Separation of quadrupolar and magnetic contributions to spin-lattice relaxation in the case of a single isotope

We present a NMR pulse double-irradiation method which allows one to separate magnetic from quadrupolar contributions in the spin–lattice relaxation. The pulse sequence fully saturates one transition while another is observed. In the presence of a Δm = 2 quadrupolar contribution, the intensity of the observed line is altered compared to a standard spin-echo experiment. We calculated analytically this intensity change for spins I = 1, , , thus providing a quantitative analysis of the experimental results. Since the pulse sequence we used takes care of the absorbed radiofrequency power, no problems due to heating arise. The method is especially suited when only one NMR sensitive isotope is available. Different cross-checks were performed to prove the reliability of the results obtained. The applicability of this method is demonstrated by a study of the plane oxygen ¹⁷O (I = ) in the high-temperature superconductor YBa₂Cu₄O₈: the ¹⁷O spin–lattice relaxation rate consists of magnetic as well as quadrupolar contributions.     

H NMR study of N(CH3)4H(ClF2CCOO)2

The proton spin–lattice relaxation times and ¹H NMR second moments were measured over a wide range of temperature. The results were compared with those of the ¹⁹F NMR relaxation that we obtained earlier. For both nuclear species, the evolution of the longitudinal magnetizations with time is observed to be strongly bi-exponential and were in good quantitative agreement with the cross-relaxation theory.     

Methyl and t-butyl reorientation in an organic molecular solid

We have determined the molecular and crystal structure of 4,5-dibromo-2,7-di-t-butyl-9,9-dimethylxanthene and measured the ¹H spin–lattice relaxation rate from 87 to 270 K at NMR frequencies of ω/2π=8.50, 22.5, and 53.0 MHz. All molecules in the crystal see the same intra and intermolecular environment and the repeating unit is half a molecule. We have extended models developed for ¹H spin–lattice relaxation resulting from the reorientation of a t-butyl group and its constituent methyl groups to include these rotors and the 9-methyl groups. The relaxation rate data is well-fitted assuming that the t-butyl groups and all three of their constituent methyl groups, as well as the 9-methyl groups all reorient with an NMR activation energy of 15.8±1.6 kJ mol⁻¹ corresponding to a barrier of 17.4±3.2 kJ mol⁻¹. Only intramethyl and intra-t-butyl intermethyl spin–spin interactions need be considered. A unique random-motion Debye (or BPP) spectral density will not fit the data for any reasonable choice of parameters. A distribution of activation energies is required.     

Brute-force NMR-ON on 90NbCu, 101mRhCu and110mAgAg

Brute-force nuclear magnetic resonance on oriented nuclei (BF-NMRON) experiments have been performed for ⁹⁰NbCu, ^101m RhCu and ^110m AgAg at about 10mK. Narrow resonance spectra were detected. Using the known values of the g-factors, the Knight shift has been deduced: K(⁹⁰NbCu) = 0.62(24) %, K(^101m RhCu) = 0.87(27)%. The effective spin–lattice relaxation times were also measured.     

Directional behavior of nuclear quadrupole resonance in YBa2Cu3O6

Powder samples of YBa₂Cu₃O₆ were magnetically aligned and the anisotropies in the systems were studied by means of Cu(1) nuclear quadrupole resonance (NQR) in the absence of external magnetic fields. Our room temperature measurements of the NQR lineshapes and the spin–lattice and spin–spin relaxation times as a function of the aligning magnetic field indicate that full microscopic alignment can be achieved by using a magnetic field of about 4.7 T, for which doublet line patterns arising from a hyperfine splitting were observed.     

A nuclear magnetic resonance study of the phase transitions and electric quadrupole Raman processes of M5H3(SO4)4·H2O (M=Na, K, Rb, and Cs) single crystals

The spin–lattice relaxation times and spin–spin relaxation times for ¹H and M in M₅H₃(SO₄)₄·H₂O (M=Na, K, Rb, and Cs) single crystals grown using the slow-evaporation method were measured as functions of temperature. Two kinds of protons were identified in the M₅H₃(SO₄)₄·H₂O structure: acid protons and water protons. Our experimental results show that the acid and water protons in Cs₅H₃(SO₄)₄·H₂O are involved in phase transitions of this crystal, whereas neither type of proton is involved in the phase transitions of the other three crystal type (M₅H₃(SO₄)₄·H₂O; M=Na, K, and Rb). Moreover, the relaxation times for the M (=Na, K, and Rb) nuclei in these crystals were found to decrease with increasing temperature and can be described with (k=2). The T₁ results for M (=Na, K, and Rb) in M₅H₃(SO₄)₄·H₂O crystals can be explained in terms of a relaxation mechanism in which the lattice vibrations are coupled to the nuclear electric quadrupole moments.     

