Pulsed Field Gradient NMR Experiments Research Articles

Dimensionality Control of Li Transport by MOFs Based Quasi‐Solid to Solid Electrolyte (Q‐SSEs) for Li−Metal Batteries

AbstractNowadays, lithium‐ion batteries (LIBs) are widely used in all walks of life and play a very important role. As complex systems composed of multiple materials with diverse chemical compositions, where different electrochemical reactions take place, battery interfaces are essential for determining the operation, performance, durability and safety of the battery. This work, set out to study the incorporation of lithium bis(fluorosulfonyl)amide (LiFSI) doped 1‐ethyl‐3‐methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIm][TFSI]) ionic liquid into an archetype Ti‐based Metal Organic Framework (MOF) ((Ti) MIL125−NH2) to create a solid to quasi‐solid (depending on the amount of IL in the system), and how it affects not only ionic transport but also the structural properties of the IL/MOF electrolyte. Remarkably high ionic conductivity values (2.13×10−3 S ⋅ cm−1 at room temperature) as well as a lithium transference number (tLi=0.58) were achieved, supported by pulsed field gradient (PFG) NMR experiments. Electrochemical characterization revealed reversible plating‐stripping of lithium and lower overpotential after 750 h at 50 °C. Additionally, a proof‐of‐concept solid state battery was fabricated resulting in a discharge capacity of 160 mAh ⋅ g−1 at 50 °C and 0.1 C rate after 50 cycles. This work presents a suitable strategy to dendrite suppression capability, allowing its implementation as interface modifiers in next‐generation solid‐state batteries.

Assessment of models for calculating the hydrodynamic radius of intrinsically disordered proteins

Diffusion measurements by pulsed-field gradient NMR and fluorescence correlation spectroscopy can be used to probe the hydrodynamic radius of proteins, which contains information about the overall dimension of a protein in solution. The comparison of this value with structural models of intrinsically disordered proteins is nonetheless impaired by the uncertainty of the accuracy of the methods for computing the hydrodynamic radius from atomic coordinates. To tackle this issue, we here build conformational ensembles of 11 intrinsically disordered proteins that we ensure are in agreement with measurements of compaction by small-angle x-ray scattering. We then use these ensembles to identify the forward model that more closely fits the radii derived from pulsed-field gradient NMR diffusion experiments. Of the models we examined, we find that the Kirkwood-Riseman equation provides the best description of the hydrodynamic radius probed by pulsed-field gradient NMR experiments. While some minor discrepancies remain, our results enable better use of measurements of the hydrodynamic radius in integrative modeling and for force field benchmarking and parameterization.

Effect of rotation in NMR diffusion experiments on micron-sized particles: A generalized theoretical treatment

We have recently developed an analytical framework to interpret the results of pulsed field gradient (PFG) NMR experiments on solution samples of micron-sized amyloid fibrils [Angew. Chem. Int. Ed. 60 (2021) 15445–15451. https://doi.org/10.1002/anie.202102408]. Here we generalize this result by reporting a rigorous theoretical model of such experiments, implemented in a form of efficient computational scheme. In particular, the new treatment fully accounts for the anisotropy of fibrils’ translational diffusion and takes into consideration the finite length of the gradient pulses. The results hold not only for the historic spin-echo sequence, but also for the widely used stimulated echo experiment. We have found that fibrils’ rotation can attenuate the echo by a factor comparable with that of translation. However, contrary to some recent claims, the rotational mechanism cannot lead to an apparent fast-diffusion situation.

The Role of Rotational Motion in Diffusion NMR Experiments on Supramolecular Assemblies: Application to Sup35NM Fibrils.

Pulsed-field gradient (PFG) NMR is an important tool for characterization of biomolecules and supramolecular assemblies. However, for micrometer-sized objects, such as amyloid fibrils, these experiments become difficult to interpret because in addition to translational diffusion they are also sensitive to rotational diffusion. We have constructed a mathematical theory describing the outcome of PFG NMR experiments on rod-like fibrils. To test its validity, we have studied the fibrils formed by Sup35NM segment of the prion protein Sup35. The interpretation of the PFG NMR data in this system is fully consistent with the evidence from electron microscopy. Contrary to some previously expressed views, the signals originating from disordered regions in the fibrils can be readily differentiated from the similar signals representing small soluble species (e.g. proteolytic fragments). This paves the way for diffusion-sorted NMR experiments on complex amyloidogenic samples.

