Transverse Magnetic Relaxation Research Articles

Spin-wave contributions to nuclear magnetic relaxation in magnetic metals

The longitudinal and transverse nuclear magnetic relaxation rates $1/T_1(T)$ and $1/T_2(T)$ are calculated for three- and two-dimensional (3D and 2D) metallic ferro- and antiferromagnets (FM and AFM) with localized magnetic moments in the spin-wave temperature region. The contribution of the one-magnon decay processes is strongly enhanced in comparison with the standard $T$-linear Korringa term, especially for the FM case. For the 3D AFM case this contribution diverges logarithmically, the divergence being cut at the magnon gap $\omega_0$ due to magnetic anisotropy, and for the 2D AFM case as $\omega_0^{-1}$. The electron-magnon scattering processes yield $T^2\ln (T/\omega_0)$ and $T^2/\omega_0^{1/2}$-terms in $1/T_1$ for the 3D AFM and 2D FM cases, respectively. The two-magnon (``Raman'') contributions are investigated and demonstrated to be large in the 2D FM case. Peculiarities of the isotropic 2D limit (where the correlation length is very large) are analyzed.

Nuclear magnetic resonance investigations into long range chain fluctuations in molten poly(ethylene-oxide)

We studied by NMR the long range relaxation of poly-(ethylene oxide) chains, in the melt; the molecular weight was varied over the range 12–450 K. The transverse magnetic relaxation curves of protons attached to the polymer were thoroughly analyzed over the time interval 0–1 s and over the amplitude range 5×10−4 to 1. The analysis revealed three ensembles of protons clearly distinguished from one another from their different relaxation rates (≈7, 102, and 103 s−1, respectively), on the one hand, and from the differences brought about by forming so-called pseudosolid spin–echoes specific to entangled polymers, on the other hand. In this work, it is shown that the main part of the relaxation curve (relative amplitude ≈80%) can be interpreted in terms of exponential modes of isotropic chain relaxation, corresponding to the partition of one chain into Gaussian submolecules. The model provided relaxation functions in very good agreement with experimental curves: the best fits showed that the submolecule molecular weight (11 K) and its associated correlation time (1 ms) are independent of the chain molecular weight. Typical values of the terminal relaxation time, τR, of chain fluctuations were 0.002 and 0.17 s, for molecular weights equal to 55 and 450 K, respectively; correspondingly, the terminal reptation times, estimated from self-diffusion data reported in the literature, were 0.002 and 2 s, respectively. On increasing the molecular weight, the isotropic chain relaxation observed from NMR was found to occur within a time interval much shorter than viscoelastic relaxation times.

Resolution enhancement in single-shot imaging using simultaneous acquisition of spatial harmonics (SMASH).

Spatial resolution in single-shot imaging is limited by signal attenuation due to relaxation of transverse magnetization. This effect can be reduced by minimizing acquisition times through the use of short interecho spacings. However, the minimum interecho spacing is constrained by limits on gradient switching rates, radiofrequency (RF) power deposition and RF pulse length. Recently, simultaneous acquisition of spatial harmonics (SMASH) has been introduced as a method to acquire magnetic resonance images at increased speeds using a reduced number of phase-encoding gradient steps by extracting spatial information contained in an RF coil array. In this study, it is shown that SMASH can be used to reduce the effects of relaxation, resulting in single-shot images with increased spatial resolution without increasing imaging time. After a brief theoretical discussion, two strategies to reduce signal attenuation and increase spatial resolution in single-shot imaging are introduced and their performance is evaluated in phantom studies. In vivo single-shot echoplanar imaging (EPI), BURST, and half-Fourier single-shot turbo spin-echo (HASTE) images are then presented demonstrating the practical implementation of these resolution enhancement strategies. Images acquired with SMASH show increased spatial resolution and improved image quality when compared with images obtained with the conventional acquisitions. The general principles presented for imaging with SMASH can also be applied to other partially parallel imaging techniques.

Quantitative tissue sodium concentration mapping of the growth of focal cerebral tumors with sodium magnetic resonance imaging.

