Determination of genuine diffusivities in heterogeneous media using stimulated echo pulsed field gradient NMR

Pulsed field gradient (PFG) NMR diffusion measurements in heterogeneous media may lead to erroneous results due to the disturbing influence of internal magnetic field gradients. Here, we present a simple theoretical model which allows one to interpret data obtained by stimulated spin echo PFG NMR in the presence of spatially varying internal field gradients. Using the results of this theory, the genuine self-diffusion coefficients in heterogeneous media may be extrapolated from the dependence of the apparent diffusivities on the dephasing time of the simulated echo PFG NMR sequence. Experimental evidence that such extrapolation yields satisfactory results for self-diffusion of hexadecane in natural sediments (sand) and of n-octanol in doped MgO pastes is provided.     

On the problem of field-gradient NMR measurements of intracrystalline diffusion in small crystallites--water in NaA zeolites as an example

Necessary conditions for measuring intracrystalline diffusion in small crystal size systems via field-gradient NMR are discussed. As an illustrative case self-diffusion coefficients of water adsorbed in NaA zeolites (average crystal diameter about 1 μm) have been measured by ¹H-NMR stimulated echoes in static magnetic field gradients of up to 180 T/m in the temperature range of 254–344 K. Obtaining intracrystalline diffusion coefficients necessitates a sufficiently high spatial resolution only provided by such large field gradients.     

Translational free random walk of spins in the presence of a parabolic magnetic field

The free random walk approach has been used to analyze the attenuation of the NMR signal due to spin dephasing in the presence of a constant and pulsed parabolic magnetic field. The spin echo sequence was chosen to examine the attenuation of the NMR signal resulting from self-diffusion. In the framework of the gaussian approach, the long-time limit calculations predict more pronounced diffusion weighting for the parabolic field than for linear magnetic field. Analytical results were obtained and compared with those from other approaches based on a variety of different of approximations.     

Water self-diffusion in Chlorella sp. studied by pulse field gradient NMR

The water self-diffusion behavior in chlorella water suspension was investigated by pulsed field gradient NMR technique. Three types of water was determined, which differs according to the self-diffusion coefficients; bulk water, extracellular and intracellular water. Intracellular and extracellular water self-diffusion were restricted, and the sizes of restriction regions were 3.4 microm and 17 microm, respectively. The water molecular exchange process between these three diffusion regions was investigated. The residence time and exchange rate constant for chlorella cells were obtained. The cell wall permeability determined from the rate constant as 3 x 10(-6) m/s agreed with the permeability 10(-6) m/s obtained from time dependence of intracellular water self-diffusion coefficient. The structural cluster model of chlorella cell is estimated to describe the extracellular water self-diffusion in chlorella water suspension.     

NMR study of tomato pericarp tissue by spin-spin relaxation and water self-diffusion

Pericarp tissues of tomato varieties Quest and Cameron were studied by low-field nuclear magnetic resonance (NMR) at a controlled temperature of 20°C. The spin-spin relaxation times and the water diffusion coefficients were measured with Carr-Parcell-Meiboom-Gill and pulsed field gradient multi-spin-echo (PFGMSE) NMR sequences. Four relaxing components were extracted from the spin-spin relaxation. The components withT ₂=11 ms,T ₂=65 ms,T ₂=430 ms andT ₂=1500 ms were related to the nonexchangeable protons and water proton in each cell compartment (i.e., cell wall-extracellular space, cytoplasm and vacuole, respectively). In contrast to the relative intensities, theT ₂ values appeared insensitive to variety and harvest period. The difference in relative intensity was related to the size of the pericarp cell. The water self-diffusion coefficients for each cell compartment were determined simultaneously with the PFGMSE sequence. The water self-diffusion coefficients for the vacuole and cytoplasm were not affected by the harvest date or variety. However, the water self-diffusion in the cell wall-extracellular space was significantly different between the two varieties.     

Water behavior in perfluorinated ion-exchange membranes

The water molecules in acid and salt forms of perfluorinated sulfocation membranes (MF-4SK) have been investigated by employing nuclear magnetic resonance (NMR) and differential scanning calorimetry (DSC) techniques. The mobility parameters, correlation time and activation energy of water molecules were estimated from the results of the temperature dependence of¹H relaxation time and compared with water self-diffusion coefficients obtained with pulsed field gradient NMR. The NMR data showed no frozen unbound water in membranes at low water content with an amount of water molecules per sulfonate groupn being comparable to the cationic hydration numberh _o, whereas DSC thermograms showed peaks which are usually interpreted as a water fusion phenomenon in the membranes. The diffusion mechanism of water molecules below 260 K is different from that above 300 K due to additional hydrogen bonds in water clusters at the low-temperature region.     

