Static Magnetic Field Gradient Research Articles

Determination of surface relaxivity from NMR diffusion measurements

Nuclear magnetic resonance (NMR) T 2-decay measurements are usually interpreted in terms of pore-size distributions. The T 2 relaxation time of a water-wet pore is proportional to the size of the pore via surface relaxivity. Quantitative knowledge of the surface relaxivity is important when T 2 spectra are to be used for further use such as NMR derived capillary curves. In this study, we demonstrate that surface relaxivity can be directly determined from NMR measurements. Diffusion of hydrogen spins is restricted by the pore size and this effect is independent of surface relaxivity. Hence, surface relaxivity can be determined by combining restricted diffusion and T 2-relaxation. The latter two effects are measured simultaneously in a NMR T 2 decay measurement performed in a static magnetic field gradient. This method generalises existing ones for uniform pore systems to full pore-size distributions of realistic rocks. We have performed laboratory NMR diffusion measurements on a number of sandstone core plugs. The surface relaxivities found from these data are compared to those obtained from other methods. This method of measuring surface relaxivity can in principle be applied to NMR data obtained in boreholes which leads to a new application of NMR logging in the characterisation of oil and gas reservoirs.

Heterogeneity at the Glass Transition: Translational and Rotational Self-Diffusion

Self-diffusion coefficients, D, have been measured in the glass forming liquids salol, glycerol, phenolphthaleine dimethyl ether (PDE), cresolphthaleine dimethyl ether (CDE), and ααβ-trinaphthylbenzene (TNB) in the supercooled regime. The NMR static magnetic field gradient technique was applied where D >10-14 m2 s-1 can be attained. The results are similar to previous diffusion experiments where an enhancement of translational diffusion was found in comparison with rotational diffusion and shear viscosity. Various models of spatial heterogeneity are related to a phenomenological environmental fluctuation model in view of recent diffusion and relaxation data close to the glass transition.

In vivo imaging of a stable paramagnetic probe by pulsed‐radiofrequency electron paramagnetic resonance spectroscopy

Imaging of free radicals by electron paramagnetic resonance (EPR) spectroscopy using time domain acquisition as in nuclear magnetic resonance (NMR) has not been attempted because of the short spin-spin relaxation times, typically under 1 microsecond, of most biologically relevant paramagnetic species. Recent advances in radiofrequency (RF) electronics have enabled the generation of pulses of the order of 10-50 ns. Such short pulses provide adequate spectral coverage for EPR studies at 300 MHz resonant frequency. Acquisition of free induction decays (FID) of paramagnetic species possessing inhomogenously broadened narrow lines after pulsed excitation is feasible with an appropriate digitizer/averager. This report describes the use of time-domain RF EPR spectrometry and imaging for in vivo applications. FID responses were collected from a water-soluble, narrow line width spin probe within phantom samples in solution and also when infused intravenously in an anesthetized mouse. Using static magnetic field gradients and back-projection methods of image reconstruction, two-dimensional images of the spin-probe distribution were obtained in phantom samples as well as in a mouse. The resolution in the images was better than 0.7 mm and devoid of motional artifacts in the in vivo study. Results from this study suggest a potential use for pulsed RF EPR imaging (EPRI) for three-dimensional spatial and spectral-spatial imaging applications. In particular, pulsed EPRI may find use in vivo studies to minimize motional artifacts from cardiac and lung motion that cause significant problems in frequency-domain spectral acquisition, such as in continuous wave (cw) EPR techniques.

Stray-field imaging of quadrupolar nuclei of half integer spin in solids

A report is presented on the observation of Hahn echoes from the following quadrupolar nuclei of half integer spin ( I) in polycrystalline solids in the large static magnetic field gradient (37.5 T/m) which exists in the fringe field of a superconducting solenoid: 7Li, 23Na, 11B, 65Cu ( I = 3 2 ); 27Al ( I = 5 2 ); 51V, 59Co ( I = 7 2 ); and 115In ( I = 9 2 ). 23Na echo-trains from NaCl (with non-selective excitation) and from Na 2SO 4 (with selective excitation) are compared quantitatively for two different RF pulse sequences: 90 x -(τ-90 y -τ-echo-) n and 90 x -(τ-90 x -τ-echo-) n . The signals obtained from RF pulses corresponding to non-selective 90 ° pulses were shown to be quantitative, whereas in the selective case smaller signals were obtained since only the central transition contributed. The loss of signal from this cause can be distinguished from small signals resulting from low density of nuclei by use of the second sequence. A 7Li image obtained from LiF in a cylindrical glass-vial is shown.

