Janez Stepišnik

Analysis of NMR self-diffusion measurements by a density matrix calculation

Abstract The density matrix formalism with the Magnus expansion of the time evolution operator is used to study the nmr response in a pulsed magnetic field gradient (mfg) spin-echo experiment. The results show that the spin-echo cannot only measure the self-diffusion coefficient but can determine the spectrum of the single-particle velocity autocorrelation function as well. The proper combination of rf and mfg pulse sequences are proposed for measuring self-diffusion in spin systems with strong dipolar coupling where the classical method fails.

Magnetic Resonance Imaging System Based on Earth's Magnetic Field

Abstract This article describes both the setup and the use of a system for magnetic resonance imaging (MRI) in the Earths magnetic field. Phase instability caused by temporal fluctuations of Earths field can be successfully improved by using a reference signal from a separate Earths field nuclear magnetic resonance (NMR) spectrometer/magnetometer. In imaging, it is important to correctly determine the phase of the NMR signal. A reference signal of a fixed‐frequency oscillator cannot be used since the Larmor frequency changes with time, following temporal fluctuations of Earths magnetic field. The reference signal frequency and phase, provided by a separate NMR spectrometer, change in the same way as Earths field, creating thereby, a stable rotating frame of reference for the measured signal. In principle, excellent homogeneity of the magnetic field enables scanning of very large volume samples. Reduction in S/N ratio due to the weak magnetic field can be partly compensated by the receiving coil design and shielding of electromagnetic pick‐up in audio frequency (AF) range. The smallest voxel examined so far is on the order of 50 mm3. Unlike in the case of strong magnetic fields, detection and processing of low frequency signal are less demanding for the electronics. The techniques used and the results of measurements are briefly presented.

The long time tail of molecular velocity correlation in a confined fluid: observation by modulated gradient spin-echo NMR

Abstract In addition to the fast correlation for local stochastic motion the molecular velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time tail decay [1] , [2] . This article presents a study by the NMR modulated gradient spin-echo method (MGSE) [3] on a system of water trapped in the space between the closely packed polystyrene beads. The results prove that the obtained dependence of spin-echo attenuation on time, gradient strength and modulation frequency nicely corresponds to the recently developed NMR approach, which is able to describe the effects of arbitrarily shaped gradient pulse sequence on the spin-echo attenuation [4] , [5] . With an MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin-phase, giving the spin-echo attenuation proportional to a value of the velocity correlation spectrum at the modulation frequency. It enables to extract the low-frequency correlation spectrum of confined water molecules. The function exhibits a negative long time tail characteristic (a low-frequency decay of the spectrum), that can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) as well as with the spectrum obtained when simulating the hydrodynamics of molecular motion constrained by capillary walls (which gives an algebraic decay).

Diffusion and flow in a porous structure by the gradient spin echo spectral analysis

The frequency analysis of relation between the NMR gradient spin echo method and the correlation of molecular motion throws a new light upon the measurement of molecular transport in porous media by magnetic resonance. The spectral analysis provides, in some other way, a known ffiffiffiffiffiffi Dt p early time dependence of attenuation or the pulse gradient spin echo sequence, and at intermediate times, it gives a not-known Dpt þ dð1 � expð� t=trÞÞ: When the displacements are getting larger than the size of compartments, the spin echo is levelling into a time-independent asymptote. In the system of packed poly-dispersed beds, the spin echo measurement of flow dispersion perpendicular to flows confirms the predicted spin echo decay. It demonstrates a clear distinction between different time regimes of signal decay, from which different properties of the porous structure can be revealed. The results gives almost identical long-time dispersion coefficient, D 0 ¼ Dp; for different flows, but the shortening of the dispersion correlation time tr with the increase of interstitial velocity. In combination with the modulated gradient sequence, the method extends the measuring range of spin echo over multi-pore length scale, and opens a new way to provide information about important properties of porous media like average pore size, the interconnectivity and the tortuosity. r 2001 Elsevier Science B.V. All rights reserved.

