Proton Spin-lattice Relaxation Data Research Articles

Location of paramagnetic defects in detonation nanodiamond from proton spin-lattice relaxation data

We developed an approach for determining location of intrinsic paramagnetic defects in nanodiamonds from the data of proton spin-lattice relaxation of the surface hydrogen atoms. The approach was applied to the detonation nanodiamond (DND) of the diameter of 5 nm. We found that dangling bonds with unpaired electron spins are located within the near-surface belt at the distance of 0.3–0.9 nm from the DND surface. The NMR data are compared with the results of EPR measurements.

Nuclear Magnetic Resonance Study of Anion and Cation Reorientational Dynamics in (NH4)2B12H12

Diammonium dodecahydro-closo-dodecaborate (NH4)2B12H12 is the ionic compound combining NH4+ cations and [B12H12]2– anions, both of which can exhibit high reorientational mobility. To study the dynamical properties of this material, we measured the proton NMR spectra and spin–lattice relaxation rates in (NH4)2B12H12 over the temperature range of 6–475 K. Two reorientational processes occurring at different frequency scales have been revealed. In the temperature range of 200–475 K, the proton spin–lattice relaxation data are governed by thermally activated reorientations of the icosahedral [B12H12]2– anions. This motional process is characterized by the activation energy of 486(8) meV, and the corresponding reorientational jump rate reaches ∼108 s–1 near 410 K. Below 100 K, the relaxation data are governed by the extremely fast process of NH4+ reorientations which are not “frozen out” at the NMR frequency scale down to 6 K. The experimental results in this range are described in terms of a gradual transition from the regime of low-temperature quantum dynamics (rotational tunneling of NH4 groups) to the regime of classical jump reorientations of NH4 groups with an activation energy of 26.5 meV. Our study offers physical insights into the rich dynamical behavior of (NH4)2B12H12 on an atomic level, providing a link between the microscopic and thermodynamic properties of this compound.

A quantum mechanical alternative to the Arrhenius equation in the interpretation of proton spin-lattice relaxation data for the methyl groups in solids.

The theory of nuclear spin-lattice relaxation in methyl groups in solids has been a recurring problem in nuclear magnetic resonance (NMR) spectroscopy. The current view is that, except for extreme cases of low torsional barriers where special quantum effects are at stake, the relaxation behaviour of the nuclear spins in methyl groups is controlled by thermally activated classical jumps of the methyl group between its three orientations. The temperature effects on the relaxation rates can be modelled by Arrhenius behaviour of the correlation time of the jump process. The entire variety of relaxation effects in protonated methyl groups have recently been given a consistent quantum mechanical explanation not invoking the jump model regardless of the temperature range. It exploits the damped quantum rotation (DQR) theory originally developed to describe NMR line shape effects for hindered methyl groups. In the DQR model, the incoherent dynamics of the methyl group include two quantum rate (i.e., coherence-damping) processes. For proton relaxation only one of these processes is relevant. In this paper, temperature-dependent proton spin-lattice relaxation data for the methyl groups in polycrystalline methyltriphenyl silane and methyltriphenyl germanium, both deuterated in aromatic positions, are reported and interpreted in terms of the DQR model. A comparison with the conventional approach exploiting the phenomenological Arrhenius equation is made. The present observations provide further indications that incoherent motions of molecular moieties in the condensed phase can retain quantum character over much broader temperature range than is commonly thought.

Pulsed-field-gradient NMR study of hydrogen diffusivity in random b.c.c. alloys V yTa 1− y

Hydrogen diffusion coefficients D in disordered b.c.c. systems V y Ta 1− y H 0.07 ( y = 0.25, 0.50 and 0.75) have been measured by means of the pulsed-field-gradient nuclear magnetic resonance over the temperature range 190–435 K. The hydrogen diffusivities are found to depend strongly on the alloy composition, the room-temperature value of D in the sample with y = 0.75 being an order of magnitude higher than those in the samples with y = 0.25 and 0.50. For all the samples studied, the temperature dependences of H diffusivity follow the Arrhenius law with the activation energies of 0.186 eV ( y = 0.25, 306–410 K), 0.182 eV ( y = 0.50, 295–401 K) and 0.102 eV ( y = 0.75, 190–435 K). These values are in reasonable agreement with those obtained from the proton spin-lattice relaxation measurements reported earlier. The jump lengths of H atoms have been estimated by comparing the measured H diffusivities with the proton spin-lattice relaxation data.