Tissue sodium concentration (TSC), as determined by in vivo 23Na magnetic resonance imaging (MRI) and the ex vivo classical 22Na radionuclide dilution assay (RDA), has been compared in a rat model of a focal glioma. The 23Na MRI method used a three-dimensional, twisted projection acquisition scheme at short echo time to minimize signal losses from relaxation of transverse magnetization. Calibration standards within the field of view allowed quantification of the sodium signal in terms of a TSC after correction for B1 nonuniformity and tissue water concentration. The 23Na MRI method measured focally increased TSC values in tumors that were equivalent statistically to the destructive 22Na RDA method. The noninvasive 23Na MRI method provided a quantitative means with which to monitor focal brain tumor growth.

Nuclear magnetic relaxation in ferrimagnetic Y3Fe5−x SixO12 films

The effect of silicon impurities on the damping of spin-echo signals from the 57Fe nuclei of tetrahedral Fe3+ ions in epitaxial yttrium-iron-garnet films was investigated. It was found that for silicon concentrations 0.015⩽x⩽0.037 the damping of the spin echo is a two-component process, which made it possible to separate nuclei into two types, differing by both the longitudinal and transverse magnetic relaxation times. For silicon concentrations 0.044⩽x⩽0.073 the decay of the echo can be described by one exponential and all nuclei in the sample have the same transverse relaxation times and the same longitudinal relaxation times. The experimental results are interpreted on the basis of the supposition that impurity “macromolecules” form around the Si4+ ions. The relaxation times of the iron nuclei in a “macromolecule” are much shorter than the relaxation times of iron nuclei belonging to the matrix ions. The radius of a “macromolecule” is estimated on the basis of percolation theory.

Transverse magnetic relaxation of 53Cr nuclei in Ag-doped CdCr 2Se 4

The decay of spin echo from 53Cr nuclei in ferromagnetic semiconductors Cd 1− x Ag x Cr 2Se 4 with spinel structures is investigated at the temperature T=4.2 K. The transverse relaxation rate T 2 −1 is studied in multidomain polycrystalline samples. The dependence of the relaxation rate on the resonance frequency and on the concentration of silver is determined. The transverse relaxation rate is separated into isotropic and anisotropic parts. Directional fluctuations of the magnetization are shown to be the source of the T 2 −1 anisotropy. The electron exchange between the Cr 4+ impurity ions with a strong spin–orbit coupling and the valence band is proposed as a possible origin of such fluctuations.

Wet Skid Properties of Filled Rubbers and the Rubber—Glass Transition

Abstract The physical relationships between wet skid resistance of filled rubber compounds and the dynamics of the corresponding bulk polymers in the rubber—glass transition zone are investigated. We show how wet grip data and their ratings correlate with dynamic glass transition temperatures in the N(uclear)M(agnetic)R(esonance) time scale for the spin—spin relaxation time T2 that characterizes the relaxation of transverse magnetization. The corresponding frequency is independent of the Larmor frequency of the NMR experiment. The amount of the frequency is located in the frequency region of the glass—rubber transition and depends on the microstructure of the used polymers. Finally, some molecular aspects of the network dynamics in the transition zone are considered. Damping curves of different rubbers can be predicted using the bead-spring-model of Kloczkowski, Mark and Frisch (KMF), considered as an extented Rouse-model of an entanglement network with tree-like connectivity and a certain number of subchains.

PEO Temporary Network in PEO/PMMA Blends: NMR Approach

Transverse magnetic relaxation properties of protons attached to PEO chains were investigated in compatible blends of hydrogenated PEO and deuterated PMMA by varying the PEO concentration and the temperature. The onset of segmental fluctuations is observed for samples that do not crystallize (φ ≤ 0.31); it occurs above Tg(PEO) but below the blend glass transition temperature, Tg(φ). At higher temperatures, for all concentrations, relaxation curves exhibit a solid-like behavior typical of a residual dipolar interaction due to the presence of a temporary network. The associated relaxation time obeys a linear temperature dependence with a reference at Tg(φ) + T0 and a linear variation with the mean segmental spacing between two consecutive entanglements along PEO chains, as calculated from the model proposed by Tsenoglou. This study extends the relationship between NMR properties and the network mesh size already observed in permanent gels and entangled homopolymers to miscible heteropolymers.

