Spin-locking of half-integer quadrupolar nuclei in nuclear magnetic resonance of solids: creation and evolution of coherences

Spin-locking of half-integer quadrupolar nuclei, such as 23Na (I=3/2) and 27Al (I=5/2), is of renewed interest owing to the development of variants of the multiple-quantum and satellite-transition magic angle spinning (MAS) nuclear magnetic resonance experiments that either utilize spin-locking directly or offer the possibility that spin-locked states may arise. However, the large magnitude and, under MAS, the time dependence of the quadrupolar interaction often result in complex spin-locking phenomena that are not widely understood. Here we show that, following the application of a spin-locking pulse, a variety of coherence transfer processes occur on a time scale of approximately 1/omegaQ before the spin system settles down into a spin-locked state which may itself be time dependent if MAS is performed. We show theoretically for both spin I=3/2 and 5/2 nuclei that the spin-locked state created by this initial rapid dephasing typically consists of a variety of single- and multiple-quantum coherences and nonequilibrium population states and we discuss the subsequent evolution of these under MAS. In contrast to previous work, we consider spin-locking using a wide range of radio frequency field strengths, i.e., a range that covers both the "strong-field" (omega1 > omegaQPAS and "weak-field" (omega1 < omegaQPAS limits. Single- and multiple-quantum filtered spin-locking experiments on NaNO2, NaNO3, and Al(acac)3, under both static and MAS conditions, are used to illustrate and confirm the results of the theoretical discussion.     

Accurate measurement of longitudinal cross-relaxation rates in nuclear magnetic resonance

The accuracy of the determination of longitudinal cross-relaxation rates in NMR can be improved by combining symmetrical reconversion with suitable operator swapping methods that lead to the averaging of differences in autorelaxation rates and eliminate the effects of cross relaxation with the environment. The principles are first discussed for an isolated two-spin system comprising a pair of 15N and 1HN nuclei subjected to chemical shift anisotropy and dipole-dipole relaxation, and then extended to include further protons. The gains in accuracy are demonstrated experimentally for the protein ubiquitin.     

Covariance nuclear magnetic resonance spectroscopy

Covariance nuclear magnetic resonance (NMR) spectroscopy is introduced, which is a new scheme for establishing nuclear spin correlations from NMR experiments. In this method correlated spin dynamics is directly displayed in terms of a covariance matrix of a series of one-dimensional (1D) spectra. In contrast to two-dimensional (2D) Fourier transform NMR, in a covariance spectrum the spectral resolution along the indirect dimension is determined by the favorable spectral resolution obtainable along the detection dimension, thereby reducing the time-consuming sampling requirement along the indirect dimension. The covariance method neither involves a second Fourier transformation nor does it require separate phase correction or apodization along the indirect dimension. The new scheme is demonstrated for cross-relaxation (NOESY) and J-coupling based magnetization transfer (TOCSY) experiments.     

Introduction to nuclear magnetic resonance

The basic principles of nuclear magnetic resonance (NMR) are presented in an elementary form using classical and elementary quantum mechanics and the experimental technique 1s explained. The motion of the magnetization by r.f. pulses, free induction decay and spectrum, transverse and longitudinal relaxation, local field and spin echo are described and the effects of molecular motion are discussed. The concepts of spin temperature and spin diffusion are presented and the advantage of using quadrupole nuclei is stressed. Finally, the specific problems of NMR in interface studies are considered and a typical example is given.     

Two-photon two-color nuclear magnetic resonance

Two-photon excitation has recently been demonstrated to be a practical means of exciting nuclear magnetic resonance (NMR) signals by radio-frequency (rf) irradiation at half the normal resonance frequency. In this work, two-photon excitation is treated with average Hamiltonian theory and shown to be a consequence of higher order terms in the Magnus expansion. It is shown that the excitation condition may be satisfied not only with rf at half resonance, but also with two independent rf fields, where the two frequencies sum to or differ by the resonance frequency. The technique is demonstrated by observation of proton NMR signals at 400 MHz while simultaneously exciting at 30 and 370 MHz. Advantages of this so-called two-color excitation, such as a dramatic increase in nutation rate over half-frequency excitation, along with a variety potential applications are discussed.     

Shiftless nuclear magnetic resonance spectroscopy

The acquisition and analysis of high resolution one- and two-dimensional solid-state nuclear magnetic resonance (NMR) spectra without chemical shift frequencies are described. Many variations of shiftless NMR spectroscopy are feasible. A two-dimensional experiment that correlates the dipole-dipole and dipole-dipole couplings in the model peptide , (15)N labeled N-acetyl-leucine is demonstrated. In addition to the resolution of resonances from individual sites in a single crystal sample, the bond lengths and angles are characterized by the two-dimensional powder pattern obtained from a polycrystalline sample.     