Phospholipid Structural Features Influence Lateral Diffusion

Rapid lateral diffusion of lipids in bilayers is a critical property for function of biological membranes. A systematic study of diffusion as a function of lipid structure in well-defined synthetic bilayers is necessary for the confident interpretation of results on lipid diffusion in natural membranes and cells. Over the past 15 years, a large data set of lipid diffusion rates was accumulated in our lab by pulsed field gradient (PFG) NMR in combination with magic-angle spinning (MAS). The advantage of PFG NMR experiments versus other methods is that NMR reports the diffusion of all matrix lipids, not the diffusion of a low concentration of probe molecules whose behavior does not necessarily reflect that of matrix lipids.

Intracrystalline Transport Barriers Affecting the Self-Diffusion of CH4 in Zeolites |Na12|-A and |Na12-xKx|-A.

Carbon dioxide must be removed from biogas or natural gas to obtain compressed or liquefied methane, and adsorption-driven isolation of CO2 could be improved by developing new adsorbents. Zeolite adsorbents can select CO2 over CH4, and the adsorption of CH4 on zeolite |Na12-xKx|-A is significantly lower for samples with a high K+ content, i.e., x > 2. Nevertheless, we show, using 1H NMR experiments, that these zeolites adsorb CH4 after long equilibration times. Pulsed-field gradient NMR experiments indicated that in large crystals of zeolites |Na12-xKx|-A, the long-time diffusion coefficients of CH4 did not vary with x, and the upper limit of the mean-square displacement was about 1.5 μm, irrespective of the diffusion time. Also for zeolite |Na12|-A samples of three different particle sizes (∼0.44, ∼2.9, and ∼10.6 μm), the upper limit of the mean-square displacement of CH4 was 1.5 μm and largely independent of the diffusion time. This similarity provided further evidence for an intracrystalline diffusion restriction for CH4 within the medium- and large-sized zeolite A crystals and possibly of clustering and close contact among the small zeolite A crystals. The upper limit of the long-time diffusion coefficient of adsorbed CH4 was (at 1 atm and 298 K) about 10-10 m2/s irrespective of the size of the zeolite particle or the studied content of K+ in zeolites |Na12-xKx|-A and |Na12|-A. The T1 relaxation time for adsorbed CH4 on zeolites |Na12-xKx|-A with x > 2 was smaller than for those with x < 2, indicating that the short-time diffusion of CH4 was hindered.

Selective Control of Ion Transport by Nanoconfinement: Ionic Liquid in Mesoporous Resorcinol-Formaldehyde Monolith.

Thermal and dynamic properties of ionic liquid (IL)-based electrolytic solution (Li+TFSI- in Pyr13+TFSI-; 1-methyl-1-propylpyrrolidinium bis(trifluoromethylsulfonyl)imide = Pyr13+TFSI-) confined in nanoporous polymer hosts were investigated with respect to the pore size/porosity and the surface chemistry of the polymer host. As host material, mesoporous resorcinol-formaldehyde (RF) polymer monoliths with three-dimensionally connected pore structure were prepared, with precise control of the pore size ranging from ca. 7 to 60 nm. Thermal analysis of RF polymer-ionic liquid composites showed stability up to almost 400 °C and a melting point depression proportional to the inverse of the pore diameter. Good ionic conductivity comparable to that of a commercial separator is obtained, which is dependent on the porosity (i.e., pore volume) of the confining host material (i.e., the number of charge carriers available in the system). Further pulsed field gradient (PFG) NMR experiments revealed that the diffusion coefficient of Pyr13+ cation becomes smaller than that of TFSI- anion inside RF pores, which is contradictory to the bulk IL system. This change in the ionic motion is due to electrostatic attraction between the pore walls and Pyr13+ cations, resulting in a layer structure composed of a Pyr13+ cation-rich layer adsorbed at the pore wall surface and a TFSI- anion-enriched bulklike layer at the pore center. Our study suggests that transport characteristics of the ions of interest can be controlled by optimizing the surface chemistry of the host framework and their motion can be separately monitored by PFG NMR spectroscopy.

