Profiles with microscopic resolution by single-sided NMR

A single-sided NMR sensor to produce depth profiles with microscopic spatial resolution is presented. It uses a novel permanent magnet geometry that generates a highly flat sensitive volume parallel to the scanner surface. By repositioning the sensitive slice across the object one-dimensional profiles of the sample structure can be produced with a space resolution better than 5 microm. The open geometry of the sensor results in a powerful testing tool to characterize arbitrarily sized objects in a non-destructive way.     

Self-diffusion coefficient by single-sided NMR

It is presented a novel method for the measure of the self-diffusion coefficient. The method exploits the fixed gradient of an open magnet, as that used in single-sided NMR, and it does not use prior information on T(2). The approach presented in this paper can be practiced also on the fringe field of superconducting magnets and it is based on the construction of the ratios between echoes taken at different interpulses separation in a Carr-Purcell-Meiboom-Gill pulse sequence. The determination of the self-diffusion coefficient facilitates the estimate of T(2) because the transverse relaxation results almost influenced by the molecular diffusion effect, also at the shorter interpulses time, when it is measured in field strongly inhomogeneous.     

NMR relaxation and NMR imaging of elastomers in the course of thermal aging

A complex aging regime occurs in the course of thermal aging of elastomers. Depending on the type and the content of the rubber filler materials, temperature, chemical environment (normally air), and time, a different aging process can be observed also by nuclear magnetic resonance (NMR) [1–6]. The methods used are the common spin-echo ¹H-NMR, including variable echo times and parameter-selective NMR-¹H-imaging (material properties imaging). The decay of the echo-magnetization is discussed on the basis of a single-chain model with a distribution of dipolar interactions. This model is based on the influence of a very fast, but anisotropic, local motion, as well as larger and slower motions, which are able to diminish the residual dipolar interaction. Carbon-black-filled natural rubber, as well as silica and carbon-black-filled E-SBR (emulsion-polymerized styrene butadiene rubber) and S-SBR (solution-polymerized SBR) are the systems under investigation, with the results showing some characteristic features of the course of aging observable by NMR.     

Two-dimensional imaging with a single-sided NMR probe

A new low field unilateral NMR sensor equipped with a two-dimensional gradient coil system was built. A new NMR-MOUSE concept using a simple bar magnet instead of the classical U-shaped geometry was used to produce magnetic field profiles comparatively homogeneous in extended lateral planes defining a suitable field of view for 2D spatial localization. Slice selection along the depth direction is obtained by means of the highly constant static magnetic field gradient produced by this magnet geometry. Implementing a two-dimensional phase-encoding imaging method 2D cross sections of objects were obtained with high spatial resolution. By retuning the probe it was possible to change the depth of the selected slice obtaining a 3D imaging method. The details of the construction of the new device are presented together with imaging tests to show the quality of space encoding.     

Characterization of sedimentary rocks with a single-sided NMR instrument

Single-sided nuclear magnetic resonance (NMR) instruments are now becoming very popular due to their interesting capability of ex situ measurements and useful applications in material testing. Measurements performed on such devices, however, are very critical due to the presence of inhomogeneous radio-frequency and magnetic fields. The presence of a very large static magnetic field gradient near the magnet surface could be usefully applied to exploit diffusion properties of materials. These features were investigated by combining the measurements with application of diffusion editing sequences. A significant improvement was obtained, allowing more information on the contribution of the separate fluids and possible considerations on petrophysical properties of the porous media investigated. In fact, the diffusion-relaxation distribution functions obtained allowed complete separation of the terms related to the fluids investigated. The experimental data demonstrate the feasible application of methods based on diffusion editing sequences, even in the presence of a very large magnetic field gradient, typically associated with a single-sided NMR device.     