Ionic and molecular Self-Diffusion in Ion-Exchange materials for fuel energetics studied by pulsed field gradient NMR

Pulsed field gradient nuclear magnetic resonance technique was applied to investigate the self-diffusion mechanism of water, alcohol molecules and Li⁻ counterions in sulfocation exchangers with different structures of the polymeric matrix. It was shown that in the homogeneous perfluorinated sulfocation exchange membranes the ionic and water translation motions are controled by the hydrogen bond network forming in ionogenic channels at the high water content. At the low solvent content, the self-diffusion coefficients of methanol and ethanol are higher than the water self-diffusion coefficients. The influence of non-ion-exchange sorbed electrolyte on Li⁺ self-diffusion coefficients was observed in the heterogeneous sulfocation exchanger KU-23.     

Self-diffusion measurements by a mobile single-sided NMR sensor with improved magnetic field gradient

A simple and fast method of measuring self-diffusion coefficients of protonated systems with a mobile single-sided NMR sensor is discussed. The NMR sensor uses a magnet geometry that generates a highly flat sensitive volume where a strong and highly uniform static magnetic field gradient is defined. Self-diffusion coefficients were measured by Hahn- and stimulated echoes detected in the presence of the uniform magnetic field gradient of the static field. To improve the sensitivity of these experiments, a Carr-Purcell-Meiboom-Gill pulse sequence was applied after the main diffusion-encoding period. By adding the echo train the experimental time was strongly shortened, allowing the measurement of complete diffusion curves in less than 1min. This method has been tested by measuring the self-diffusion coefficients D of various organic solvents and poly(dimethylsiloxane) samples with different molar masses. Diffusion coefficients were also measured for n-hexane absorbed at saturation in natural rubber with different cross-link densities. The results show a dependence on the concentration that is in good agreement with the theoretical prediction. Moreover, the stimulated-echo sequence was successfully used to measure the diffusion coefficient as a function of the evolution time in systems with restricted diffusion. This type of experiment proves the pore geometry and gives access to the surface-to-volume ratio. It was applied to measure the diffusion of water in sandstones and sheep Achilles tendon. Thanks to the strong static gradient G(0), all diffusion coefficients could be measured without having to account for relaxation during the pulse sequence.     

NMR 1D-imaging of water infiltration into mesoporous matrices

It is shown that coupling nuclear magnetic resonance (NMR) 1D-imaging with the measure of NMR relaxation times and self-diffusion coefficients can be a very powerful approach to investigate fluid infiltration into porous media. Such an experimental design was used to study the very slow seeping of pure water into hydrophobic materials. We consider here three model samples of nuclear waste conditioning matrices which consist in a dispersion of NaNO₃ (highly soluble) and/or BaSO₄ (poorly soluble) salt grains embedded in a bitumen matrix. Beyond studying the moisture progression according to the sample depth, we analyze the water NMR relaxation times and self-diffusion coefficients along its 1D-concentration profile to obtain spatially resolved information on the solution properties and on the porous structure at different scales. It is also shown that, when the relaxation or self-diffusion properties are multimodal, the 1D-profile of each water population is recovered. Three main levels of information were disclosed along the depth-profiles. They concern (i) the water uptake kinetics, (ii) the salinity and the molecular dynamics of the infiltrated solutions and (iii) the microstructure of the water-filled porosities: open networks coexisting with closed pores. All these findings were fully validated and enriched by NMR cryoporometry experiments and by performing environmental scanning electronic microscopy observations. Surprisingly, results clearly show that insoluble salts enhance the water progression and thereby increase the capability of the material to uptake water.     

1H NMR study of water relaxation and self-diffusion in human serum albumin aqueous solutions

Summary Water proton spin-lattice relaxation and self-diffusion in aqueous solutions of human serum albumin have been studied by¹H NMR as a function of the protein concentration. Spin-lattice relaxation data, which display a nonlinear behaviour with the protein concentration, could be fitted with a two-phase model taking into account the experimentally determined hydration (?bound?) water values. Despite a similar trend is registered for the water self-diffusion coefficient, such a model has been found unable to explain the related experimental data taken as a function of the biomolecule concentration. On the other hand, the solute-induced proton self-diffusion decrease could be satisfactorily interpreted by postulating an enhanced probability of hydrogen-bond formation occurring within the ?vicinal? water surrounding the biomolecules for several hydration shells. The consistency within the two models is discussed in connection with the magnetic interactions occurring within the solute-solvent systems.     