Influencing the satellite transitions of half-integer quadrupolar nuclei for the enhancement of magic angle spinning spectra

Double frequency sweeps can induce spin transitions in a set of satellites of a half-integer quadrupolar nucleus by simultaneously passing through resonance for a satellite pair. It is shown that by transferring population from the outer spin levels to the inner |1/2 and |−1/2 levels an increased intensity for central transition spectra is obtained. Although Magic Angle Spinning in principle interferes with this process, and the adiabaticity of the passages is different for every crystallite in a powder, enhanced spectra with undistorted line shapes are obtained for I=3/2 (²³Na) and 5/2 (²⁷Al) spins experiencing quadrupolar interactions with ω_Q in the range 0.1–3 MHz. Even at spinning speeds up to 30 kHz significant enhancements are obtained. An analysis of the combined effects of double frequency sweeps (DFS) and MAS indeed shows strongly different effects for different crystallites in powder ranging from no gain at all to the theoretical maximum gain of 2I. As the effects are randomly distributed over all orientations on a sphere this is averaged over the whole line shape. Therefore, undistorted powder patterns are obtained enhanced by the average gain over the individual crystallites. Saturation of the satellite transitions, which can only be achieved if spin–spin relaxation is sufficiently strong, leads to identical results. Optimization of the sweeps should be toward an optimal effect on the population transfer to the central levels and chosen short with respect to spin–lattice relaxation times.     

Application of High-Resolution NMR Spectroscopy in Analyzing Ionites

The ¹H and ¹³C NMR spectra of granulated carboxylic cationite MAC-3 and fibrous anionites FIBAN (A-5, A-7, and A-9) have been investigated. The dependence of the chemical shifts and times of spin–spin relaxation of the water protons and carbon nuclei of MAC-3 on the water content in a sample has been investigated. A comparison of the carbon spectra of polyelectolytes and FIBAN fibrous anionites swollen in water has been made. It is shown that the carbon spectra of the ionites swollen in water represent fairly narrow lines practically for all groups of the skeleton, and therefore the structure of the ionites can be analyzed using a high-resolution NMR.     

Contributions of Spin–Lattice Relaxation to the Echo Decay of Planar Cu in High-Temperature Superconductors

Measurement ofT_2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT_2Gand show thatT_2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa₂Cu₄O₈, we find a correction on the order of 10% inT_2Gand using the corrected values we find that the isotope ratio⁶³T_2G/⁶⁵T_2Gagrees with theory.     

Measurement of Relaxation Rates of N and H Backbone Protons in Proteins with Tailored Initial Conditions

Several methods are presented for the selective determination of spin–lattice and spin–spin relaxation rates of backbone protons in labeled proteins. The relaxation rates of amide protons in ¹⁵N labeled proteins can be measured by using two-way selective cross-polarization (SCP). The measurement of H^α relaxation rates can be achieved by combining this method with homonuclear Hartmann–Hahn transfer using doubly selective irradiation. Various schemes for selective or nonselective inversion of the longitudinal proton magnetization lead to different initial recovery rates. The methods have been applied to lysine K6 in ¹⁵N-labeled human ubiquitin and to leucine L5 in ¹⁵N- and ¹³C-labeled octapeptide YG*G*F*LRRI (GFL) in which the marked residues are ¹⁵N- and ¹³C-labeled.     

Biomolecular solid state NMR with magic-angle spinning at 25K

A magic-angle spinning (MAS) probe has been constructed which allows the sample to be cooled with helium, while the MAS bearing and drive gases are nitrogen. The sample can be cooled to 25 K using roughly 3 L/h of liquid helium, while the 4-mm diameter rotor spins at 6.7 kHz with good stability (±5 Hz) for many hours. Proton decoupling fields up to at least 130 kHz can be applied. This helium-cooled MAS probe enables a variety of one-dimensional and two-dimensional NMR experiments on biomolecular solids and other materials at low temperatures, with signal-to-noise proportional to 1/T. We show examples of low-temperature ¹³C NMR data for two biomolecular samples, namely the peptide Aβ_14–23 in the form of amyloid fibrils and the protein HP35 in frozen glycerol/water solution. Issues related to temperature calibration, spin–lattice relaxation at low temperatures, paramagnetic doping of frozen solutions, and ¹³C MAS NMR linewidths are discussed.     