Solubilization of active ingredients of different polarity in Pluronic® micellar solutions – Correlations between solubilizate polarity and solubilization site

The solubilization of two pharmaceutically active ingredients (AI) with significantly different water solubility, namely carbamazepine and fenofibrate (solubility of 150ppm and 10ppm, respectively), has been investigated using a series of Pluronics® (Poloxamers) containing different ethylene oxide and propylene oxide (EO/PO) units in the molecule. The results show largely enhanced solubilization of fenofibrate by Pluronic® micelles that increases with the PPO chain length provided the temperature is above the critical micelle temperature (cmt). In contrast the more water-soluble carbamazepine only shows a moderate increase in solubilization upon addition of Pluronics®. Small angle neutron scattering (SANS) and pulsed field gradient (PFG) NMR experiments show that the solubilization of fenofibrate occurs in the core of the micelles, whereas carbamazepine shows no direct association with the micelles. These clearly different solubilization mechanisms for the two AIs were confirmed by Nuclear Overhauser Enhancement Spectroscopy (NOESY) experiments, which show that fenofibrate interacts only with the PPO core of the micelle, whereas carbamazepine interacts with both PPO and PEO similarly. Accordingly, the large enhancement of the solubilization of fenofibrate is related to the fact that it is solubilized within the PPO core of the Pluronic® micelles, while the much more moderate increase of carbamazepine solubility is attributed to the change of solvent quality due to the presence of the amphiphilic copolymer and the interaction with the EO and PO units in solution.

Local coordination and dynamics of a protic ammonium based ionic liquid immobilized in nano-porous silica micro-particles probed by Raman and NMR spectroscopy.

Room temperature ionic liquids confined in a solid material, for example, nano-porous silica, are particularly propitious for energy related applications. The aim of this study is to probe the molecular interactions established between the protic ionic liquid diethylmethylammonium methanesulfonate (DEMA-OMs) and silica, where the latter consists of nano-porous micro-particles with pores in the size range of 10 nm. The changes in the local coordination and transport properties induced by the nano-confinement of the ionic liquid are investigated by a combination of Raman and solid-state NMR spectroscopy. In particular, one-dimensional (1D) (1)H and (29)Si and two-dimensional (2D) (29)Si{(1)H} HETOCR solid-state NMR are combined to identify the sites of interaction at the silica-ionic liquid interface. Pulsed field gradient (PFG) NMR experiments are performed to estimate the self-diffusion of both bulk and nano-confined DEMA-OMs. Complementary information on the overall coordination and interaction scheme is achieved by Raman spectroscopy. All these advanced experimental techniques are revealed to be crucial to differentiate between ionic liquid molecules residing in the inter- or intra-particle domains.

Nuclear Magnetic Resonance Study of Water-Polymer Interactions and Self-Diffusion of Water in Polymer Films

The diffusivity and distribution of water in the butyl methacrylate and methacrylic acid copolymer films swollen in water have been investigated using the NMR relaxation and pulse field gradient (PFG) NMR techniques. The contributions of polymer matrix protons, surface water and bound water have been determined from 1H NMR spectra and relaxation functions. PFG NMR experiments showed that the echo attenuation function depends on the diffusion time indicating that water inside the swollen film is trapped in restricted confinement. The data obtained have been discussed using published physical models for diffusion of water in polymeric materials. The sizes of pores inside the film were estimated using the published model approaches giving the range of 0.8-1.0 μm. Magnetization decays as well as the spin-spin relaxation times of water saturated polymer films were also determined in this study. NMR relaxation provided additional information on the water distribution in the porous microstructure. The volume-averaged water mobility decreased with increasing hydrophobic content of the polymers.