Comparison of H5 and H8 relaxation rates of a 2H/ 13C/ 15N labeled RNA oligonucleotide with selective protonation at C5 and C8

Uniformly 13C/ 15N enriched ribonucleotide monophosphates have been prepared with extensive deuterium enrichment of the non-exchangeable positions. The purine C8 and pyrimidine C5 base positions were selectively protonated prior to incorporation of the individual nucleotide triphosphates into an RNA oligonucleotide. The longitudinal and transverse relaxation rates of the H8 and H5 resonances of this deuterated molecule were compared with the relaxation rates of the corresponding protonated, 13C/ 15N enriched RNA molecule. Deuteration disrupts the efficiency of 1H– 1H dipolar relaxation and reduces the longitudinal and transverse magnetization relaxation rates on average to 25% and 68%, respectively, of the values measured for the non-deuterated RNA molecule. Importantly, the longitudinal relaxation rates remain sufficiently rapid (>1s −1) to permit the use of short recovery delays in multidimensional NMR experiments without significant loss of sensitivity.

Preparation and characterization of a uniformly 2 H/ 15 N-labeled RNA oligonucleotide for NMR studies.

An RNA oligonucleotide that contains the binding site for Escherichia coli ribosomal protein S8 was prepared with uniform 15N isotopic enrichment and uniform deuterium enrichment at all non-exchangeable sites using enzymatic methods. The RNA binding site, which contains 44 nt, forms a hairpin in solution and requires Mg2+for proper folding. The longitudinal magnetization recovery rates of the exchangeable protons were compared for the [2H,15N]-enriched RNA molecule and for the corresponding fully [2H,15N]-enriched RNA hairpin. It was found that 1H-1H dipolar relaxation significantly contributes to the recovery of exchangeable proton longitudinal magnetization. The exchangeable proton resonance line widths were less affected by deuteration, indicating that chemical exchange with H2O remains the dominant mechanism of transverse magnetization relaxation. Nevertheless, deuteration of this RNA hairpin was found to enhance the sensitivity of NOE-based experiments relative to the fully protonated hairpin and to simplify 2D NMR spectra. The increased signal-to-noise ratio facilitated the assignment of the cytidine amino resonances and several of the purine nucleotide amino resonances and permitted the identification of NOE crosspeaks that could not be observed in spectra of the fully protonated RNA hairpin.

Pulsed field gradient NMR and nuclear magnetic relaxation studies of water mobility in hydrated collagen II.

Transverse nuclear magnetic relaxation and self-diffusion of water were measured in hydrated collagen II. Self-diffusion measurements were conducted by pulsed field gradient NMR (PFG NMR) and weighting of the different species in the signal by variable T2 relaxation in the experiment. Two fractions of water protons were detected, one with a short T2 value but high diffusivity and one with a long T2 value and low, completely restricted diffusion. The distance of the diffusion barriers was determined to be 2.3 microns. Possible reasons for the restriction in the movement of the water molecules in comparison with structural models of collagen II are discussed.

Effect of Residual Dipolar Interactions on the NMR Relaxation in Cross-Linked Elastomers

For elastomer networks above the glass transition temperature Tg, a unified approach is presented to relate the residual dipolar couplings in various independent NMR experiments to the cross- link density. This is demonstrated on a series of cross-linked poly(styrene-co-butadiene) elastomers. The presence of dynamic physical and permanent chemical cross-links leads to a nonzero average of the homonuclear and heteronuclear dipolar couplings, which results in a solid-like NMR relaxation behavior. The residual dipolar couplings are expressed as a function of the effective number of statistical segments Ne between the physical and N e between the chemical cross-link points, using a simplified network model with Gaussian statistics. These effective numbers are extracted for each sample of the series from the 13C-edited transverse 1H magnetization relaxation of the CH group. It is shown that the respective Ne values can be used to scale the time domain of various NMR experiments such as (a) the free induction decay, (b) the 13C-edited 1H transverse magnetization relaxation, (c) the cross-polarization curves, and (d) the 1 H magnetization exchange between the CH and CH2 groups. This proves the validity of the unified view on the dipolar interactions in elastomer networks and provides a way to estimate the cross-link density.