A new view of the spin echo diffusive diffraction in porous structures

Analysis with the characteristic functional of stochastic motion is used to clarify details of the diffraction-like effect at the gradient spin echo measurement of self-diffusion in porous structures. This approach shows that the phase interference of spins rebounding at boundaries brings about the diffraction, when the mean displacement of scattered spins is equal to the phase grating caused by the applied magnetic field gradient. The diffraction patterns convey information about morphology of the surrounding media only at times long enough that boundaries restrict further spin displacements. The method explains the dependence of diffraction on the time and width of gradient pulses, as observed at the experiments and the simulations.

Low-frequency velocity correlation spectrum of fluid in a porous media by modulated gradient spin echo

In addition to the fast correlation for local stochastic motion, the molecular velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time-tail decay. Here we present its study by the NMR modulated gradient spin-echo method (MGSE) [1] on a system of water trapped in the space between the closely packed polystyrene beads. With MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin phase. It gives the spin echo attenuation proportional to a value of the molecular velocity correlation spectrum at the modulation frequency. Covering the frequency range between Hz and MHz, it is a complement to the quasi-elastic neutron scattering, and so a suitable technique for the investigation of low frequency molecular dynamics in fluids. In our experiment, it enables to extract the low frequency correlation spectrum of water molecules confined in porous media. The function exhibits a negative long time-tail characteristic (a low frequency decay of the spectrum), which can be interpreted as a molecular back scattering on boundaries. The results can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) [2] as well as with the spectrum obtained when simulating the hydrodynamics of molecular motion constrained by capillary walls (which gives an algebraic decay) [3]. Despite much work on theories and simulation, which predict slow negative long time tail of molecular velocity correlation dynamics in confined fluids, the obtained velocity correlation spectrum is the first experimental evidence to confirm these effects. The obtained dependence of spin echo attenuation on time, gradient strength and modulation frequency is also the first experimental verification of the recently developed approach to the spin echo in porous media, that uses the spin phase average with the cumulant expansion to get the attenuation as a discord of spin spatial coherence [4].

Autocorrelation spectra of an air-fluidized granular system measured by NMR

The power spectrum of displacement fluctuation of beads in the air-fluidized granular system is measured by a novel NMR technique of modulated gradient spin-echo. The results of measurement together with the related spectrum of the velocity fluctuation autocorrelation function fit well to an empiric formula based on to the model of bead caging between nearest neighbours; the cage breaks up after a few collisions \cite{Menon1}. The fit yields the characteristic collision time, the size of bead caging and the diffusion-like constant for different degrees of system fluidization. The resulting mean squared displacement increases proportionally to the second power of time in the short-time ballistic regime and increases linearly with time in the long-time diffusion regime as already confirmed by other experiments and simulations.

The elimination of magnetic susceptibility artifacts in the micro-image of liquid-solid interfaces: internal gradient modulation by the CPMG RF train

Distortions of magnetic resonance images near solid-liquid interface appear as the result of the restriction to spin self-diffusion in the proximity of impermeable boundary as well as of a susceptibility difference. The spectral analysis of spin echo enables to resolve, in a simple way, how various RF-gradient pulse sequences reduce the effect of the internal magnetic field induced by the susceptibility difference at interfaces. The 1D diffusion-weighted imaging of water in the narrow notch tested efficiency of some sequence. The notch was milled in a piece of Plexiglas. The method can be used to distinguish the susceptibility effect from the effects of applied gradients when investigating the transport of fluid through a porous structure.

Spectroscopy: NMR down to Earth

High-precision nuclear magnetic resonance spectroscopy generally requires the use of powerful magnets. But using Earths magnetic field allows us to gain some of the same information on the cheap.

Velocity autocorrelation spectra in molten polymers measured by NMR modulated gradient spin-echo

The segmental dynamics in molten linear polymers is studied by the NMR method of modulated gradient spin-echo, which directly probes a spectrum of molecular velocity autocorrelation function. Diffusion spectra of mono-disperse poly(isoprene-1.4) with different molecular masses, measured in the frequency range 0.1–10 kHz at a temperature of , have a form similar to the spectrum of Rouse chain dynamics, which implicates the tube-Rouse motion as the dominant dynamic process in this frequency range. The scaling of the center-of-mass diffusion coefficient, given from the fitting parameters, changes from into at around Kuhn steps, which is less than predicted by theory and simulations, while the correlation times of the tube-Rouse mode do not follow the anticipated scaling.