Anisotropy and spatial restriction of conduction electron diffusion in perylene radical cation salt

Conduction electron motion was analyzed in (PE) 4 3+•••(PE) 2(PF 6 −) 3 · 2 THF (PE: perylene, THF: tetrahydrofuran) by pulsed electron spin resonance in static magnetic field gradients.

Decoupling of lithium and proton self-diffusion in supercooled LiCl:7H2O: A nuclear magnetic resonance study using ultrahigh magnetic field gradients

Self-diffusion coefficients of lithium ions and water protons (DLi and DH) in the glass-forming electrolyte LiCl:7H2O have been measured by nuclear magnetic resonance spin-echo experiments using ultrahigh static magnetic field gradients up to 184 T m−1. The measurements were complemented by measurements of 7Li and 1H spin-lattice relaxation times. The data cover the temperature range from 313 K down to 173 K, i.e., 34 K above the glass transition temperature Tg=139 K. In this range DLi and DH change over five orders of magnitude. The self-diffusion data exhibit a strong non-Arrhenius temperature dependence which is typical for fragile glass formers. In the supercooled regime the ratio of the self-diffusion coefficients DH/DLi increases gradually with decreasing temperature, reflecting a decoupling of these diffusive modes. These results are discussed in relation to the behavior of the viscosity, electrical conductance and reorientational correlation time of water in this temperature range. It is found that lithium ion diffusion is closely coupled to these other transport processes, while proton diffusion begins to decouple at T<1.5 Tg. Additionally, an analysis of 1H and 7Li magnetic relaxation rates 1/T1 is given. It is found that the intermolecular modes causing 1H–1H dipolar relaxation and 7Li quadrupolar relaxation also decouple from the viscosity. The results are discussed in the framework of similar phenomena observed with other fragile glasses and, more specifically, of structural changes known to occur in supercooled LiCl:H2O systems.

Restricted diffusion of the conduction electrons in quasi-one-dimensional organic conductors.

The spin-echo height in the electron spin resonance (ESR) of conduction electrons in the 1D organic metal $(\mathrm{FA}{)}_{2}{\mathrm{PF}}_{6}$, observed in static magnetic field gradients, exhibits a conspicuous curvature to a flatter slope after a faster decay for initial values of the pulse separation time. This curvature is explained by a model which takes into account restrictions to the free diffusional motion of electrons in the conducting channels of the system.

The CPMG Pulse Sequence in Strong Magnetic Field Gradients with Applications to Oil-Well Logging

It is shown that transverse relaxation measurements obtained from CPMG echo trains are valid even in the presence of strong, static magnetic field gradients. In the context of in situ measurements for water or oil exploration, low magnetic fields and short echo spacings are utilized to minimize diffusional effects. Under these conditions, it is shown that, for T 1 = T 2, the inverse Laplace transformation of the echo train is essentially independent of field homogeneity. For T 1 ≠ T 2, the error in determining T 2 does not exceed ∼12%, even for high T 1/ T 2 ratios. In most porous media, T 1/ T 2 is less than 3, in which case the error is below 8%. Analytical expressions for the echo amplitudes including relaxation are derived based on the density-matrix formalism. We define recursion relations that give the density matrix at echo i by a simple multiplication of the density matrix at echo i − 1 with a set of operators describing the evolution between consecutive echoes. The echo intensity is shown to be a function of the ratio between the radiofrequency strength and the receiver bandwidth. The optimal signal-to-noise ratio is obtained when this ratio is unity. The paper provides the theoretical framework for interpreting data obtained in situ by a modern NMR logging instrument. Furthermore, the results are directly applicable to magnetic resonance imaging.

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.

A Modified Hahn Echo Pulse Sequence for Proton Magnetic Resonance (1H-MR) Measurements of Percent Soluble Solids of Fruits

A fruit ripeness sensor being developed uses proton magnetic resonance to nondestructively determine percent by weight soluble solids in whole fruits. Results were compared to refractometer measurements of soluble solids content. In many fruits, soluble solids is nearly equivalent to percent sugar content, which is in turn related to ripeness. The principle used measures the effect of simple sugars (which constitute the majority of the soluble solids in many fruits) on self diffusion of water. Self diffusion can be measured using the Hahn Echo pulse sequence in the presence of a static magnetic field gradient. A modification of the Hahn Echo pulse sequence is described which solved two practical problems related to the application of the technique to rapid sorting; it increased the speed of the measurement and it greatly reduced the effects of sample size and shape. The improvement was demonstrated using experiments on cylindrical samples cut from apples.