Classes of hydration sites at protein-water interfaces: the source of contrast in magnetic resonance imaging

Immobilized protein solute, approximately 20 wt %, alters the longitudinal and transverse nuclear magnetic relaxation rates 1/T1 and 1/T2 of solvent water protons in a manner that makes their values indistinguishable from those of a typical human tissue. There is now a quantitative theory at the molecular level (S.H. Koenig and R. D. Brown III (1993) Magn. Reson. Med. 30:685-695) that accounts for this, as a function of magnetic field strength, in terms of several distinguishable classes of water-binding sites at the protein-water interface at which significant relaxation and solute-solvent transfer of proton Zeeman energy occur. We review the arguments that these several classes of sites, characterized by widely disparate values of the resident lifetimes tau M of the bound waters, are associated with different numbers of hydrogen bonds that stabilize the particular protein-water complex. The sites that dominate relaxation-and produce contrast in magnetic resonance imaging (MRI), which derives from 1/T1 and 1/T2 of tissue water protons-have tau M approximately 10(-6)s. These, which involve four hydrogen bonds, occupy < or = 1% of the protein-water interface. Sites that involve three bonds, although more numerous, have < or = 20% smaller intrinsic effect on relaxation. The greater part of the "traditional" hydration monolayer, with even shorter-lived hydrogen-bonded waters, has little influence on solvent relaxation and is relatively unimportant in MRI. Finally, we argue, from the data, that most of the protein of tissue (a typical tissue is mostly protein) must be rotationally immobile (with Brownian rotational relaxation times slower than that of a 5 x 10(7) Da (very heavy) globular protein). We propose a functional basis for this immobilization ("cytoplasmic order"), and then indicate a way in which this order can break down ("cytoplasmic chaos") as a result of neoplastic transformation (cancer) and alter water-proton rates of pathological tissue and, hence, image contrast in MRI.

Proton Transverse Nuclear Magnetic Relaxation in Oxidized Blood: a Numerical Approach

When red blood cells are deoxygenated, hemoglobin, which is then transformed into deoxyhemoglobin or methemoglobin, becomes paramagnetic. The transverse nuclear magnetic relaxation rate of water protons is considerably enhanced by this chemical transformation. A general agreement exists about the origin of the phenomenon--local field inhomogeneities induced by paramagnetic centers randomly distributed within the cell--but the localization of the region that dominates the relaxation is unclear. We addressed this problem with a computer simulation devoted to the determination of transverse magnetic relaxation of water protons in the presence of superparamagnetic MRI contrast agent candidates. The simulation confirms an earlier experimental result that shares equitably the responsibility for the observed relaxation between intracellular and extracellular water.

Constant-Relaxation Methods for Diffusion Measurements in the Fringe Field of Superconducting Magnets

A number of new NMR methods have been introduced for measuring molecular self-diffusion coefficients in the fringe field of superconducting magnets, avoiding the determination of longitudinal and transverse magnetization relaxation rates. Constant-relaxation methods based on the stimulated-echo product signals allow the determination of both constant and time-dependent diffusion coefficients. A density-operator formalism taking into account phenomenologically the effect of relaxation and diffusion encoding on the Liouville coordinates has been used to introduce and characterize an inhomogeneous mixed echo. This echo corresponds to a spatial and temporal superposition of a conventional spin echo and a stimulated echo. The mixed echo is generated by the action of a pulse sequence based on a stimulated-echo three-pulse sequence with an insertion of a Carr-Purcell-like pulse sequence in the last pulse interval. A constant relaxation method using a Carr-Purcell mixed-echo pulse sequence has been developed. It has proved to be advantageous when T 2 is not very small compared to T 1 . The performance and limitations of these methods are discussed and demonstrated experimentally.

