Deuterium stimulated-echo-type PGSE NMR experiments for measuring diffusion: application to a liquid crystal.

The accessibility of molecular self-diffusion coefficients in anisotropic materials, such as liquid crystals or solids, by stimulated-echo-type (2)H PGSE NMR is examined. The amplitude and phase modulation of the signal in the stimulated-echo-type sequence by the static quadrupole coupling during the encoding/decoding delays is suppressed by adjusting the pulse flip angles and the phase cycle. For nuclei that experience both nonnegligible quadrupole and dipole couplings, the application of magic echoes during the evolution periods of stimulated echo is demonstrated as a helpful technique in the case of slow diffusion. These findings are demonstrated by experimental results in the thermotropic liquid crystal of partially deuterated 8CB. The obtained diffusion coefficients are also compared to data obtained by a (1)H homonuclear-decoupling-type PGSE NMR method in the same material.     

Time-dependent velocities in porous media dispersive flow.

Pulsed Gradient Spin Echo (PGSE) NMR methods may be used to measure the asymptotic dispersion coefficient as well as the velocity autocorrelation function (VACF) in porous media flow. The VACF can be measured in the frequency domain using repetitive gradient pulse trains, and in the time domain using double PGSE encoding. The one dimensional double PGSE method, and the two dimensional velocity exchange experiment (VEXSY) are briefly outlined and their application to flow in monodisperse 0.5 mm diameter beads packs described, both axial and transverse VACFs being examined. The measured correlation times are shown to agree well with calculated values. The asymptotic dispersion coefficients agree with literature values in the case of transverse flow while in axial flow it is shown that asymptotic conditions are not achieved, even for observation times longer than the correlation time for flow around a bead.     

Nuclear magnetic resonance in inhomogeneous magnetic fields

The response of the spin system has been investigated by numerical simulations in the case of a nuclear magnetic resonance (NMR) experiment performed in inhomogeneous static and radiofrequency fields. The particular case of the NMR-MOUSE was considered. The static field and the component of the radiofrequency field perpendicular to the static field were evaluated as well as the spatial distribution of the maximum NMR signal detected by the surface coil. The NMR response to various pulse sequences was evaluated numerically for the case of an ensemble of isolated spins (1/2). The behavior of the echo train in Carr-Purcell-like pulse sequences used for measurements of transverse relaxation and self-diffusion was simulated and compared with the experiment. The echo train is shown to behave qualitatively differently depending on the particular phase schemes used in these pulse sequences. Different echo trains are obtained, because of the different superposition of Hahn and stimulated echoes forming mixed echoes as a result of the spatial distribution of pulse flip angles. The superposition of Hahn and stimulated echoes originating from different spatial regions leads to distortions of the mixed echoes in intensity, shape, and phase. The volume selection produced by Carr-Purcell-like pulse sequences is also investigated for the NMR-MOUSE. The developed numerical simulation procedure is useful for understanding a variety of experiments performed with the NMR-MOUSE and for improving its performance. Copyright 2000 Academic Press.     

Spatial dependence of dispersion

The use of Pulsed Gradient Spin Echo (PGSE) NMR to investigate flow in porous media is well established. Using two pairs of position-encoding pulses in the PGSE experiment gives the possibility of examining velocity fluctuations, by comparing displacements, during the two encoding intervals. This method may be used to measure the asymptotic dispersion coefficient as well as the Velocity Auto-Correlation Function (VACF) in porous media flow. Some examples of two-dimensional maps of density and velocity distributions are accompanied by the first attempt to perform localized measurements of flow dispersion in porous media.     

Erratum to: Hydrodynamic dispersion in β-lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through β-lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.     

Cross-relaxation effects in stimulated-echo-type PGSE NMR experiments by bipolar and monopolar gradient pulses

Exchange of longitudinal spin polarization by dipolar cross relaxation between nonequivalent spins results in a modulation of the stimulated echo signal on increasing the encoding/decoding delays and in a multiexponential decay on increasing the diffusion time. These artifacts are suppressed by 180° pulses inserted in the middle of the gradient encoding/decoding periods. The efficiency of the gradient encoding is preserved if bipolar gradient pulses are used instead of monopolar pulses. The behavior of the different pulse sequences is demonstrated by ¹⁹F PGSE NMR experiments in a lyotropic liquid crystal in both isotropic micellar and oriented nematic phases.     

