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.     

Dynamic properties of water in silicalite-1 powder

Self-diffusion of D₂O in partially filled silicalite-1 crystals was studied at 25°C by ²H nuclear magnetic resonance (NMR) with bipolar field gradient pulses and longitudinal Eddy-current-delay. For the first time, reliable experimental diffusion data for this system were obtained. Analysis of NMR diffusion decays revealed the presence of a continuous distribution of apparent self-diffusion coefficients (SDCs) of water, ranging from 10⁻⁷ to ∼10⁻¹⁰ m²/s, which include values much higher and lower than that of bulk water (∼10⁻⁹ m²/s) in liquid phase. The observed distribution of SDC changes with variation of the diffusion time in the range of 10–200 ms. A two-site Kärger exchange model was successfully fitted to the data. Finally, the water distribution and exchange in silicalite-1 pores were described by taking into account (a) a gas-like phase in the zeolite pores, a gas-like phase in mesopores and an intercrystalline gas-like phase and (b) intercrystalline liquid droplets with intermediate exchange rate with the other phases. The other phases experience fast exchange on the NMR diffusion time scale. Diffusion coefficients and mean residence times of water in some of these states were estimated.     

Determination of Very Slow Diffusion of Paramagnetic Ions by NMR Spectroscopy

In this paper, we propose a new method of measuring the very slow paramagnetic ion diffusion coefficient using a commercial high-resolution spectrometer. If there are distinct paramagnetic ions influencing the hydrogen nuclear magnetic relaxation time differently, their diffusion coefficients can be measured separately. A cylindrical phantom filled with Fricke xylenol gel solution and irradiated with gamma rays was used to validate the method. The Fricke xylenol gel solution was prepared with 270 Bloom porcine gelatin, the phantom was irradiated with gamma rays originated from a ⁶⁰Co source and a high-resolution 200 MHz nuclear magnetic resonance (NMR) spectrometer was used to obtain the phantom ¹H profile in the presence of a linear magnetic field gradient. By observing the temporal evolution of the phantom NMR profile, an apparent ferric ion diffusion coefficient of 0.50 μm²/ms due to ferric ions diffusion was obtained. In any medical process where the ionizing radiation is used, the dose planning and the dose delivery are the key elements for the patient safety and success of treatment. These points become even more important in modern conformal radio therapy techniques, such as stereotactic radiosurgery, where the delivered dose in a single session of treatment can be an order of magnitude higher than the regular doses of radiotherapy. Several methods have been proposed to obtain the three-dimensional (3-D) dose distribution. Recently, we proposed an alternative method for the 3-D radiation dose mapping, where the ionizing radiation modifies the local relative concentration of Fe²⁺/Fe³⁺ in a phantom containing Fricke gel and this variation is associated to the MR image intensity. The smearing of the intensity gradient is proportional to the diffusion coefficient of the Fe³⁺ and Fe²⁺ in the phantom. There are several methods for measurement of the ionic diffusion using NMR, however, they are applicable when the diffusion is not very slow.     

Pulsed-Field-Gradient Measurements of Time-Dependent Gas Diffusion

Pulsed-field-gradient NMR techniques are demonstrated for measurements of time-dependent gas diffusion. The standard PGSE technique and variants, applied to a free gas mixture of thermally polarized xenon and O₂, are found to provide a reproducible measure of the xenon diffusion coefficient (5.71 × 10⁻⁶m²s⁻¹for 1 atm of pure xenon), in excellent agreement with previous, non-NMR measurements. The utility of pulsed-field-gradient NMR techniques is demonstrated by the first measurement of time-dependent (i.e., restricted) gas diffusion inside a porous medium (a random pack of glass beads), with results that agree well with theory. Two modified NMR pulse sequences derived from the PGSE technique (named the Pulsed Gradient Echo, or PGE, and the Pulsed Gradient Multiple Spin Echo, or PGMSE) are also applied to measurements of time dependent diffusion of laser polarized xenon gas, with results in good agreement with previous measurements on thermally polarized gas. The PGMSE technique is found to be superior to the PGE method, and to standard PGSE techniques and variants, for efficiently measuring laser polarized noble gas diffusion over a wide range of diffusion times.     