Velocity distributions remotely measured with a single-sided NMR sensor

The pulsed field gradient nuclear magnetic resonance (PFG NMR) method has proved to be a powerful non-invasive technique to measure molecular displacement in various systems. It has been largely implemented with conventional NMR magnets where the volume for housing the flow setup is restricted. In this work we present the first approach to measure velocity distributions ex situ implementing a pulsed field gradient sequence on a single-sided NMR sensor. The open geometry of these sensors provides access to NMR measurements of a large number of applications previously excluded by the geometry of conventional closed magnets. Both, the distortions to the displacement encoding observed when implementing a PFG sequence in the presence of strongly inhomogeneous B0 and B1 fields, and the performance of the modifications proposed to eliminate these distortions are shown by means of numerical simulations. An alternating stimulated spin-echo PFG sequence implemented to remotely measure velocity distributions was combined with a multi-echo acquisition scheme to significantly increase the sensitivity of the method. The technique was implemented to measure the velocity propagator in a fluid undergoing laminar flow and good agreement with the theoretical result is observed.     

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 velocimetry and spectroscopy at microscopic resolution in small rheometric devices

We describe several different rheometric devices for use within the nuclear-magnetic-resonance probe of a standard widebore microimaging system. These include both vertical and horizontal Couette cells and the cone- and -plate cell, which produce shearing flows, and the four-roll mill and the opposed-jet (cross-flow junction) cells which produce extensional flow. We demonstrate that velocity images can be obtained for each and that detailed information about local shear and extension rates can be extracted. These systems have considerable potential for use in the study of non-Newtonian viscosity, and of molecular ordering under shear or extension.     

Simple mobile single-sided NMR apparatus with a relatively homogeneous B0 distribution

This work presents a simple design for a mobile single-sided nuclear magnetic resonance (NMR) apparatus with a relatively homogeneous static magnetic field (B₀) distribution. In the proposed design, the B₀ magnetic field of the apparatus is synthesized using only two permanent magnet blocks, i.e., a cube (main) magnet and a small shim magnet placed above the main magnet. The magnetic flux of the shim magnet partially cancels out that of the main magnet, subsequently creating a smooth B₀ profile above the shim magnet where low-resolution NMR experiments are performed. Compared with many previously published designs, this straightforward design simplifies the construction of the apparatus and simultaneously generates a B₀ field parallel to the apparatus surface, allowing the use of a simple loop-type radiofrequency (RF) coil. Additionally, an apparatus prototype is constructed according to the proposed design. Weighing only 1.8 kg, the constructed apparatus has a compact structure and can be held in the palm of a hand. The apparatus generates a B₀ strength of about 0.0746 T. Within a B₀ field deviation of 3 mT, the region with a relatively homogeneous B₀ distribution extends to about 11 mm above the shim magnet. The proposed apparatus can detect a clear Hahn echo or Carr-Purcell-Meiboom-Gill (CPMG) echoes of a pencil eraser block or a bottle of oil placed on the apparatus in 5 s with signal averaging using an RF transmitter power of only 19 W; the detection range of the apparatus exceeds 6 mm. The strength of the residual static magnetic field gradient of the apparatus is roughly estimated at 0.58 T/m. Applying different CPMG echo spacings in this residual static gradient leads to various transverse relaxation time (T₂) contrasts for liquids with distinct viscosities such as water and oil. Two nondestructive inspection applications of the apparatus, including correlating the concentrations of magnetic nanoparticle solutions with their measured transverse relaxation rates (R₂) and monitoring the outgassing from an opened bottle of oxygen-supersaturated water by measuring its longitudinal relaxation rate (R₁), are also demonstrated.     

Diffusion measurements by microscopic NMR imaging

Proton NMR images of the brains of living mice with voxel sizes as small as 80 × 80 × 500 μm were acquired at 9.3 T by the 2D FT spin-echo method. Using gradients of 3.75 G/cm, images with pixel dimensions below 50 μm were of low sensitivity because of degradation of the echo due to diffusion and flow. In the absence of bulk flow, this decrease in image intensity as image pixel size is decreased can be used to measure the local self-diffusion coefficient of water (D_H2O) in small samples. By this method, D_H2O at 22°C was estimated to be 2.59, 2.13, 1.59, and 0.84 × 10⁻⁵ cm²/s in pure water, 10% gelatin, mouse skeletal muscle, and rat liver, respectively.     

