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.     

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.     

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.     

3D imaging with a single-sided sensor: an open tomograph

An open tomograph to image volume regions near the surface of large objects is described. The central achievement in getting such a tomograph to work is the design of a fast two-dimensional pure phase encoding imaging method to produce a cross-sectional image in the presence of highly inhomogeneous fields. The method takes advantage of the multi-echo acquisition in a Carr-Purcell-Meiboom-Gill (CPMG)-like sequence to significantly reduce the experimental time to obtain a 2D image or to spatially resolve relaxation times across the sensitive volume in a single imaging experiment. Depending on T(2) the imaging time can be reduced by a factor of up to two orders of magnitude compared to the one needed by the single-echo imaging technique. The complete echo train decay has been also used to produce T(2) contrast in the images and to spatially resolve the T(2) distribution of an inhomogeneous object, showing that variations of structural properties like the cross-link density of rubber samples can be distinguished by this method. The sequence has been implemented on a single-sided sensor equipped with an optimized magnet geometry and a suitable gradient coil system that provides two perpendicular pulsed gradient fields. The static magnetic field defines flat planes of constant frequency parallel to the surface of the scanner that can be selected by retuning the probe frequency to achieve slice selection into the object. Combining the slice selection obtained under the presence of the static gradient of the open magnet with the two perpendicular pulsed gradient fields, 3D spatial resolution is obtained.     

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.     

Surface UV aging of elastomers investigated with microscopic resolution by single-sided NMR

Depth profiles taken from the surface of UV irradiated natural rubber sheets have been measured with microscopic resolution using a Profile NMR-MOUSE. An NMR observable related to the sum of the spin echoes in the Carr-Purcell-Meiboom-Gill pulse sequence was used to characterize the cross-link density changes produced by the action of UV radiation in each sheet. The aging process was investigated as function of irradiation time and penetration depth. An exponential attenuation law with a space dependent absorption coefficient describes the change in the NMR observable with penetration depth. An Avrami model is used to describe the dependence of the absorption coefficient on the aging time. The method can be applied to investigate the effect of various aging agents on the surfaces of elastomers.     

Velocity distributions in magnetron sputter

Results of the particle simulation of magnetron sputter are presented. Using a kinetic code, we obtain the spatial profiles of plasma density, potential, and velocity distribution function, along with the electron temperature, the ion density, the current density, and the deposition profiles at the anode surface. The result of simulation is compared with the Child-Langmuir law applied to the magnetron discharge and the global model. The velocity distribution function of electrons is Maxwellian, but that of ions is non-Maxwellian near the cathode with the majority in the energy range below 50 eV     

Velocity distributions in glottal models

Velocity distributions within three models of the human larynx, namely, a rigid plexiglas model, an excised canine larynx, and a computational model are investigated with experimental and theoretical analyses. A plexiglas wind tunnel with interchangeable glottal constrictions was used as a two-dimensional steady-flow model to measure velocity and pressure for various glottal shapes. A canine excised larynx was used as a prototype pulsatile flow model to study pressure and velocity variations during phonation. Results of the plexiglas modelling indicated a parabolic laminar velocity profile upstream of the glottal constriction and turbulent and asymmetric velocity profiles downstream of the glottal constriction. The time-averaged velocities of the excised larynx had similarities with the plexiglas model results, and instabilities and asymmetries were also demonstrated by the computational method.     

NMR detection and one-dimensional imaging using the inhomogeneous magnetic field of a portable single-sided magnet

A portable, nuclear magnetic resonance (NMR) probe is described which utilises the intrinsic inhomogeneity of the field produced by a single-sided magnet to provide spatial encoding of the NMR signal. The probe uses a longitudinally magnetized hollow cylinder, and a figure-8 radiofrequency (RF) surface coil. The system has been used to measure NMR relaxation times and one-dimensional NMR profiles of rubber phantoms.     

Velocity distributions and density fluctuations in a granular gas

Velocity distributions in a vibrated granular monolayer are investigated experimentally. Non-Gaussian velocity distributions are observed at low vibration amplitudes but cross over smoothly to Gaussian distributions as the amplitude is increased. Cross-correlations between fluctuations in density and temperature are present only when the velocity distributions are strongly non-Gaussian. Confining the expansion of the granular layer results in non-Gaussian velocity distributions that persist to high vibration amplitudes.     

Momentum distributions in nuclei measured with relativistic heavy ions

In a peripheral reaction between relativistic heavy ions, where one nucleon is knocked out of the projectile, the momentum distribution of the remaining fragment reflects the momentum distribution of the knocked out nucleon. This has been proven in a previous paper. Here we study how the final-state interaction between the knocked out nucleon and the observed fragment influences the result: The real part of the optical potential which describes the final-state interaction shifts the experimental momentum distribution by a value 〈k_∥〉 of a few tens of MeV/c and the imaginary part reduces the cross sections by a factor 2 roughly. We also derive the cross section for a proton as target.     

Velocity distributions in dissipative granular gases

Motivated by recent experiments reporting non-Gaussian velocity distributions in driven dilute granular materials, we study by numerical simulation the properties of 2D inelastic gases. We find theoretically that the form of the observed velocity distribution is governed primarily by the coefficient of restitution eta and q=N(H)/N(C), the ratio between the average number of heatings and the average number of collisions in the gas. The differences in distributions we find between uniform and boundary heating can then be understood as different limits of q, for q>1 and q less, similar 1, respectively.     

Velocity distributions of granular gases with drag and with long-range interactions

We study velocity statistics of electrostatically driven granular gases. For two different experiments, (i) nonmagnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(upsilon) approximately exp(-/upsilon/). This behavior is consistent with the kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gases are sensitive to the fluid environment and to the form of the particle interaction.     

Velocity and velocity-difference distributions in Burgers turbulence

We consider the one-dimensional Burgers equation randomly stirred at large scales by a Gaussian short-time correlated force. Using the method of dissipative anomalies, we obtain velocity and velocity-difference probability density functions and confirm the results with high-resolution numerical simulations.     

Velocity imaging by ex situ NMR

A pulsed field gradient stimulated spin-echo NMR sequence is combined with imaging methods to spatially resolve velocity distributions and to measure 2D velocity maps ex situ. The implementation of these techniques in open sensors provides a powerful non-invasive tool to measure molecular displacement in a large number of applications inaccessible to conventional closed magnets. The method is implemented on an open tomograph that provides 3D spatial localization by combining slice selection in the presence of a uniform static magnetic field gradient along the depth direction with pulsed field gradients along the two lateral directions. Different pipe geometries are used to demonstrate that the sequence performs well even in the extremely inhomogeneous B0 and B1 fields of these sensors.     

Validity of wave-front reconstruction and propagation of ultrabroadband pulses measured with a Hartmann-Shack sensor

Wave-front reconstruction for ultrabroadband laser pulses is verified by use of a Hartmann-Shack sensor. We estimate the accuracy of numerical wave-front propagation by comparing numerical with experimental results and verify that wave fronts of ultrabroadband laser pulses from a hollow fiber can be propagated correctly by a single polychromatic wave-front measurement to a place where detection is not practicable, e.g., inside a vacuum chamber or laser focus.     

Wavefront sensing and reconstruction from gradient and Laplacian data measured with a Hartmann-Shack sensor

A new wavefront sensing and reconstruction technique is presented. It is possible to measure Laplacian and gradient information of a wavefront with a Hartmann-Shack setup. By simultaneously using the Laplacian and gradient data we reconstruct the wavefront by sequentially solving two partial differential equations.