On the role of experimental imperfections in constructing 1H spin diffusion NMR plots for domain size measurements

We discuss the precision of 1D chemical-shift-based ¹H spin diffusion NMR experiments as well as straightforward experimental protocols for reducing errors. The ¹H spin diffusion NMR experiments described herein are useful for samples that contain components with significant spectral overlap in the ¹H NMR spectrum and also for samples of small mass (<1 mg). We show that even in samples that display little spectral contrast, domain sizes can be determined to a relatively high degree of certainty if common experimental variability is accounted for and known. In particular, one should (1) measure flip angles to high precision (≈±1° flip angle), (2) establish a metric for phase transients to ensure their repeatability, (3) establish a reliable spectral deconvolution procedure to ascertain the deconvolved spectra of the neat components in the composite or blend spin diffusion spectrum, and (4) when possible, perform 1D chemical-shift-based ¹H spin diffusion experiments with zero total integral to partially correct for errors and uncertainties if these requirements cannot fully be implemented. We show that minimizing the degree of phase transients is not a requirement for reliable domain size measurement, but their repeatability is essential, as is knowing their contribution to the spectral offset (i.e. the J₁ coefficient). When performing experiments with zero total integral in the spin diffusion NMR spectrum with carefully measured flip angles and known phase transient effects, the largest contribution to error arises from an uncertainty in the component lineshapes which can be as high as 7%. This uncertainty can be reduced considerably if the component lineshapes deconvolved from the composite or blend spin diffusion spectra adequately match previously acquired pure component spectra.     

Ionic diffusion and structural changes in lithium compounds

⁷Li NMR measurements have been performed to study milling effects on ionic diffusion in lithium cobalt oxide, LiCoO₂ and piezoelectric compound, LiNbO₃ prepared by mechanical milling method. The milling process gives quite different effects on NMR spectra of these compounds. Both ⁷Li MAS and static NMR spectra of the milled LiCoO₂ show the line broadening with increasing milling time. ⁵⁹Co static spectra also show specific changes in the line shape with increasing milling time. These results would be attributed to the change in an electronic state of Co 3d orbitals because of charge compensation associated with oxygen vacancies and/or defects. ⁷Li static NMR spectrum of milled LiNbO₃ shows complicated line shape with increasing milling time. It is explained by superposition of two spectra arising from mobile Li⁺ ions and non-mobile ones settled on the fixed site. It is shown that the ratio of mobile Li⁺ ions increases up to a maximum of 9.4% with increasing milling time. Milling effects on the Li⁺ ionic diffusion in LiCoO₂ and LiNbO₃ are discussed in connection with changes in local structure.     

New prospects in studying Li diffusion—two-time stimulated echo NMR of spin-3/2 nuclei

The measurement of diffusion parameters like activation energies and translational jump rates of small cations plays a key role in materials science. Especially the in-depth investigation of Li diffusion in ionic conductors is of great interest, because suitable ionic conductors are needed for, e.g., the development of new secondary ion battery systems. As the standard tracer method is not applicable to study Li diffusion due to the lack of a suitable radioactive isotope, Li diffusion is alternatively probed by solid state NMR techniques. With the different NMR methods being available, diffusion processes can be studied on different length- and timescales. In the present paper we use two-time spin-alignment echo (SAE) NMR for the direct, i.e., model independent, measurement of extremely small translational Li jump rates. To this end, different crystalline and glassy ion conductors like Li_xTiS₂, Li₄SiO₄ as well as LiNbO₃ served as model substances to reveal the special features of this technique. SAE-NMR, which was originally developed for deuterons, has also been applied in a few cases to spin-3/2 nuclei, like ⁷Li, before. The corresponding correlation functions yield not only information about diffusion parameters but also about geometric properties of the diffusion pathways, making SAE-NMR a powerful method which complements well-established NMR techniques.     

