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The problem of restricted diffusion in spherical pores is examined under conditions of finite gradient pulse width in pulsed gradient spin echo (PGSE)-NMR experiments. Closed form analytic expressions are derived, and the case of interconnected pores is briefly examined. An expression, based on the pore hopping approximation, is presented that predicts the echo attenuation for diffusion between pores under any gradient waveform. [ABSTRACT FROM AUTHOR]

Abstract: We present a propagator-resolved 2D exchange spectroscopy technique for observing fluid motion in a porous medium. The susceptibility difference between the matrix and the fluid is exploited to produce an inhomogeneous internal magnetic field, causing the Larmor frequency to change as molecules migrate. We test our method using a randomly packed monodisperse 100μm diameter glass bead matrix saturated with distilled water. Building upon previous 2D exchange spectroscopy work we add a displacement dimension which allows us to obtain 2D exchange spectra that are defined by both mixing time and spatial displacement rather than by mixing time alone. We also simulate our system using a Monte Carlo process in a random nonpenetrating monodisperse bead pack, finding good agreement with experiment. A simple analytic model is used to interpret the NMR data in terms of a characteristic length scale over which molecules must diffuse to sample the inhomogeneous field distribution. [Copyright &y& Elsevier]

Abstract: This paper demonstrates how the multi-linear PARAFAC model can with advantage be used to decompose 2D diffusion–relaxation correlation NMR spectra prior to 2D-Laplace inversion to the T 2–D domain. The decomposition is advantageous for better interpretation of the complex correlation maps as well as for the quantification of extracted T 2–D components. To demonstrate the new method seventeen mixtures of wheat flour, starch, gluten, oil and water were prepared and measured with a 300MHz nuclear magnetic resonance (NMR) spectrometer using a pulsed gradient stimulated echo (PGSTE) pulse sequence followed by a Carr–Purcell–Meiboom–Gill (CPMG) pulse echo train. By varying the gradient strength, 2D diffusion–relaxation data were recorded for each sample. From these double exponentially decaying relaxation data the PARAFAC algorithm extracted two unique diffusion–relaxation components, explaining 99.8% of the variation in the data set. These two components were subsequently transformed to the T 2–D domain using 2D-inverse Laplace transformation and quantitatively assigned to the oil and water components of the samples. The oil component was one distinct distribution with peak intensity at D =3×10−12 m2 s−1 and T 2 =180ms. The water component consisted of two broad populations of water molecules with diffusion coefficients and relaxation times centered around correlation pairs: D =10−9 m2 s−1, T 2 =10ms and D =3×10−13 m2 s−1, T 2 =13ms. Small spurious peaks observed in the inverse Laplace transformation of original complex data were effectively filtered by the PARAFAC decomposition and thus considered artefacts from the complex Laplace transformation. The oil-to-water ratio determined by PARAFAC followed by 2D-Laplace inversion was perfectly correlated with known oil-to-water ratio of the samples. The new method of using PARAFAC prior to the 2D-Laplace inversion proved to have superior potential in analysis of diffusion–relaxation spectra, as it improves not only the interpretation, but also the quantification. [Copyright &y& Elsevier]

Abstract: Two-dimensional (2D) nuclear magnetic resonance (NMR) methods for the investigation of correlation and exchange have been introduced in recent years and have been applied to a range of different systems. Here, we report on the use of 2D NMR diffusion–diffusion correlation spectroscopy for the investigation of diffusion anisotropy in cellular plant tissues and of diffusion–diffusion exchange spectroscopy for the study of the diffusive exchange of dextran in a dispersion of polyelectrolyte multilayer hollow capsules. Furthermore, diffusion–relaxation correlation spectroscopy was applied to both systems. [Copyright &y& Elsevier]

In this paper we present a method to determine the pore and grain size heterogeneity using a correlation between the transverse relaxation time and the susceptibility induced inhomogeneous magnetic field. By using a CPMG echo train, we are able to correlate T(2) with the inhomogeneous internal magnetic field, B(z)(i). We first introduce a simple simulation to study the correlation between the internal magnetic field gradient, ∣g∣, and B(z)(i), where this correlation is analogous to the T(2)-B(z)(i) correlation with horizontal inversion. We then acquire experimental data from two samples, one a simple bead pack, and the other a more complicated sandstone rock core. We find that indeed this method can indicate the presence of pore and grain size heterogeneities in the sample., (Published by Elsevier Inc.)

In a Newtonian fluid, vorticity diffuses at a rate determined by the kinematic viscosity. Here we use rapid NMR velocimetry, based on a RARE sequence, to image the time-dependent velocity field on startup of a fluid-filled cylinder and therefore measure the diffusion of vorticity. The results are consistent with the solution to the vorticity diffusion equation where the angular velocity on the outside surface of the fluid, at the cylinder's rotating wall, is fixed. This method is a means of measuring kinematic viscosity for low viscosity fluids without the need to measure stress., (Copyright 2010 Elsevier Inc. All rights reserved.)