An effective phase shift diffusion equation method for analysis of PFG normal and fractional diffusions

Pulsed field gradient (PFG) diffusion measurement has a lot of applications in NMR and MRI. Its analysis relies on the ability to obtain the signal attenuation expressions, which can be obtained by averaging over the accumulating phase shift distribution (APSD). However, current theoretical models are not robust or require approximations to get the APSD. Here, a new formalism, an effective phase shift diffusion (EPSD) equation method is presented to calculate the APSD directly. This is based on the idea that the gradient pulse effect on the change of the APSD can be viewed as a diffusion process in the virtual phase space (VPS). The EPSD has a diffusion coefficient, Kβ(t)D radβ/sα, where α is time derivative order and β is a space derivative order, respectively. The EPSD equations of VPS are built based on the diffusion equations of real space by replacing the diffusion coefficients and the coordinate system (from real space coordinate to virtual phase coordinate). Two different models, the fractal derivative model and the fractional derivative model from the literature were used to build the EPSD fractional diffusion equations. The APSD obtained from solving these EPSD equations were used to calculate the PFG signal attenuation. From the fractal derivative model the attenuation is exp(−γβgβδβDf1tα), a stretched exponential function (SEF) attenuation, while from the fractional derivative model the attenuation is Eα,1(−γβgβδβDf2tα), a Mittag–Leffler function (MLF) attenuation. The MLF attenuation can be reduced to SEF attenuation when α=1, and can be approximated as a SEF attenuation when the attenuation is small. Additionally, the effect of finite gradient pulse widths (FGPW) is calculated. From the fractal derivative model, the signal attenuation including FGPW effect is exp-Df1∫0τKβ(t)dtα. The results obtained in this study are in good agreement with the results in literature. Several expressions that describe signal attenuation have not been reported and that can be of great importance for the PFG experiments. This EPSD equation method provides a new, simple path to calculate signal attenuation of PFG NMR experiments.

Studies on supramolecular gel formation using DOSY NMR.

Herein, we present the results obtained from our studies on supramolecular self-assembly and molecular mobility of low-molecular-weight gelators (LMWGs) in organic solvents using pulsed field gradient (PFG) diffusion ordered spectroscopy (DOSY) NMR. A series of concentration-dependent DOSY NMR experiments were performed on selected LMWGs to determine the critical gelation concentration (CGC) as well as to understand the behaviour of the gelator molecules in the gel state. In addition, variable-temperature DOSY NMR experiments were performed to determine the gel-to-sol transition. The PFG NMR experiments performed as a function of gradient strength were further analyzed using monoexponential DOSY processing, and the results were compared with the automated Bayesian DOSY transformation to obtain 2D plots. Our results provide useful information on the stepwise self-assembly of small molecules leading to gelation. We believe that the results obtained from these experiments are applicable in determining the CGC and gel melting temperatures of supramolecular gels.

Xenon in l-Alanyl-l-Valine Nanochannels: A Highly Ideal Molecular Single-File System

Xenon-129 pulsed field gradient NMR and hyperpolarized xenon-129 spin tracer exchange NMR experiments were performed on polycrystalline l-Ala-l-Val (AV) and l-Val-l-Ala (VA) nanochannels under identical conditions of temperature and Xe pressure. Displacements of up to 3 μm were measured in specimens with mean crystallite lengths of around 50–100 μm. The combination of the two NMR techniques yielded the most definitive evidence for molecular single file diffusion to date, in which the time-scaling of the mean squared displacement is proportional to the square-root of time. The PFG-NMR echo attenuation data yield single-file mobility factors of 6 ± 0.7 × 10–13 m2 s–1/2 and 4.4 ± 0.2 × 10–13 m2 s–1/2. The results establish Xe in AV nanochannels, in particular, as an ideal experimental model system for fundamental studies of single-file diffusion dynamics.

Pore-Scale Mixing and Transverse Dispersivity of Randomly Packed Monodisperse Spheres

We show that transverse dispersion in flow through randomly packed monodisperse spheres (sphere diameter d) is a velocity-dependent superposition of three separable random processes-diffusion with coefficient D(r), intrinsic mechanical dispersion with dispersivity l(m)=d/33 caused by advection on streamlines, and a newly identified coupled mechanical dispersion with dispersivity l(c)=d/11, which arises by coupled advection and transverse diffusion at the pore scale. The velocity dependence of the transverse dispersivity is derived from first principles. Our analysis is insensitive to details of the pore geometry and is verified by pulsed field gradient NMR experiments which covered 4.5 orders of magnitude in reduced velocity.