Electrochemical determination of the lithium ion diffusion coefficient in TiS2

Long-time chronoamperometry of TiS₂ electrodes immersed in saturated LiClO₄/DMF solution was employed to investigate the charge transport processes which govern the rate of Li⁺ intercalation in TiS₂. The intercalation rate and hence, the current, appears to be controlled by the rate of Li⁺ diffusion within the TiS₂. A model has been developed which predicts the current-time behavior under the control of Li⁺ solid state diffusion. The close agreement of this model with the experimental data allows the solid state diffusion coefficient and other transport parameters (such as effective electrode area) to be evaluated from the measured average grain boundary distance. Typical TiS₂ grain boundary distances in the 3–10 μm range yield a geometric mean value of 1.3 × 10^?9 cm²/s for the solid state diffusion coefficient; this is in close agreement with previously reported diffusivities as measured by NMR spin-lattice relaxation techniques.     

2D CP/MASC Isotropic Chemical Shift Correlation Established byH Spin Diffusion

A new 2D solid-state CP/MAS¹³C NMR exchange experiment for through-space isotropic chemical shift correlation is proposed and demonstrated. Through-space correlation is established via a second cross polarization from¹³C to¹H and subsequent¹H spin diffusion. A third cross polarization results in the final¹³C–¹³C isotropic chemical shift correlation. The¹H spin diffusion time is a variable parameter allowing different mean square magnetization displacements to be probed. Experimental results on mixtures of differently¹³C-labeled alanine and polyethylene indicate that this site-selective 2D technique can be used to characterize domain sizes and proximities over a wide range of length scales (1–200 nm) in solids such as polymers or biological materials.     

Observation of anomalously fast diffusion in 3He–4He solid solutions near the BCC-HCP transition

The pulsed NMR technique was used to investigate diffusion on the BCC-HCP phase-equilibrium and melting curves of a dilute solution of ³He in ⁴He. The contributions from all coexisting phases were identified using the spin-echo method. It is established that, along with the contributions from the equilibrium BCC and HCP phases or from bulk liquid (in the melting curve measurements), there is an additional diffusional process that is characterized by an anomalously high diffusion coefficient. It is found that the latter is close to the diffusion coefficient in liquid helium, while the diffusion itself is spatially restricted. The observed effect may be caused by the formation of liquid droplets in the course of the BCC-HCP transition.     

A mixed basis approach in the SGP-limit

A perturbation method for computing quick estimates of the echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit is presented. The perturbation basis involves (relatively few) dipole distributions on the boundaries generating a small perturbation matrix in O(s²) time, where s denotes the number of boundary elements. Several approximate eigenvalues and eigenfunctions to the diffusion operator are retrieved. The method is applied to 1D and 2D systems with Neumann boundary conditions.     

Dynamic light scattering and <Superscript>31</Superscript>P NMR spectroscopy study of the self-assembly of deoxyguanosine 5'-monophosphate

Self-assembling properties of deoxyguanosine 5'-monophosphate in isotropic solutions of concentrations from 0.5 wt% to 15 wt% were investigated by dynamic light scattering (DLS) and ³¹P NMR spectroscopy. A slow diffusive mode with a diffusion coefficient D _slow∼ 10^-12 m²/s was detected by DLS for the whole concentration range. This mode is assigned to the translational motion of large globular aggregates, similar to those observed in DNA and other polyelectrolyte solutions. The existence of such aggregates was confirmed by freeze fracture electron microscopy. Close to the isotropic-cholesteric phase transition, at 4 wt% c 10 wt%, also a faster diffusive mode is observed in the polarized DLS response and a very fast mode is detected by depolarized DLS. These modes are related to translational and rotational diffusion of the columnar stacks of guanosine molecules, which are favorably formed in the relatively narrow pretransitional region. The stacking was also revealed from the appearance of a secondary resonance line in the ³¹P NMR spectra. Using the hydrodynamic theory of Tirado and Garcia de la Torre, the length of the cylindrical stacks was found to be L = 364±78 ?, which is significantly larger than the values reported for other guanosine derivatives. Received 13 July 2001 and Received in final form 17 October 2001     

