were measured using pulsed-field gradient nuclear magnetic resonance (pfg-NMR). NIR data were calibrated with reference droplet-size measurements by partial least-square (PLS) regression. The results of at-line analysis showed that the NIR models reached high performance to predict droplet-size in mayonnaise. Furthermore, separate, and global models were used for droplet size prediction for different fat content mayonnaise. For the second part of study, a diode-array NIR spectrometer was directly integrated in the process line for mayonnaise manufacturing and real-time NIR measurements were performed. The process was modulated with different milling speeds and the effect on NIR measurements was explored. The chemometric analysis performed on the NIR process data allowed following the droplet size changes due to changing milling speed. Overall, NIR provided a good correlation with droplet-size of mayonnaise and can support applications such as real-time monitoring of droplet-size during mayonnaise manufacturing process to optimize process and product properties.

Investigation of domain structures in monomethoxy poly(ethylene glycol)‐b‐poly(caprolactone) grafted poly(acrylic acid) by NMR diffusion studies

AbstractAssociating polymers developed by grafting a block copolymer of monomethoxy poly(ethylene glycol)‐b‐poly(caprolactone) (MPEG‐b‐PCL) onto poly(acrylic acid) undergo an irreversible sol–gel transition on heating. The influence of various physicochemical parameters on the thermoresponsive behaviour was examined by rheology and NMR studies. Pulsed field gradient NMR diffusion studies were performed to probe the mechanism of thermally induced gelation. Analysis of the diffusion data reveals the presence of loosely and strongly associated structures which respond differently to variation in temperature. It is observed that the polymer solution, which is visibly homogeneous, is heterogeneous on a mesoscopic scale with a distribution of domains. Detailed investigation of the thermally induced sol–gel transition shows that the mechanism of gelation involves irreversible alterations in the domain structure and size. © 2022 Society of Industrial Chemistry.

Ionic conduction within non-stoichiometric N-Methylimidazole-Acetic Acid Pseudo-Protic ionic liquid mixtures

We recently suggested that proton conduction mechanisms, such as the Grotthuss mechanism, could occur in an equimolar mixture of N-methylimidazole (C1Im) and acetic acid (CH3COOH), which is a pseudo-protic ionic liquid (pPIL). Appropriate amounts of C1Im and CH3COOH were mixed in various molar ratios to investigate the concentration dependence of proton conduction. At a mole fraction of xC1Im = 0.2, the ionic conductivity was the highest, despite the highest viscosity. Proton dynamics and carriers are crucial in rapid proton conduction. To clarify the proton conduction mechanism and the identities of the chemical species within the non-equimolar pPILs [C1Im]x[CH3COOH](1 –x), pulsed-field gradient nuclear magnetic resonance and Raman spectroscopy were performed. C1HIm+ predominantly existed at xC1Im = 0.2 due to proton transfer from CH3COOH, and CH3COO–···CH3COOH hydrogen bonding occurred. With an increasing molar ratio of C1Im, the molecular complex C1Im-CH3COOH formed, with the species distribution function exhibiting a maximum at approximately xC1Im = 0.5. Although the self-diffusion coefficients were small and the viscosity increased with decreasing C1Im concentration, the ionic conductivity increased. In addition, the self-diffusion coefficients of the labile hydrogen atoms were the largest among all of the hydrogen atoms at xC1Im = 0.2, suggesting that a specific proton conduction mechanism occurred via hydrogen bonding. Furthermore, the proton conduction mechanism could be controlled by altering the composition of the pPIL.

High-Entropy Polyanionic Lithium Superionic Conductors

High-entropy ceramics are attracting large interest because of their unique materials properties. Nevertheless, the effect of entropy on the lithium transport remains largely elusive. Here, we report, for the first time, about medium- and high-entropy polyanionic lithium superionic conductors crystallizing in the F–43m space group and adopting the so-called argyrodite structure. The Li6PS5[Cl0.33Br0.33I0.33], Li6P[S2.5Se2.5][Cl0.33Br0.33I0.33], and Li6.5[Ge0.5P0.5][S2.5Se2.5][Cl0.33Br0.33I0.33] materials were structurally characterized using complementary synchrotron and neutron scattering techniques in combination with 31P magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy. We show that, in contrast to other high-entropy ceramics, an unequal distribution of elements over the respective crystallographic sites occurs in these materials. Using electrochemical impedance spectroscopy (EIS) and 7Li pulsed field gradient (PFG) NMR spectroscopy, we demonstrate that introducing entropy (compositional disorder) marginally affects the room-temperature ionic conductivity (∼10–3 S cm–1) but instead lowers the activation energy for conduction to 0.22 eV. Our results emphasize the possibility of increasing entropy in polyanionic materials, thereby opening up compositional space for the search of Li-ion conductors with unprecedented properties.

Influence of vanillic acid immobilization in Nafion membranes on intramembrane diffusion and structural properties.