Molecular Diffusion and DNP Enhancement in Aqueous Char Suspensions

The heterogeneous1H dynamic nuclear polarization (DNP) effect is studied at low magnetic fields for a system consisting of several newly synthesized carbon chars suspended in water. By using Fourier Transform pulsed-field-gradient spin–echo NMR spectroscopy, several different self-diffusion coefficients have been observed in aqueous char suspensions, corresponding to regions of differing water mobility in the porous structure. Proton spin–lattice relaxation data generally confirm the results of molecular diffusion measurements. Through utilization of the Torrey model, the influence of “cage effects” on DNP enhancement in porous media is discussed. Results suggest that short-range nuclear–electronic interactions in pores have a dominant effect on DNP enhancement in char suspensions.

1H and2H NMR Relaxation in Hydrogen-Bonded Solids Due to a Complex Motion: Classical Jumps over a Barrier and Incoherent Tunneling

Equations for the temperature dependence of proton and deuteron spin–lattice relaxation rates and second moments due to a complex motion consisting of classical jumps over a potential barrier and quantum mechanical tunneling through the barrier have been derived. Asymmetric double and triple potential wells are considered. These equations have been employed to analyze proton spin–lattice relaxation data for solid naphthazarin in the laboratory and rotating frames as a function of temperature. It is shown that tunneling plays an important role in the proton transfer dynamics of this compound.

Evidence for the high-temperature spin-relaxation anomaly in metal hydrides.

Proton spin-lattice relaxation data ${\mathit{R}}_{1}$ (1/${\mathit{T}}_{1}$) are reported for the solid solution ${\mathrm{Nb}}_{0.5}$${\mathrm{V}}_{0.5}$${\mathrm{H}}_{0.36}$. In the region of the previously reported anomaly (T>700 K), a strong frequency dependence is observed by extending the measurements to a high frequency, 341 MHz. The correlation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$ is determined and is found to decrease with increasing temperature. The mean-square magnetic-field fluctuation ${\mathit{M}}_{2}$ responsible for the relaxation is also determined. Surprisingly, ${\mathit{M}}_{2}$ increases rapidly with increasing temperature, suggesting an excited state with a large spin interaction, such as molecular hydrogen.

Anomalous spin diffusion in classical Heisenberg magnets.

Time-dependent spin-autocorrelation functions at $T=\ensuremath{\infty}$ for classical Heisenberg magnets in dimensionalities $d=1, 2, \mathrm{and} 3$ are investigated by means of a computer simulation. These functions are shown to exhibit power-law long-time tails of form ${t}^{\ensuremath{-}{\ensuremath{\alpha}}_{d}}$ with characteristic exponents ${\ensuremath{\alpha}}_{d}$ which differ significantly from the values ${\ensuremath{\alpha}}_{d}^{(\mathrm{SD})}=\frac{d}{2}$ predicted by the phenomenological spin-diffusion theory: ${\ensuremath{\alpha}}_{1}=0.609\ifmmode\pm\else\textpm\fi{}0.005$, ${\ensuremath{\alpha}}_{2}=1.050\ifmmode\pm\else\textpm\fi{}0.025$, ${\ensuremath{\alpha}}_{3}\ensuremath{\simeq}1.6$. The method to employ computer simulations for this problem differs from methods previously employed. Anomalous spin diffusion is confirmed by existing proton spin-lattice relaxation data for the quasi-1D $s=\frac{5}{2}$ Heisenberg antiferromagnet ${(\mathrm{C}{\mathrm{H}}_{3})}_{4}$NMn${\mathrm{Cl}}_{3}$.