Multinuclear NMR Study of Structure and Mobility in Cyclic Model Lithium Conducting Systems

The transport of the lithium ions is the basis of lithium ion conductivity of currently used electrolytes. Understanding how the transport of lithium ions within the matrix is influenced by the interactions with solvating moieties is needed to improve their performance. Along these lines well-defined model compounds based on cyclotriphosphazene (CTP) and hexaphenylbenzene (HPB) cores, bearing side groups of ethylene carbonate, a common solvent for lithium salts used as electrolytes in Li-ion batteries (Thielen et al. Chem. Mater, 23, 2120, 2011) and blended with different amounts of Lithium bis(trifluoromethanesulfonyl) imide (LiTFSI) have been studied by multinuclear nuclear magnetic resonance (NMR) spectroscopy. The local dynamics of the matrix was probed by ¹H and ³¹P NMR, while the local dynamics of the Li⁺ cations was unraveled by ⁷Li and ¹³C NMR. Transport of both ions was studied by pulsed-field gradient (PFG) NMR. Based on the different temperature dependences of the dynamics the bulk ion transport is not attributed to local dynamics, but to translational diffusion best characterized by PFG NMR. Although the glass transition temperatures of the blends are low, their conductivities are only in the range of typical polymer electrolytes. The results of NMR spectroscopy are in accord with the conjecture that the coordination between the cyclic carbonate functionality and the Li⁺-ion is too tight to allow for fast ion dynamics.     

Stable isotope-enhanced two- and three-dimensional diffusion ordered C NMR spectroscopy (SIE-DOSY C NMR)

The feasibility of obtaining high quality homonuclear or heteronuclear diffusion-ordered ¹³C NMR data is shown to be greatly improved by using ¹³C isotopically-enriched samples. Stable isotope-enhanced diffusion ordered (SIE-DOSY) ¹³C NMR has been applied to ¹³C-enriched carbohydrates, and has been used to determine diffusion coefficients for pentose and hexose monosaccharides, and a disaccharide and trisaccharide. These 2D spectra were obtained with as little as 8 min of acquisition time. Fully resolved 3D DOSY-HMQC NMR spectra of [U-¹³C]xylose, [U-¹³C]glucose, and [1-¹³C^gal]lactose were obtained in 5 h. Sample derivatization with [carbonyl-¹³C]acetate (peracetylation) extends the usefulness of the technique to included non-labeled sugars; the ¹³C-carbonyl – carbohydrate ring proton ¹H–¹³C correlations also provide additional structural information, as shown for the 3-D DOSY-HMQC analysis of a mixture of maltotriose and lactose per-[carbonyl-¹³C]acetates.     

Carbon-13 and tin-119 relaxation studies of some axially symmetrical organotin compounds

We have studied a variety of axially symmetrical tin compounds by ¹¹⁹Sn and ¹³C NMR. Tin was observed at two field strengths and, except for Ph₃SnCl, T₁ is field independent and governed mainly by spin-rotation. A chemical-shift anisotropy of 136 ppm is observed for ¹¹⁹Sn in Ph₃SnCl. Deverell's relationship provides a good estimate of the values of the spin-rotational constants and the theory of Woessner, Snowden, and Huntress leads to the values of the rotational diffusion constants.     