Silica-poly(dimethylsiloxane) mixtures: n.m.r. approach to the crystallization of adsorbed chains

This work deals with the crystallization of polymer chains within silica-poly(dimethylsiloxane) mixtures, irrespective of the type of crystalline structure that is actually present in the system. An analysis of the transverse magnetization relaxation function is proposed as a method for melting point determination as well as for determination of the extent of crystallization as a function of time during an isothermal crystallization. We first pay attention to pure poly(dimethylsiloxane) (PDMS), for which we have measured the enthalpy of fusion per mole of structural units and defined the isothermal crystallization kinetics. The results obtained for the mixtures are compared to those obtained for pure PDMS. It turns out that the presence of silica particles does not affect the dimensionality of the crystalline growth. However, it reduces the extent of crystallization and has two antagonistic effects on the overall rate of crystallization. The first is a nucleation effect which is dominant at low silica volume fractions, and the second effect is a topological constraint which becomes dominant and hinders the crystalline growth at high silica volume fractions. As a result of the competition between these two effects, the overall rate of crystallization goes through a maximum with increasing silica volume fraction.

NMR and Viscoelastic Investigations into the Structure and Dynamics of Emulsion Copolymer Gels

Structural and dynamical properties of copolymer gels containing free branched chains which were prepared by styrene-butadiene emulsion copolymerization are investigated. The gel fraction of the emulsion copolymers was varied within a large range (15-90%) by adding different chain transfer agents duringthe polymerization process. NMR experiments were performed on homogeneous polymer films obtained by coalescence of the particles upon drying of the dispersions. Properties of dry extracted gels, gels swollen by free chains, or gels fully swollen by a good solvent were investigated to bring out the statistical structure of the gels. A time-temperature superposition principle was found to provide a good analysis of the time dependence of the transverse magnetic relaxation functions

Nuclear magnetic resonance approach to the characterization of the phase diagram of polyacrylonitrile in ternary solutions

This work deals with the properties of the temperature-concentration phase diagram of ternary poly-acrylonitrile solutions that were mainly observed from the transverse magnetic relaxation of protons attached to polymer chains, used to disclose the presence of solid-state domains. The binary solvent was a mixture of dimethylformamide (DMF) and water; the molar fraction of monomeric units was varied from 0 to 0.5, while the relative molar fractions of DMF and water were 1:1 or 2:1. The solvent quality was found to decrease upon addition of water. A curve (liquidus) that relates the temperature of formation of solid-state domains to the initial polymer concentration in solution was drawn from nuclear magnetic resonance (n.m.r.). The demixing part of the liquidus, determined as a plateau from n.m.r., was identified on observing a cloud-point curve. The main feature of the phase diagram concerns the specific behaviour of solutions observed whenever the concentration of disordered segments becomes lower than half the initial polymer concentration.

Transverse nuclear magnetic relaxation rate of the cuprate superconductors.

We simplify the Pennington-Slichter expression for the transverse NMR relaxation rate (${\mathit{T}}_{2\mathit{G}}^{\mathrm{\ensuremath{-}}1}$) in the cuprate superconductors, and use our result to calculate spin-fluctuation parameters in the normal state and ${\mathit{T}}_{2\mathit{G}}$ for the superconducting state of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$.

Application of spin-spin relaxation to measurement of surface area and pore size distributions in a hydrating cement paste

Nuclear magnetic resonance (NMR) relaxation analysis has been applied to interpret the evolution of microstructure in a cement paste during hydration. Measurements of transverse magnetic relaxation were made in fully and partially filled white cement pastes for hydration times between 1 h and 6 mo. It was found that only the evaporable water molecules contributed to the echo amplitude in the NMR measurement, while both the evaporable and the hydrated water contribute to the amplitude of the free induction decay. The spin-spin relaxation rate was found to increase markedly during hydration and can be directly related to the total surface area of the CSH gel accessible to evaporable water. The amount of water consumed during the hydration process was determined independently from the amplitude of the NMR echo signal extrapolated to the beginning of the pulse sequence. A numerical inversion of the full spin-spin relaxation profile, determined with a CPMG pulse sequence, was interpreted as a pore volume distribution function. The measurements of total surface area, amount of water consumed, and pore distributions were performed in situ nondestructively, throughout the hydration period for a single sample of cement paste.