Proton and carbon-13 relaxation and molecular motion in glassy bisphenol-A polycarbonate

An interpretation of proton and carbon-13 spin–lattice relaxation in glassy polycarbonate is developed which is consistent with the geometry, time scale, and amplitude determined from chemical shift anisotropy line shape collapse. The line shape data indicate π flips and libration about the same axis as the predominant motions. A correlation function incorporating these motions is developed to quantitatively interpret the proton spin–lattice relaxation data and the line shape collapse. The π flip process is described as an inhomogeneous distribution of correlation times using the Williams–Watts fractional exponential. An apparent activation energy of 46 kJ/mol is determined with the fractional exponent remaining constant at 0.15. The librational motion is described by the Gronski formalism where the amplitude increases with the square root of temperature; and the rotational diffusion constant, linearly with temperature. Rotational diffusion constants fall in the range of 108 to 109 s−1 which is comparable to those observed in solution in sterically hindered polycarbonates. The librational motion only contributes to spin–lattice relaxation at the higher temperatures so that only an order of magnitude estimate of the restricted rotational diffusion constant results. This correlation function is then applied to carbon-13 T1 data taken at various positions across the chemical shift anisotropy line shape on an isotopically enriched system. Little change in spin–lattice relaxation with position is observed which is consistent with the broad distribution of π flip correlation times. The rate of carbon-13 spin–lattice relaxation is also fairly well predicted. Comparisons are made with magic angle sample spinning spin–lattice relaxation both in the laboratory and rotating frame. The former is fairly well approximated by the correlation function while the latter requires a significant spin–spin contribution to be reconciled with the rest of the interpretation.

Multifield, temperature and concentration dependence of spin relaxation and local motion in 2,2-propane diyl-bis(4-hydroxyphenyl) polyformal

13C and proton spin-lattice relaxation data were determined as a function of field, temperature and concentration for 2,2-propane diyl-bis(4-hydroxyphenyl) polyformal in C 2D 2Cl 4. The concentration of polymer was varied from a few per cent by weight up to the bulk rubber and temperature was varied from −20°C to +120°C. The relaxation data is interpreted in terms of several local motions including segmental motion, phenylene group rotation, methyl group rotation and formal group rotation. Segmental motion is described by a correlation function developed by Hall and Helfand which allows for cooperative and single bond transitions. The phenylene group rotation is described by the Woessner anisotropic stochastic diffusion model except at high concentration (⩾50 wt%) where the phenylene data is simulated by restricted rotation. Methyl group rotation is described by the Woessner three fold jump model, and the formal group rotation is described by double trans-gauche rotations about the C-O axes. At a concentration of 5 wt%, the time scale of segmental motion is slightly slower than in bisphenol-A-polycarbonate. However, the time scales of phenylene group and methyl group rotations are nearly identical for both polymers. A comparison is also made with chloral polyformal, another similar polyformal. The effect of concentration on local motion was monitored by 13C spin-lattice relaxation measurements at three Larmor frequencies over the range of 5 to 100 wt% polymer at a temperature 40°C above the glass transition of this polyformal. The rate of local chain motion decreases as the concentration of polymer increases with the exception of methyl group rotation which remains constant. The correlation times for several local backbone motions are fit to free volume theory which yields a fractional free volume of 0.38 for the solvent (C 2D 2Cl 4) and 0.28 for the polymer.

Nuclear spin-lattice relaxation in trans-polyacetylene (CH)x. A confined soliton model including nuclear spin flip diffusion

A « confined soliton model » in which the solitons move over a small part of the chain is developed. The on-chain nuclei are relaxed directly by contact hyperfine interactions whilst the remainder nuclei relax via nuclear spin flip diffusion. It is found that the proton spin-lattice relaxation data can be rationalized in terms of the fast and confined one-dimensional hopping motion of the soliton whilst that for enriched 13C one requires in addition a much more dominating mechanism that of nuclear spin flip diffusion.

Cross relaxation in hydrated collagen

Proton relaxation in collagen which was hydrated at two different water contents and various ratios of D 2O H 2O was studied. The proton spin-lattice relaxation data for isotope substitution are presented and analyzed, and proton and deuteron relaxation rates at the same frequency (9.21 MHz) are compared. The physical significance of relaxation equations describing cross relaxation in a two-component system containing macromolecules and water is discussed. The experimental results demonstrate the importance of cross relaxation in every term of the relaxation equations, not just in the terms involving an exchange of magnetization of the two phases.

Hydration number of the Li ion by pulsed magnetic resonance

Proton spin-lattice relaxation data as a function of concentration in aqueous solutions of LiCl and LiBr are interpreted in terms of a two state model. The data and this model, which is based upon the assumption of two kinds of water, bound and free, give a hydration number for the Li + ion of 4.9.