Relaxation times and line widths of isotopically-substituted nitroxides in aqueous solution at X-band

Optimization of nitroxides as probes for EPR imaging requires detailed understanding of spectral properties. Spin lattice relaxation times, spin packet line widths, nuclear hyperfine splitting, and overall lineshapes were characterized for six low molecular weight nitroxides in dilute deoxygenated aqueous solution at X-band. The nitroxides included 6-member, unsaturated 5-member, or saturated 5-member rings, most of which were isotopically labeled. The spectra are near the fast tumbling limit with T₁∼T₂ in the range of 0.50–1.1 μs at ambient temperature. Both spin–lattice relaxation T₁ and spin–spin relaxation T₂ are longer for ¹⁵N- than for ¹⁴N-nitroxides. The dominant contributions to T₁ are modulation of nitrogen hyperfine anisotropy and spin rotation. Dependence of T₁ on nitrogen nuclear spin state m_I was observed for both ¹⁴N and ¹⁵N. Unresolved hydrogen/deuterium hyperfine couplings dominate overall line widths. Lineshapes were simulated by including all nuclear hyperfine couplings and spin packet line widths that agreed with values obtained by electron spin echo. Line widths and relaxation times are predicted to be about the same at 250 MHz as at X-band.     

Paramagnetic Proton Nuclear Spin Relaxation Theory of Low-Symmetry Complexes for Electron Spin Quantum NumberS=

A generalization of the modified Solomon–Bloembergen–Morgan (MSBM) equations has been derived in order to describe paramagnetic relaxation enhancement (PRE) of paramagnetic complexes characterized by both a transient (Δ^ZFS_t) and a static (Δ^ZFS_s) zero-field splitting (ZFS) interaction. The new theory includes the effects of static ZFS, hyperfine coupling, and angular dependence and is presented for the case of electron spin quantum numberS= , for example, Mn(II) and Fe(III) complexes. The model gives the difference from MSBM theory in terms of a correction term δ which is given in closed analytical form. The theory may be important in analyzing the PRE of proton spin–lattice relaxation dispersion measurements (NMRD profiles) of low-symmetry aqua–metal complexes which are likely to be formed upon transition metal ions associated with charged molecular surfaces of biomacromolecules. The theory has been implemented with a computer program which calculates solvent water protonT₁NMRD profiles using both MSBM and the new theory.     

Stable reconstruction of the T(2) distribution by low-resolution NMR measurements and the classical markov and hausdorf momentum problem

Assuming that an original distribution is a probabilistic measure and the Laplace transforms are known only for a finite number of points that are affected by errors, we develop a method for reconstructing weak-sense mean values obtained by integrating smooth functions with the measure. Our method is useful in NMR if the NMR signal can be represented as a superposition of exponential terms. In these circumstances, we show how the data processing can be related to the classical Hausdorf momentum problem. First, we clarify the meaning of stable spectrum reconstruction, and then develop stable filtering and a mean value reconstruction algorithm. Our method has been tested on both simulated and real sets of spin–spin relaxation curves with noise. In view of this, our method could provide an efficient and accurate reconstruction of spin–spin relaxation data. For any reader interested in applications, a “practical recipe” that is almost self-consistent has been included.     

Consequences of Xe–H Cross Relaxation in Aqueous Solutions

We have investigated the transfer of polarization from ¹²⁹Xe to solute protons in aqueous solutions to determine the feasibility of using hyperpolarized xenon to enhance ¹H sensitivity in aqueous systems at or near room temperatures. Several solutes, each of different molecular weight, were dissolved in deuterium oxide and although large xenon polarizations were created, no significant proton signal enhancement was detected in -tyrosine, α-cyclodextrin, β-cyclodextrin, apomyoglobin, or myoglobin. Solute-induced enhancement of the ¹²⁹Xe spin–lattice relaxation rate was observed and depended on the size and structure of the solute molecule. The significant increase of the apparent spin–lattice relaxation rate of the solution phase ¹²⁹Xe by α-cyclodextrin and apomyoglobin indicates efficient cross relaxation. The slow relaxation of xenon in β-cyclodextrin and -tyrosine indicates weak coupling and inefficient cross relaxation. Despite the apparent cross-relaxation effects, all attempts to detect the proton enhancement directly were unsuccessful. Spin–lattice relaxation rates were also measured for Boltzmann ¹²⁹Xe in myoglobin. The cross-relaxation rates were determined from changes in ¹²⁹Xe relaxation rates in the α-cyclodextrin and myoglobin solutions. These cross-relaxation rates were then used to model ¹H signal gains for a range of ¹²⁹Xe to ¹H spin population ratios. These models suggest that in spite of very large ¹²⁹Xe polarizations, the ¹H gains will be less than 10% and often substantially smaller. In particular, dramatic ¹H signal enhancements in lung tissue signals are unlikely.     