Water signal attenuation in diffusion-weighted 1H NMR experiments during cerebral ischemia: influence of intracellular restrictions,extracellular tortuosity,and exchange

The “concept of restricted intracellular water diffusion at permeable boundaries,” which was recently used to model diffusion-weighted ¹H NMR experiments on glioma cells, was applied to measurements on the rat brain in vivo. Combined with the “concept of extracellular tortuosity,” various physiological states of the brain were simulated. Hereby, a variable intracellular volume fraction, intracellular exchange time, and extracellular tortuosity factor were considered for young, adult, and ischemic rat brains. The model simulated the cytotoxic shift of extracellular water, changes in membrane permeability and tissue morphology, and was able to explain the diffusion time dependence as well as the non-monoexponentiality of the diffusion attenuation curves. Preliminary diffusion time dependent experiments on the healthy rat brain (¹H NMR imaging) agreed well with the theoretical concept. Hereby, the intracellular water signal was separated from extracellular signal contributions by large diffusion weighting. It showed the characteristic of restricted diffusion as well as a signal decay due to the exchange of intracellular water across the plasma membrane. A map of the mean intracellular exchange time for water in living animal brain was determined, and the upper limit in rat brain was evaluated to 15 ms. The presented methods can be applied to correlate local differences in a map of exchange times with tissue morphology and to detect pathological deviations of the exchange time, e.g., during ischemia.     

β NMR on8Li in the superiqnic conductor Li3N

Polarized⁸Li nuclei were produced in a Li₃N single crystal by irradiation with polarized neutrons, Β-ray detected NMR signals and spin-lattice relaxation of⁸Li were observed between B and 300 K. In Li₃N there are two non-equivalent Li sites. The corresponding two quadrupole split NMR spectra could be resolved. From the measured relaxation rates activation enthalpies for two diffusion processes were deduced.     

NMR studies of hydrogen diffusion in hydrogen uranyl phosphate tetrahydrate (HUP)

¹H NMR spin-lattice relaxation times, T₁ (Zeeman) and T_1ϱ (rotating frame) and spin-spin relaxation times, T₂, and ³¹P NMR solid-echoes are reported for phase I and II of hydrogen uranyl phosphate tetrahydrate (HUP) at temperatures in the range 200–323 K. The spectral density functions extracted from the measured relaxation times for phases I and II are consistent with a 2D diffusion mechanism for hydrogen motion. ³¹P second moments determined from the solid-echoes show that all the hydrogens diffuse rapidly in phase I, and that the hydrogen-bond site nearest to the phosphate oxygen is not occupied in phase II. The mechanism for diffusion in phase II is discussed.     

Frequency-selective REDOR and spin-diffusion relays in uniformly labeled whole cells

Solid-state NMR is a powerful and non-perturbative method to measure and define chemical composition and architecture in bacterial cell walls, even in the context of whole cells. Most NMR studies on whole cells have used selectively labeled samples. Here, we introduce an NMR sequence relay using frequency-selective REDOR (fsREDOR) and spin diffusion elements to probe a unique amine contribution in uniformly ¹³C- and ¹⁵N-labeled Staphylococcus aureus whole cells that we attribute to the d-alanine of teichoic acid. In addition to the primary peptidoglycan structural scaffold, cell walls can contain significant amounts of teichoic acid that contribute to cell-wall function. When incorporated into teichoic acid, d-alanine is present as an ester, connected via its carbonyl to a ribitol carbon, and thus has a free amine. Teichoic acid d-Ala is removed during cell-wall isolations and can only be detected in the context of whole cells. The sequence presented here begins with fsREDOR and a chemical shift evolution period for 2D data acquisition, followed by DARR spin diffusion and then an additional fsREDOR period. fsREDOR elements were used for ¹³C observation to avoid complications from ¹³C–¹³C couplings due to uniform labeling and for ¹⁵N dephasing to achieve selectivity in the nitrogens serving as dephasers. The results show that the selected amine nitrogen of interest is near to teichoic acid ribitol carbons and also the methyl group carbon associated with alanine. In addition, its carbonyl is not significantly dephased by amide nitrogens, consistent with the expected microenvironment around teichoic acid.