New perspectives of NMR in ultrahigh static magnetic field gradients

The magnetic field gradient nuclear magnetic resonance (NMR) stimulated echo experiment measures the incoherent (or self) part of the intermediate scattering function S( Q,t) ∼ 〈 exp[ − i Qr(O)] exp[ i Qr(t)]〉 with a ‘generalized’ scattering vector Q = γ· g·τ (γ is the gyromagnetic ratio, g is the magnetic field gradient, τ is the evolution time). With ultrahigh static field gradients up to ≈ 180 T/m, a prototype of which has recently been installed in Mainz, Q-values up to > 10 −2 Å −1 become accessible. The first part of the paper focusses on details of this technical development and points out the close analogy with incoherent neutron scattering. In the second part, the enormous new possibilities of this kind of gradient NMR are demonstrated through a collection of most recent applications: the measurement of small self-diffusion coefficients down to about 10 −15 m 2s −1 in supercooled liquids and in molecular crystals, long chain polymer dynamics, restricted diffusion in systems of confined mesocopic geometries and anomalous diffusion on fractal structures.

Demonstration of a microwave trap for cesium atoms

We report on the first realization of a microwave trap for neutral atoms, as proposed originally for use with spin-polarized hydrogen [1]. This trap is advantageous for attaining Bose condensation because it can contain strong or weak field seekers, while static magnetic traps contain only the less-stable weak-field seeking states. In this experiment, Cs atoms were confined in the microwave field of a room-temperature spherical resonator (Q≈5500) whose TE 110 mode is tuned to the blue of the ground state hyperfine splitting (9.2 GHz). Using up to 83 W of microwave power, the trap is shallow (≤100μK), large (≈1 cm) and cannot, by itself, hold Cs atoms up against gravity. We levitate atoms in the trapping state ( F=4, m F=4 ground state) with a static magnetic field gradient. The trap is loaded with atoms cooled to 5 μK in optical molasses. To detect the atoms, we either release them from the trap and detect their fluorescence as they fall through a probe laser beam, or we observe them with a ccd camera as we illuminate them with laser pulses. Plans for applying this technique to spin-polarized hydrogen will be discussed in a separate presentation [2].

Rapid Rotating-Frame Imaging Using an RF Pulse Train (RIPT)

The rotating-frame imaging (RFI) method has proven useful for measuring the spatial distributions of NMR-visible nuclides without the aid of static magnetic field gradients. However, traditional RFI has several disadvantages, including relatively poor time efficiency and high RF power deposition in the sample. A B 1-gradient imaging technique, rapid rotating-frame imaging using an RF pulse train (RIPT), is discussed which can reduce both the image data-acquisition time and the RF power deposition by several orders of magnitude compared to RFI. The method is most readily applied to samples having only one resonance line, but a chemical-shift-selective version is also described which permits imaging of arbitrary lines in multipeak spectra. It is shown that RIPT images can be produced even when sample relaxation times are only a few milliseconds. Furthermore, by adding a suitable preparation period to the sequence, the RIPT signal intensity can be weighted by the relaxation time constant. Finally, postprocessing techniques are described which correct some of the image distortions common to most B 1-gradient imaging techniques.

Diffusion Imaging in the Presence of Static Magnetic-Field Gradients

Problems associated with large, static magnetic-field gradients are reviewed and illustrated with pulsed-field-gradient NMR diffusion-imaging experiments on two model systems. The model systems chosen are a water-filled cylinder and a water-filled annulus between two concentric cylinders both oriented transversely to the polarizing magnetic field. The latter system exhibits large magnetic-field gradients (∼5 G cm −1), and the simplicity of the geometry permits an analytical description of the magnetic-field distribution in the sample; calculations of the field distribution are consistent with direct measurements made using the chemical-shift-imaging technique. Diffusion-imaging experiments based on either spin- or stimulated-echo sequences are reliable for the single-tube system in which static gradients are negligible. However, for the double-tube system, the large static gradients prevent reliable diffusion imaging by spin-echo methods and cause artifacts in the results of standard stimulated-echo techniques. A superior alternating-pulsed-field-gradient technique, for which echo attenuation is less sensitive to the effects of the static background magnetic-field gradients, provides reliable diffusion-coefficient images for the double-tube system.