Velocity and diffusion imaging in dynamic NMR microscopy

The imposition of resolution gradients in a pulsed-gradient spin-echo (PGSE) NMR sequence induces motionally dependent phase and amplitude modulation in the image, a technique which we have termed dynamic NMR microscopy. Fourier analysis of this modulation gives a dynamic displacement profile for each pixel which can then be analyzed to obtain velocity and diffusion maps. The application of this method at high spatial resolution is motivated by a desire to measure vascular flow in living plants and variations in molecular self-diffusion under the influence of velocity shear in narrow capillaries. The theory of dynamic NMR microscopy is presented and potential artifacts discussed, including the effect of slice selection gradients, PGSE gradient nonuniformity, and specific problems associated with the measurement of self-diffusion in the presence of velocity gradients. It is demonstrated that a double-echo PGSE pulse sequence can be used to restore coherent phase shifts associated with steady-state flow, and examples of self-diffusion maps and signed velocity maps from sequences of phase-encoded images obtained by projection reconstruction are given. This method has been applied at 20,um transverse resolution in laminar capillary flow.     

A modified PGSE for measuring diffusion in the presence of static magnetic field gradients

With a proper timing of pi pulses, it is possible to reduce the effect of the static internal magnetic field gradient on the measurement of diffusion with the pulsed gradient spin echo (PGSE). A pulse sequence that in the first order eliminates the effect of weak internal static gradients in a standard PGSE experiment is introduced. The method should be applied in the cases, where strong and short magnetic gradient pulses are used to investigate the motion of liquid in heterogeneous samples with large susceptibility differences such as porous media.     

Hydrodynamic dispersion in [Formula: see text] -lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through [Formula: see text] -lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.     

Erratum to: Hydrodynamic dispersion in $ \beta$-lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through b \beta -lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.     

Hydrodynamic dispersion in $ \beta$ -lactoglobulin gels measured by PGSE NMR

The displacement scale dependent molecular dynamics of solvent water molecules flowing through b \beta -lactoglobulin gels are measured by pulse gradient spin echo (PGSE) nuclear magnetic resonance (NMR). Gels formed under different p H conditions generate structures which are characterized by magnetic resonance imaging (MRI) and PGSE NMR measured dynamics as homogeneous and heterogeneous. The data presented clearly demonstrate the applicability of the theoretical framework for modeling hydrodynamic dispersion to the analysis of protein gels.     

E-H-Zyklotronechos in Plasmen

A new echo type with free electrons in a slight inhomogeneous magnetic field excited by one electric and one magnetic pulse is calculated. Thus features of cyclotron echos and spin echoes are combined. The first electric pulse accelerates all (cold) particles to the same velocity as in the case of usual cyclotron echoes. The second magnetic pulse (at t = τ) rotates the plane of precession in phase space, quite in analogy to the motion of magnetic moments in the case of spin echoes. The echo arises at t = 2τ. The E-H echoes make relaxation and diffusion measurements in plasmas possible, using the methods proved useful in spin echo technique. There are no complications as in the case of E-E cyclotron echoes which are based on the fact that a velocity-dependent collision frequency is necessary for the nonlinearity of that echo mechanism.     

Electron spin-echo experiments in photo-excited triplet states in an external magnetic field

Electron spin-echo experiments in the photo-excited triplet states of quinoxaline-d₆ and naphthalene-d₈ at 1·2 K in an external magnetic field are presented. These include two-pulse Hahn echoes, three-pulse stimulated echoes and Carr-Purcell pulse-echo trains. The decay of the Hahn and stimulated echoes as a function of pulse interval yields measures of the spin relaxation times. Furthermore, the Hahn echo is used to obtain E.P.R. line shapes and the dynamics of the triplet sublevel populations. The angular dependence of the Hahn echo is also investigated. The Hahn echo decay time and decay modulation suggest the kind of role played by nuclear spins in the loss of electron spin phase coherence. Some promising characteristics of the pulse method are discussed.     