Surface phenomena investigated by nuclear magnetic resonance

This paper reviews recent achievements in the application of Nuclear Magnetic Resonance to surface phenomena, especially to molecules adsorbed on surfaces of porous crystals. Basic principles of Nuclear Magnetic Resonance are treated only as far as it is necessary to understand potentialities of this method in a study of absolute number (section 2.1), electronic environment (section 2.2), arrangement (section 2.3), and of thermal motion (section 2.4) of nuclei which are part of the absorbate or adsorbent. The structure of an important group of porous crystals, called zeolites of faujasite type, is briefly discussed (section 3.1) and recent results concerning the state of water (section 3.2) and of simple cyclic hydrocarbons (section 3.3) adsorbed in these crystals are reviewed.     

Multispin moments edited by multiple-quantum NMR: application to elastomers

The spin system response to the five-pulse sequence used for measurements of double-quantum and triple-quantum buildup curves is evaluated in the initial excitation/reconversion regime. The multispin dipolar network that is present also in many soft solids like elastomers was considered. It is proved rigorously that the relevant quantity for analysis of double-quantum build-up curves in the initial regime is the second van Vleck moment. The higher-order moments edited by double-quantum as well as higher-order coherences in the multiple-quantum build-up experiments are different from van Vleck moments. These results can be applied to compare (1)H residual moments edited by double-quantum and triple-quantum experiments with those measured by other NMR methods. The sensitivity of multiple-quantum coherences to the changes in the values of residual dipolar couplings for cross-linked natural rubber under uniaxial elongation is also discussed. Under such conditions (1)H second van Vleck moments were measured for different elongation ratios of a cross-linked natural rubber. Moreover, (1)H triple-quantum edited moments were also measured for the same sample under uniaxial compression. The dependence of the second van Vleck moment and the time of the maximum of the double-quantum buildup curve on the cross-link density of natural rubber measured at low magnetic field was also investigated.     

Surface diffusion investigated by ion current noise method

The surface diffusion for two magnesium isotopes on polycrystalline tungsten and ionic thermal desorption are studied by a method based on the ion current noise arising from the fluctuation of the work function as a result of random fluctuations of the magnesium adsorbate density. The activation energy for surface diffusion for magnesium isotopes have been determined by measuring the spectral density functions and their parameters.     

Surface effects and dipolar correlations of confined and constrained liquids investigated by NMR relaxation experiments and computer simulations.

Local order and molecular dynamics of liquids near surfaces strongly deviate from the behavior in the bulk. This in particular refers to liquid crystals above the bulk isotropization temperature. Transverse relaxation data of 5CB examined in porous glasses with different pore sizes are reported. A strong pore size effect was found. For the interpretation, a simple diffusion-adsorption computer simulation was carried out. Molecules can diffuse from the isotropic bulk part of the pore fluid to the ordered surface layer and vice versa. The residual dipolar correlation function is characterized by a slowly decaying tail owing to repeated returns of molecules to the surface. At each return the molecular orientation correlation is recovered as far as the surface sites visited have orientations correlated to the initial site. That is, molecular orientation is controlled by the "reorientation mediated by translational displacement" process considered in previous papers.     

Molecular mobility in fixed-bed reactors investigated by multiscale NMR techniques

The complex problem of a fixed-bed reactor consisting of catalytically active particles provides an exceptional opportunity of combining a wide range of NMR methods which have become available over time as tools to probe porous media. This work demonstrates the feasibility of different NMR techniques for the investigation of the intra- and interparticle pore space over length scales from nanometers up to centimeters. Many industrially relevant cracking reactions leave a coke residue on the inner surface of the porous catalyst particles so that the active sites become inaccessible to the reactants. Moreover, the pore space shrinks due to the formation of coke, thereby hindering molecular transport. The presence of the coke residue and its influence on the mobility of adsorbed fluid molecules are probed by 129Xe spectroscopy, NMR cryoporometry, relaxation dispersion measurements, and investigations of the reduced diffusivity in the intraporous space. The voids surrounding the random arrangement of catalyst pellets represent another pore space of much larger dimensions, the properties of which can be more directly investigated by mapping the fluid density and the velocity distribution from velocity-encoded imaging. Propagator representations averaged over large sample volumes are discussed and compared to velocity images obtained in selected axial slices of the reactor.     