Excitation of spin flips in geonium at small cyclotron quantum numbers: Transition rates and frequency shifts.

The most accurate measurements of the electron g factor involve the observation of spin flips of a single electron trapped in a magnetic field and having a cyclotron quantum number very near the ground state. This paper examines the excitation of these flips, finding the following results: The spin-flip rate and the observed shape of the anomaly resonance can be substantially altered when the quantum nature of the cyclotron motion is taken into account. Excitation by rf magnetic field gradient, while in principle the preferable method, may not be feasible at liquid-helium temperatures due to slow transition rates. Excitation by driven oscillations in a static magnetic field gradient is accompanied by several frequency shifts which have not been very important to date but which are likely to significantly affect future measurements.

Elimination of susceptibility distortions and reduction of diffusion attenuation in NMR microscopy by line-narrowed 2DFT.

NMR imaging at high field strengths is adversely affected by magnetic susceptibility variations within the specimen. This is especially true in NMR microscopy. We present results using a line-narrowed imaging sequence which overcomes the image distortions associated with the frequency encoded readout method. Signal attenuation due to diffusion in static magnetic field gradients is also reduced.

Direct imaging of magnetic field gradients by group spin-echo selection.

A new image processing method for single-echo gradient echo imaging is presented which extracts local phase gradient information by k-space filtering instead of by phased reconstruction and spatial differentiation. It is shown that local phase gradient directions and semiquantitative local phase gradient magnitudes can be directly measured, even in regions where phased image reconstruction suffers from multiple phase foldovers due to strong phase modulations. The directional information thus obtained can be used as a reference to identify and correct phase modulation foldovers in phase maps which may be computed from the same raw data. The method is applied here to measure static magnetic field gradients and illustrates fundamental k-space signal properties of gradient echo imaging. Based on this concept, image artifacts caused by conventional strong k-space filtering in gradient echo imaging are discussed.

A new method for studying diffusion using a static magnetic field gradient

In this Communication we demonstrate the principle of a technique based upon zero-quantum coherence for measuring diffusion coefficients, which circumvents all of the above problems associated with pulsed magnetic field gradients by using a static magnetic field gradient, while still retaining differentiation between the individual components of multicomponent systems

NMR self-diffusion measurements using a radio-frequency field gradient combined with water signal suppression. Application to the pH-dependent solubilization of hydroxyquinoline in SDS micellar solutions

A novel NMR method for determining self-diffusion coefficients by means of a radio-frequency field gradient (instead of a static magnetic field gradient as is usually the case) has been combined with a suppression technique aimed at eliminating the huge solvent signal, in order to obtain a proper digitization of the weak resonances of a low-concentration species. The suppression technique makes use of the inhomogeneity of the normal coil of the NMR probe. This permits an accurate measurement of the self-diffusion coefficient of a solubilizate (hydroxyquinoline) at low concentration in aqueous solutions of micellized sodium dodecylsulfate, and determination of its partition coefficient as a function of pH.

Calcified intracranial lesions: detection with gradient-echo-acquisition rapid MR imaging.

Seventeen patients with partially calcified intracranial lesions, as documented by CT, were evaluated with MR imaging at 1.5 T. All patients were imaged with both conventional spin-echo techniques and reduced flip-angle gradient-echo-acquisition (GEA) sequences, during which a signal is acquired in the absence of a 180 degrees radiofrequency pulse. GEA parameters were implemented so that T2* effects were maximized on these scans. In all 17 patients GEA images showed marked hypointensity throughout the entire area of calcification, matching the calcified region as seen on CT. In contrast, spin-echo findings in the calcified portions of the lesions were extremely variable, precluding confident identification of calcification on these images. The depiction of regions of calcification as marked hypointensity on GEA images can be ascribed to T2* shortening from static local magnetic field gradients at interfaces of regions differing in magnetic susceptibility, a phenomenon that is well documented in vitro, when various diamagnetic solids are placed in aqueous suspension. However, we cannot exclude the possible additional role of accompanying paramagnetic ions, which sometimes are present with diamagnetic calcium salts in various intracranial calcifications. Since the hypointensity due to calcification on GEA images is not specific, noncontrast CT could be used to confirm its presence. Although this lack of specificity and the artifacts that emanate from diamagnetic susceptibility gradients at or near air-brain interfaces somewhat limit the application of GEA techniques, we suggest that rapid MR imaging using GEA sequences can consistently demonstrate intracranial calcification, and that this technique thus seems to be a useful adjunct to conventional spin-echo imaging.