Pulsed field gradient (PFG) NMR in combination with quasielastic neutron scattering (QENS) was used to investigate self-diffusion of water and acetone in Nafion membranes with and without immobilized vanillic acid (VA). Complementary characterization of these membranes was performed by small angle X-ray scattering (SAXS) and NMR relaxometry. This study was motivated by the recent data showing that an organic acid, such as VA, in Nafion can preserve its catalytic activity in the presence of water even at high intra-polymer water concentrations corresponding up to 100% ambient relative humidity. However, there is currently no clear understanding of how immobilized organic acid molecules influence the microscopic transport properties and related structural properties of Nafion. Microscopic diffusion data measured by PFG NMR and QENS are compared for Nafion with and without VA. For displacements smaller than the micrometer-sized domains previously reported for Nafion, the VA addition was not observed to lead to any significant changes in the water and/or acetone self-diffusivity measured by each technique inside Nafion. However, the reported PFG NMR data present evidence of a different influence of acetone concentration in the membranes with and without VA on the water permeance of the interfaces between neighboring micrometer-sized domains. The reported diffusion data are correlated with the results of SAXS structural characterization and NMR relaxation data for water and acetone.

Diffusion measurements of hydrocarbons in H-MCM-41 extrudates with pulsed-field gradient nuclear magnetic resonance spectroscopy.

Mesoporous materials are promising catalysts for production of biofuels. Herein, H-MCM-41 catalysts with different concentrations of the silica Bindzil binder (10–50 wt%) were prepared and characterized using pulsed-field gradient (PFG) NMR in the powder form and as extrudates. Effective diffusion coefficients (De) are measured in all cases. Diffusivities of n-hexadecane were found smaller for extrudates as compared to the powder catalysts. The estimates of diffusive tortuosity were also determined. PFG NMR data showed one major component that reveals diffusion in interconnected meso- and micropores and one other minor component (1–2%) that may correspond to more isolated pores or may represent complex effects of restricted diffusion. Therefore, several approaches including initial slope analysis of spin-echo attenuation curves, two-component fitting and Laplace inversion were used to discuss different aspects of diffusional transport in the studied H-MCM-41 materials. Correlations between De and the amount of Bindzil, the specific surface area, the micropore volume, the particle size, the total acid sites and the Lewis acid sites are discussed.

Dynamic Water Promotes Lithium-Ion Transport in Superconcentrated and Eutectic Aqueous Electrolytes

Superconcentrated aqueous electrolytes have shown promise as safe and high-voltage lithium-ion battery (LIB) electrolytes. However, the interplay of lithium-ion solvation structure and dynamics with fast Li-ion transport has not been elucidated yet. Here, we combine the ultrafast femtosecond mid-IR spectroscopy, dielectric relaxation spectroscopy, pulsed-field gradient NMR, and molecular dynamics simulation for investigating the solvation structure and Li-ion transport mechanism in superconcentrated aqueous electrolytes. We found the existence of water molecules with vibrational and rotational properties very similar to those of bulk water, even at extremely high salt concentrations (28 m). Our experimental results show that the electrolytes have a heterogeneous solvation environment, and bulk-like water molecules promote fast Li-ion transport. We anticipate that the molecular understanding of the superconcentrated aqueous electrolytes obtained here would facilitate the design of solvation structures to overcome the limit of dilute LIB electrolytes.

Effect of LDH platelets on the transport properties and carbonation of anion exchange membranes

We report on an extensive study on nanocomposite Anion Exchange Membranes (AEMs) based on tetramethylammonium Polysulfone ionomer and Layered Double Hydroxide (LDH) as nanofiller. The AEMs were investigated in both OH− and HCO3− forms, comparing swelling capacity and transport properties. Ionic conductivity measurements were performed both by Electrochemical Impedance Spectroscopy and Ziv and Dekel's method, while the water and ions mobility by 1H Pulse Field Gradient (PFG) NMR spectroscopy.One of the most serious problems to be addressed in AEMs fuel cell technology is that of the significant loss of performance when CO2 is present in the reaction oxidant gas (e.g., air) due to the phenomenon of carbonation. In this work, the carbonation kinetics of AEMs and the effect of LDH filler were addressed through 13C NMR spectroscopy (including diffusometry and relaxometry measurements). The presence of LDH platelets in the AEM significantly reduces the conversion rate of hydroxide groups. The interaction between the polymer chains and the anionic clay lamellae creates a suitable network that benefits the membrane's ionic conductivity, its mechanical properties (DMA tests), and finally reduces the rate of alkaline degradation.

Pulsed Field Gradient Nuclear Magnetic Resonance and Diffusion Analysis in Battery Research

Pulsed-field gradient nuclear magnetic resonance (PFG-NMR) is a widely used method for determining the diffusion coefficient of ions and molecules both in the bulk and when confined (e.g., within p...