Determination of Velocity Autocorrelation Functions by Multiple Data Acquisition in NMR Pulsed-Field Gradient Experiments

An extension of NMR pulsed-field gradient experiments toward the generation, acquisition, and analysis of multiple echoes is presented. In contrast to currently used measurements where a single or double encoding of displacements by gradient pulses is followed by an acquisition of the echo signal at the end of the sequence, sampling and analyzing the intermediately occurring echoes allows a direct distinction between coherent and dispersive contributions to fluid motion without additional referencing measurements. It is shown that a series of gradient pulse pairs, leading to a train of echoes, can be employed to map the time-dependence of the velocity autocorrelation function between displacements within a single experiment for a system undergoing flow or motion.     

Filter-exchange PGSE NMR determination of cell membrane permeability

A new PGSE NMR sequence is introduced for measuring diffusive transport across the plasma membrane of living cells. A “diffusion filter” and a variable mixing time precedes a standard PGSE block for diffusion encoding of the NMR signal. The filter is a PGSE block optimized for selectively removing the magnetization of the extracellular water. With increasing mixing time the intra- and extracellular components approach their equilibrium fractional populations. The rate of exchange can be measured using only a few minutes of instrument time. Water exchange over the plasma membrane of starved yeast cells is studied in the temperature range +5 to +32 °C.     

Stimulated photon echo under excitation by incoherent and coherent pulses

Excitation of stimulated photon echo by two incoherent pulses obtained from one source and one coherent pulse is considered. The dependence of the average amplitude of stimulated echo on the parameters of noise pulses is determined. The results can be used for analysis of the corresponding algorithm of excitation of stimulated spin echo, as well as in calculations of characteristics of the signal processors based on the phenomena of photon and spin echoes.     

Multiple echoes, multiple quantum coherence, and the dipolar field: demonstrating the significance of higher order terms in the equilibrium density matrix.

It is well known that dipolar field effects lead to multiple spin echoes in a simple two-RF pulse experiment (the MSE experiment). We show here that coherence transfer echoes (which identify the existence of multiple quantum coherences in liquid NMR) and multiple spin echoes have a common origin. Using density matrix theory we have calculated the phase and timing of multiple spin echoes from all quadrature phase combinations of RF pulses. We show for the MSE experiment that there is a one-to-one correspondence between the time domain echo order and the multiple quantum coherence order. The experimental confirmation of these phase predictions shows that multiple spin echoes provide independent evidence for the breakdown of the high temperature approximation as proposed by Warren et al. (Science 262, 2005 (1993)).     

The Spatial Dependence of Spin-Echo Signals

The signals in NMR spin echoes which are refocused by 90° pulses are spatially modulated. The spatial modulation is not normally observed in images or profiles obtained using Hahn or stimulated echoes, but may cause errors if the sample structure varies on the distance scale of the modulation. Localized spectra measured using stimulated echoes will also show errors under these conditions. Simple Fourier-transform arguments show that conditions which allow the modulation to become visible in an image or profile have the effect of introducing a second echo into the time-domain acquisition window. Phase cycling may be used to remove the spatial dependence of the signals.     

Two-pulse nutation echoes generated by gradients of the radiofrequency amplitude and of the main magnetic field

A two-pulse NMR nutation spectroscopy scheme is suggested that leads to a new type of spin echoes. The amplitude of the radiofrequency (RF) pulses as well as the external magnetic field are assumed to be subject to gradients G(1) and G(0), respectively, in the same but otherwise arbitrary direction. Multiple echoes are predicted and observed at times k(G(1)/G(0))tau(1) and tau -/+ k(G(1)/G(0))tau(1) (k = 1, 2, 3, ...) after the second RF pulse, where tau(1) represents the radiofrequency pulse duration, and tau is the spacing of the RF pulses. Based on these echoes, a method for diffusion measurements is proposed that simultaneously provides the spin-lattice relaxation time and the self-diffusion coefficient.