In the Earth's magnetic field, it is possible to observe spin systems consisting of unlike spins that exhibit strongly coupled second-order NMR spectra. Such spectra result when the J-coupling between two unlike spins is of the same order of magnitude as the difference in their Larmor precession frequencies. Although the analysis of second-order spectra involving only spin-(1/2) nuclei has been discussed since the early days of NMR spectroscopy, NMR spectra involving spin-(1/2) nuclei and quadrupolar (I>(1/2)) nuclei have rarely been treated. Two examples are presented here, the tetrahydroborate anion, BH4-, and the ammonium cation, NH4+. For the tetrahydroborate anion, (1)J((11)B,(1)H)=80.9Hz, and in an Earth's field of 53.3microT, nu((1)H)=2269Hz and nu((11)B)=728Hz. The (1)H NMR spectra exhibit features that both first- and second-order perturbation theory are unable to reproduce. On the other hand, second-order perturbation theory adequately describes (1)H NMR spectra of the ammonium anion, (14)NH4+, where (1)J((14)N,(1)H)=52.75Hz when nu((1)H)=2269Hz and nu((14)N)=164Hz. Contrary to an early report, we find that the (1)H NMR spectra are independent of the sign of (1)J((14)N,(1)H). Exact analysis of two-spin systems consisting of quadrupolar nuclei and spin-(1/2) nuclei are also discussed.

We present a new method for observing fluid diffusion in a porous medium. The method employs 2D exchange spectroscopy for molecules diffusing in the presence of local magnetic field inhomogeneities, in our case distilled water in various sized glass bead packs. Our experiment involves an acquisition and evolution time domain with the two Fourier domains corresponding to the spectral distribution of local fields. We show that exchange in the internal magnetic field can be seen in a 2D spectrum with a characteristic time on the order of that required to diffuse 0.15 sphere diameters with similar behavior found for computer simulations. The method is potentially useful for studying the internal migrations in more complicated systems such as sandstones or other porous media.

Dynamic nuclear polarization (DNP) is introduced as a powerful tool for polarization enhancement in multi-dimensional Earth's field NMR spectroscopy. Maximum polarization enhancements, relative to thermal equilibrium in the Earth's magnetic field, are calculated theoretically and compared to the more traditional prepolarization approach for NMR sensitivity enhancement at ultra-low fields. Signal enhancement factors on the order of 3000 are demonstrated experimentally using DNP with a nitroxide free radical, TEMPO, which contains an unpaired electron which is strongly coupled to a neighboring (14)N nucleus via the hyperfine interaction. A high-quality 2D (19)F-(1)H COSY spectrum acquired in the Earth's magnetic field with DNP enhancement is presented and compared to simulation.

We present a simple method by which the dimensions of shear-induced multilamellar vesicles (MLVs), also known as onions, can be measured during the shearing process itself. This approach is based on the use of a closely spaced train of magnetic field gradient pulses applied during a CPMG echo sequence. The CPMG train compensates flow effects while the frequency-dependence of apparent diffusion can reveal the onion size. We present here a simple phenomenological model for restricted diffusion in multilamellar vesicles, which may be used to interpret the resulting diffusion spectrum. We demonstrate this approach with MLVs formed from the lamellar phase of sodium dodecyl sulfate (SDS) in water and octanol.

Multidimensional NMR techniques used in the measurement of molecular displacements, whether by diffusion or advection, and in the measurement of nuclear spin relaxation times are categorised. Fourier-Fourier, Fourier-Laplace and Laplace-Laplace methods are identified, and recent developments discussed in terms of the separation, correlation and exchange perspective of multidimensional NMR spectroscopy.

We present a novel method for obtaining high resolution NMR spectra in the presence of grossly inhomogeneous magnetic fields, such as those encountered in one-sided access NMR. Our method combines the well-known principle of reference deconvolution with NMR imaging in order to resolve spectral features with frequency resolution orders of magnitude smaller than the prevailing line-broadening due to field inhomogeneity. We demonstrate that, in cases of inhomogeneous field line-broadening more than an order of magnitude larger than the spectral features to be resolved, rather than performing reference deconvolution on the sample as a whole, it is more favourable in terms of SNR to divide the target region of a sample into smaller sub-regions, by means of chemical shift imaging, and then to perform reference deconvolution on the individual sub-region spectra, finally summing the results In this way, significant resolution enhancements can be obtained in the presence of severe magnetic field inhomogeneity without an unacceptable loss in SNR.