Erratum: “A general framework to quantify the effect of restricted diffusion on the NMR signal with applications to double pulsed field gradient NMR experiments” [J. Chem. Phys. 130, 104702 (2009)

Erratum: “A general framework to quantify the effect of restricted diffusion on the NMR signal with applications to double pulsed field gradient NMR experiments” [J. Chem. Phys. 130, 104702 (2009)

Carbohydrate particles as protein carriers and scaffolds: physico-chemical characterization and collagen stability

The preservation of protein properties after entrapping into polymeric matrices and the effects of drying the emulsions still remains uncertain and controversial. Carbohydrate particles were designed and prepared by homogenization of gum arabic and maltodextrin mixture, with collagen hydrolysate (CH) followed by spray-drying. The encapsulation of CH in the carbohydrate matrix was achieved with an efficiency of 85 ± 2 %. The morphology and the size of the particles, before (40–400 nm) and after spray-drying (<20 μm), were characterized by scanning electron microscopy and dynamic light scattering. Measurements of the nuclear relaxation times and application of diffusion ordered spectroscopy, obtained through pulsed field gradient NMR experiments, have been performed to determine the structure of the CH–polysaccharide conjugates and to clarify the mechanism of CH immobilization in the polysaccharide matrix. In vitro release profiles in ultrapure water and in cellular medium reveal that the diffusion rate of CH from the polymeric matrix to the dialysis solution decreases in average 30–50 % over time, compared to free CH molecules. In cellular medium at 37 °C, the complete release of CH from the particles is achieved only after 24 h, demonstrating a significant decrease in the CH mass transfer process when compared with free CH. The findings of this study outline the ability of gum arabic/maltodextrin matrices to entrap and preserve CH original properties after the spray-drying process and support the potential of the polymeric scaffold for protein delivery and tissue engineering.

Identification of Multiple Diffusion Rates in Mixed Solvent Anion Exchange Membranes Using High Resolution MAS NMR

High resolution magic angle spinning (HRMAS) 1H NMR in combination with 2D exchange NOESY and pulsed field gradient (PFG) NMR diffusion experiments have been used to characterize 1 N methanol swollen polymer anion exchange membranes (AEM) presently being developed for alkaline fuel cells. Standard static 1H NMR experiments on these materials have proven unsuccessful due to severe signal broadening. New experimental methods for increased resolution are needed to determine distinct solvent environments and transport properties. Using HRMAS NMR, resonances from water and methanol in both a free (bulk-like) environment and membrane-associated environment within the AEM were observed. 1H HRMAS PFG NMR experiments identified different molecular diffusion environments in the solvent, while 1H 2D NOESY exchange NMR experiments confirmed spatial contacts between membrane-associated species and the membrane. These results demonstrate that 1H HRMAS is an ideal technique for the characterization of individual environments and diffusion rates in polymer membranes with mixed solvent systems.

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.

In Situ PFG NMR of Silicalite-1 Synthesis Mixtures

The interactions between tetrapropylammonium cations and the silica nanoparticles present in silicalite-1 precursor solutions were characterized at 70 °C using in situ pulsed field gradient (PFG) NMR experiments. In situ PFG NMR results show that the organocation diffusion coefficients at 70 °C are larger than those at 25 °C. Although the adsorption isotherms calculated from the diffusion data present similar trends at both temperatures, the adsorption isotherms at 70 °C could not be accurately described using a Lineweaver–Burk analysis. Therefore, the Freundlich equation was used to fit the adsorption data and Gibbs free energies between 6 and 15 kJ/mol were obtained. Time evolution studies show that organocation diffusion coefficients increased with the time, reached a maximum at about 6 days, and trended to a plateau towards the end of the synthesis. This maximum in the diffusion coefficient of the organocation coincides in time with the exothermic–endothermic transition that is known to occur near the...

GPU accelerated Monte Carlo simulation of pulsed-field gradient NMR experiments

The simulation of diffusion by Monte Carlo methods is often essential to describing NMR measurements of diffusion in porous media. However, simulation timescales must often span hundreds of milliseconds, with large numbers of trajectories required to ensure statistical convergence. Here we demonstrate that by parallelising code to run on graphics processing units (GPUs), these calculations may be accelerated by over three orders of magnitude, opening new frontiers in experimental design and analysis. As such cards are commonly installed on most desktop computers, we expect that this will prove useful in many cases where simple analytical descriptions are not available or appropriate, e.g. in complex geometries or where short gradient pulse approximations do not hold, or for the analysis of diffusion-weighted MRI in complex tissues such as the lungs and brain.