Surface effects on liquid crystals constrained in nanoscaled pores investigated by field cycling NMR relaxometry and Monte Carlo simulations

Proton relaxation rates of nematic liquid crystals confined in nanoporous cavities were measured in a broad frequency range with the help of field cycling nuclear magnetic resonance relaxometry. The shape of relaxation dispersion curves in confined materials strongly deviates from the behavior in bulk, both above and below the bulk isotropization temperature. A strong increase in relaxation rates, exceeding by two orders of magnitude that of the bulk sample, is observed in the range of a few kilohertz. Relaxation rates in bigger pores decreased. Experimental findings are interpreted in terms of surface-induced orientational order and diffusion between sites with different orientations of local directors. With the aid of Monte Carlo simulations, two processes affecting low-frequency relaxation could be identified: (a) exchange losses of molecules from the surface-ordered phase to the bulk-like phase, and (b) Reorientations Mediated by Translational Displacements, which dominate the long-time scale and account for the recovery of correlation in molecular orientations as molecules probe different surface sites. It is shown that the width of the oriented layer may strongly affect the slope of dispersion curves and that cross-over between plateau and power law dispersion regimes shifts towards lower frequencies for bigger pores.     

Enhanced sensitivity to residual dipolar couplings of elastomers by higher-order multiple-quantum NMR

The homonuclear and heteronuclear residual dipolar couplings in elastomers reflect changes in the cross-link density, temperature, the uniaxial and biaxial extension or compression as well as the presence of penetrant molecules. It is shown theoretically that for an isolated methyl group the relative changes in the intensity of the homonuclear double-quantum buildup curves in the initial time regime due to variation of the residual dipolar coupling strength is less sensitive than the changes in the triple-quantum filtered NMR signal when considering the same excitation/reconversion time. For a quadrupolar nucleus with spin I=2 the sensitivity enhancement was simulated for four-quantum, triple-quantum, and double-quantum buildup curves. In this case the four-quantum build-up curve shows the highest sensitivity to changes of spin couplings. This enhanced sensitivity to the residual dipolar couplings was tested experimentally by measuring 1H double-quantum, triple-quantum, and four-quantum buildup curves of differently cross-linked natural rubber samples. In the initial excitation/reconversion time regime, where the residual dipolar couplings can be measured model free, the relative changes in the intensity of the four-quantum buildup curves are about five times higher than those of the double-quantum coherences. For the first time proton four-quantum coherences were recorded for cross-linked elastomers.     

Segmental anisotropy in strained elastomers detected with a portable NMR scanner

Single-side NMR is particularly suitable for measurements of segmental anisotropy induced in elastomers by uniaxial forces or local strain. Proton transverse nuclear magnetic relaxation was investigated with the NMR-MOUSE by recording the Hahn-echo decay in cross-linked natural rubber bands. This provided information on the dependence of the Hahn-echo decay on the angle between the direction of the uniaxial stretching force and the axis Z defined direction perpendicular to the magnet pole faces of the NMR-scanner. The anisotropy effect on the Hahn-echo decay is correlated with the extension ratio, and it is more evident in the liquid-like regime of the decay. A weaker segmental anisotropy is detected by 1H solid- and Hahn-echo decays recorded by multi-pulse sequences. A qualitative understanding of the angular dependence is obtained by an analytical theory of the Hahn-echo decay adapted to the case of stretched elastomers and to strongly inhomogeneous magnetic fields. Using angular-dependent 1H residual second van Vleck moments and correlation times reported previously [P.T. Callaghan and E.T. Samulski, Macromolecules 30, 113 (1997)] from stretched natural rubber bands the segmental anisotropy measured in inhomogeneous magnetic fields by the Hahn-echo decay was numerically simulated. As an example of a macroscopic distribution of local segmental anisotropy, 1H Hahn-echo decays were measured by the NMR-MOUSE sensor in a stretched cross-linked natural rubber plate with a circular cut in the center.     

Surface relaxation of Pt(111) investigated by ion scattering

The energy levels of some specific forms of screened Coulomb potential, as a function of the perturbation parameter λ, are shown to have a branch cut along the negative real axis, and singularities on the second sheet along $\text{|λ| e}{}^{\mathrm{<mtext>\pm (</mtext><mtext>3</mtext><mtext>2</mtext><mtext>)i\pi </mtext>}}$ for |λ| → 0. As a consequence, the energy levels have an asymptotic series in λ, which cannot be used to describe the energy levels to an arbitrary accuracy.