In vivo magnetic resonance diffusion measurement in the brain of patients with multiple sclerosis.

Measurement of water self-diffusion in the brain in 25 patients with multiple sclerosis was performed by magnetic resonance imaging. Quantitative diffusion measurements were obtained using single spin-echo pulse sequences with pulsed magnetic field gradients of different magnitude. Twenty-two of these patients also underwent measurement of the transverse relaxation time (T2). Only one plaque was evaluated in each patient. Based on prior knowledge, 12 plaques were classified as being 3 mo or less in age, and 7 plaques were classified as being more than 3 mo old. In all 25 plaques, water self-diffusion was found to be higher than in apparently normal white matter. Furthermore, water self-diffusion was found to be higher in acute plaques compared with chronic plaques. Finally, a slight tendency toward a relationship between the diffusion capability and T2 was found. We believe that an increased diffusion capability signifies an increase of the extracellular water space, which probably is related to the degree of demyelination. Thus, measurement of water self-diffusion in multiple sclerosis plaques may contribute to the study of pathogenesis of demyelination.     

Self-diffusion of water and benzene molecules adsorbed in synthetic opal samples

The self-diffusion of adsorbed molecules of water and benzene in porous synthetic opals has been studied by pulsed field gradient nuclear magnetic resonance. The study indicates two “phases” of water molecules differing by the self-diffusion coefficients, indicating two types of porosities existing in the synthetic opals. The smallest self-diffusion coefficient characterizes water in ultramicropores found on the surface of nanospheres. The form of the diffusion decay depends on temperature in the region of high temperatures as a result of exchange between pores of different sizes. The ultramicropores are inaccessible for the largest benzene molecules. Water adsorption and self-diffusion data confirm that annealing of the opal samples at 1293 K caused the collapse of ultramicropores.     

Structural and dynamic properties of polyoxyethylene sorbitan monooleate micelle in water dispersion studied by pulsed field gradient NMR

The diffusion phenomenon of a nonionic surfactant, polyoxyethylene sorbitan monooleate (POE-SMO), micelle in aqueous solution was investigated by pulsed field gradient nuclear magnetic resonance (PFG NMR) with a high gradient strength of 17.4 T/m at the diffusion timet _d varied from 3 to 300 ms. This high gradient strength allowed us to measure the slow self-diffusion coefficient of POE-SMO micelle, and the short diffusion time below 10 ms showed the restricted diffusion of the micelle. At the shortt _d the self-diffusion of the micelle was restricted and the restricted sizes were 1.8, 1.5, and 0.8 μm for the POE-SMO concentration of 100, 200 and 300 mM, respectively, and 0.6 μm for the POE-SMO only. The possible reason of this restriction was assumed to be the formation of a spatial network or a micellar clustering. Furthermore, a proton exchange between water molecule and surfactant OH group on the micelle surface was proposed. With respect to this proposal, the residence time of the proton at the micelle surface and the thickness of the surface were investigated from proton self-diffusion coefficients by PFG NMR.     

Determination of water self-diffusion coefficient in complex food products by low field 1H PFG-NMR: comparison between the standard spin-echo sequence and the T1-weighted spin-echo sequence

In 1990, Van Den Enden et al. proposed a method for the determination of water droplet size distributions in emulsions using a pulsed-field-gradient nuclear magnetic resonance (PFG-NMR) T1-weighted stimulated-echo technique. This paper describes both the T1-weighted spin-echo sequence, an improved method based on this earlier work, and, the standard PFG spin-echo sequence. These two methods were compared for water self-diffusion coefficient measurement in the fatty protein concentrate sample used as a 'cheese model.' The transversal and longitudinal relaxation parameters T1 and T2 were determined according to the temperature and investigated for each sample; fat-free protein concentrate sample, pure anhydrous milk fat, and fatty protein concentrate sample. The water self-diffusion in fat-free protein concentrate samples followed a linear behavior. Consequently, the water self-diffusion coefficient could be easily characterized for fat-free protein concentrate samples. However, it seemed more complicated to obtain accurate water self-diffusion in fatty protein concentrate samples since the diffusion-attenuation data were fitted by a bi-exponential function. This paper demonstrates that the implementation of the T1-weighted spin-echo sequence, using the different T1 properties of water and fat phases, allows the accurate determination of water self-diffusion coefficient in a food product. To minimize the contribution of the 1H nuclei in the fat phase on the NMR echo signal, the fat protons were selectively eliminated by an additional 180 degrees pulse. This new method reduces the standard errors of diffusion data obtained with a basic spin-echo technique, by a factor of 10. The effectiveness of the use of the T1-weighted spin-echo sequence to perform accurate water self-diffusion coefficients measurement in fatty products is thus demonstrated.     