Suppression of antiferromagnetic spin fluctuation in Zn-substituted YBa2Cu3O7

We have prepared Zn-substituted YBa₂Cu_3−xZn_xO₇ (YBCO, x=0.0–0.09) and performed ^63,65Cu nuclear quadrupole resonance (NQR) measurements for the plane site at 300 and 100 K as a function of Zn concentration. The substitutional effects are observed in resonant frequencies and linewidths of spectra, and relaxation times as well as in the superconducting transition temperature. The spin–lattice relaxation rate 1/T₁ is reduced for the higher Zn concentration and the reduction is more significant at 100 K. The ratio of ^63,65Cu spin–lattice relaxation rates suggests that a magnetic contribution due to the antiferromagnetic spin fluctuation becomes weak as the Zn concentration increases. These effects confirm that the antiferromagnetic spin fluctuation of Cu 3d spins is suppressed by the Zn substitution due to the absence of local moment at the zinc site.     

Expanding the Frequency Range of the Solid-State T1 ρ Experiment for Heteronuclear Dipolar Relaxation

Solid-state spin–lattice relaxation in the rotating frame permits the investigation of dynamic processes with correlation times in the range of microseconds. The relaxation process in organic solids is driven by the fluctuation of the local magnetic field due to the dipole–dipole interaction of the probe nuclei (¹³C,¹⁵N) with ¹H in close proximity. However, its effect is often hidden by a competing relaxation process due to the contact between the rotating frame ¹³C/¹⁵N Zeeman and ¹H dipolar reservoirs. In most cases the latter process becomes superior for the commonly applied low and moderate spin-lock fields and practically does not provide information about the molecular dynamics. To suppress this undesired process and to expand the dynamic range of T_{1 ρ} experiments, we present two approaches. The first one uses a resonance offset of the frequency of the spin-lock irradiation, which leads to a significant enhancement of the effective spin-lock frequency without the application of destructive high transmitter powers. We derive the theory and demonstrate the applicability of the method on various model compounds. The second approach utilizes heteronuclear ¹H decoupling during the ¹³C/¹⁵N spin-lock irradiation which disrupts the contact between the ¹³C/¹⁵N Zeeman and ¹H dipolar reservoirs. We demonstrate the method and discuss the results qualitatively.     

Tuning the bottleneck effect in Ag metallic host doped with magnetic Gd and non-magnetic Sb ions

The Ag metallic host doped with Gd and Sb is an excellent model system to study the bottleneck effect associated to the conduction-electron (c-e) spin-flip scattering mechanism. Electron spin resonance of Gd³⁺ in both, Ag-(Gd doped)- and Ag-(Gd and Sb doped)-systems, reveal the presence of bottleneck which can be tuned by the amount of Gd and Sb impurities. The increase of the Gd concentration leads to a c-e spin-flip relaxation rate to the magnetic Gd³⁺ ions larger than that to the lattice, favoring the bottleneck regime. Whereas the effect of the non-magnetic impurities (Sb ions) is to increase, via spin–orbit scattering, the spin-flip relaxation rate of the c-e to the lattice, weakening the bottleneck regime.     

Sensitivity of Saturation Transfer Electron Spin Resonance Extended to Extremely Slow Mobility in Glassy Materials

A novel extension of the saturation transfer (ST) ESR technique that enables the determination of extremely long rotational correlation times of nitroxide spin labels up to values around 10⁴s is proposed. The method is based on the observation that the integral of ST-ESR spectra is sensitive to the spin–lattice relaxation time of the electron of the spin label, which in turn is directly dependent upon the rotational correlation time. The method is applied to the spin label TEMPOL (4-hydroxy-2,2,6,6-tetramethylpiperidine-N-oxyl) in glycerol. From the known viscosity data and the related rotational correlation times of the TEMPOL spin label in glycerol, the rotational correlation times of unknown samples can be determined. The method is especially applicable to systems with a very high viscosity, such as glassy materials. The method is applied to a 20 wt% glucose–water mixture in the glassy state, giving a value for the highest limiting rotational correlation time of about 10³s at a temperature of 45 K below the glass transition temperature of this system. This is an extension by six decades for the rotational correlation time, as compared to the current application of ST-ESR.