Translational Mobility of Components and Structure of Water–Ethanol Solutions

The concentration dependences of self-diffusion coefficients of water and ethanol molecules in water–ethanol solutions are obtained by the method of nuclear magnetic resonance spectroscopy with the pulse magnetic field gradient. On the basis of the ideas of hydration of ethanol molecules, the obtained dependences are interpreted and assumptions are made about the structural organization of water–ethanol solutions in the region of diluted and concentrated solutions.     

Application of a portable nuclear magnetic resonance surface probe to porous media

A portable nuclear magnetic resonance (NMR) surface probe was used to determine the time-dependent self-diffusion coefficient D(t) of water molecules in two fluid-filled porous media. The measuring equipment and the inhomogeneous magnetic fields in the sensitive volume of the probe are described. It is discussed how to evaluate D(t) using a surface probe from the primary and stimulated echoes generated in three-pulse experiments. Furthermore, the evaluation of D(t) allows one to determine the geometrical structure of porous materials.     

129Xe diffusion in a ferroelectric liquid crystal

Measurements of ¹²⁹Xe self-diffusion and shielding as a function of temperature were performed to cover the different phases of the ferroelectric liquid crystal FELIX-R&;D. The shielding data prove untwisting of the helical structure in the nematic phase (i.e. non-chiral nematic phase) of FELIX-R&;D. Self-diffusion measurements were carried out in a direction parallel to the main magnetic field of the NMR spectrometer. However, in order to yield the anisotropy of the xenon self-diffusion tensor a few measurements also were performed in the perpendicular direction. A special technique, based on the observation of the second spin echo instead of the conventional first one, was applied to avoid convection problems. The experiments reveal all the phase transitions and a continuous decrease in the self-diffusion constant along the external magnetic field, D‖, when moving from the isotropic to the smectic C? phase. The respective activation energy E‖ appears to vary remarkably, however, being about the same in the isotropic and smectic C? phases. In the smectic mesophases significantly faster xenon self-diffusion was detected in the perpendicular direction than in the parallel direction. The detected self-diffusion constant D ⊥ in the perpendicular direction seems to remain almost constant in the smectic mesophases and close to the value of the self-diffusion constant in the isotropic phase. The results are in agreement with the structural features of smectic phases and indicate redistribution of xenon atoms towards the interlayer space of smectic mesophases.     

A novel application of NMR microscopy: measurement of water diffusion inside bioadhesive bonds.

The self-diffusion coefficient of water (D) inside bioadhesive bonds formed by dry and prehydrated hydrophilic matrices has been spatially resolved using nuclear magnetic resonance (NMR) microscopy. One-dimensional profiles showing the variation of D inside bioadhesive bonds were calculated from nine diffusion-weighted profiles obtained immediately after bond formation and every 5 min for 30 min. The resulting data indicated that the hydration state of a hydrophilic matrix can significantly and dramatically influence the dynamics of water movement inside a bioadhesive bond.     

Radiofrequency magnetic field gradient echoes have reduced sensitivity to susceptibility gradients

The amplitudes of gradient-echoes produced using static field gradients are sensitive to diffusion of tissue water during the echo evolution time. Gradient-echoes have been used to produce MR images in which image intensity is proportional to the self-diffusion coefficient of water. However, such measurements are subject to error due to the presence of background magnetic field gradients caused by variations in local magnetic susceptibility. These local gradients add to the applied gradients. The use of radiofrequency (RF) gradients to produce gradient-echoes may avoid this problem. The RF magnetic field is orthogonal to the offset field produced by local magnetic susceptibility gradients. Thus, the effect of the local gradients on RF gradient-echo amplitude is small if the RF field is strong enough to minimize resonance offset effects. The effects of susceptibility gradients can be further reduced by storing magnetization longitudinally during the echo evolution period. A water phantom was used to evaluate the effects of background gradients on the amplitudes of RF gradient-echoes. A surface coil was used to produce an RF gradient of between 1.3 and 1.6 gauss/cm. Gradient-echoes were detected with and without a 0.16 gauss/cm static magnetic field gradient applied along the same direction as the RF gradient. The background static field gradient had no significant effect on the decay of RF gradient-echo amplitude as a function of echo evolution time. In contrast, the effect of the background gradient on echoes produced using a 1.6 gauss/cm static field gradient is calculated to be significant. This analysis suggests that RF gradient-echoes can produce MR images in which signal intensity is a function of the self-diffusion coefficient of water, but is not significantly affected by background gradients.