1H multiple-quantum nuclear magnetic resonance investigations of molecular order in polymer networks. II. Intensity decay and restricted slow dynamics

We present an approach towards the analysis of the intensity decay in proton multiple-quantum experiments on polymeric networks in terms of slow fluctuations of the residual dipole-dipole coupling tensor. Solutions for individual spin pairs as well as the three-spin system of methyl groups are derived, and the influence of the cycle time of the multiple-quantum pulse sequence is evaluated. The multiple-quantum strategy discussed herein features the advantage that the magnitude of the fluctuating part of the residual dipole-dipole coupling constant and the correlation time of the slow process can be determined independently of the integral residual coupling constant as well as its distribution. The theory is applied to experiments on end-linked poly(dimethylsiloxane) model networks with mono- and bimodal chain length distributions, where it is found that, for all samples, correlation times of the slow processes average to about 1 ms, and that the magnitude of the fluctuating part of the dipole-dipole coupling is significantly smaller than the average dipole-dipole coupling constant. This observation is interpreted in terms of considerably restricted reorientations of topological constraints.     

Hyphenation of capillary separations with nuclear magnetic resonance spectroscopy

The hyphenation of small-volume separations to information-rich detection offers the promise of unmatched analytical information on the components of complex mixtures. Nuclear magnetic resonance (NMR) spectroscopy provides information about molecular structure, although sensitivity remains an issue for on-line NMR detection. This is especially true when hyphenating NMR to capillary separations as the observation time and analyte mass are decreased to the point where reduced information is obtained from the eluting analytes. Because of these limitations, advances in instrumental performance have a large impact on the overall performance of a separation–NMR system. Instrumental aspects and the capabilities of cLC–NMR, CEC–NMR and CE–NMR are reviewed, and applications that have used this technology highlighted. Recent trends towards small volume capillary scale separations are emphasized, as is the recent success of capillary-isotachophoresis (cITP)–NMR.     

Effect of internal gradients in the nuclear magnetic resonance measurement of the surface-to-volume ratio

We consider a system of spins diffusing in a static inhomogeneous (nonuniform-gradient) magnetic field B in a restricted geometry and in the presence of surface relaxation. We show that the short-time diffusional decay of nuclear magnetization is controlled by the field scattering kernel F(t) identical with [B(t)-B(0)](2), which is a measure of the average field inhomogeneity sampled by the spins in time t and does not depend on the particular sequence of radio-frequency pulses used. Magnetization in arbitrary sequences can be straightforwardly computed by evaluating elementary integrals of F(t). Diffusion takes place while the field is on, so that the spins precess as they diffuse, in contrast to the simpler problem of purely classical diffusion considered in [P. P. Mitra, P. N. Sen, and L. M. Schwartz, Phys. Rev. B 47, 8565 (1993)] which is applicable only to the ideal pulsed-field gradient experiment. We compute the short-time asymptotic form of F(t) and find that it depends on the surface-to-volume ratio (S/V) of the pore space as well as on the average of the gradients over the bounding surface. In a system with nonuniform gradients that vary faster near the surface than in the bulk, as for internal susceptibility fields, this gradient surface average may be much larger than the gradients in the bulk, significantly enhancing the apparent S/V. We discuss the application of our results to the widely used Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence as well as proposing a modification of it, which we term "padded" CPMG, that may be preferable in systems with significant surface relaxation. We indicate how each sequence can be used to probe the internal fields.     

29Si nuclear magnetic resonance of dialkylpolysilanes

The silicon-29 nuclear magnetic resonance spectra of a number of dialky- and alkylmethylpoly-silanes are reported. Polysilanes composed of asymmetrically substituted silylenes (i.e., alkylmethylsilylenes) exhibited very broad resonance lines attributed to diastereomeric chemical shifts of stereogenic silylenes alpha and beta to the observed nucles Symmetrically substituted polysilanes showed a single narrow peak. The ²⁹Si chemical shifts for these polysilanes decrease with increasing steric bulk of the substituents, varying inversely with the electronic excitation energy.     

Theory of covariance nuclear magnetic resonance spectroscopy

Covariance nuclear magnetic resonance (NMR) spectroscopy provides an effective way for establishing nuclear spin connectivities in molecular systems. The method, which identifies correlated spin dynamics in terms of covariances between 1D spectra, benefits from a high spectral resolution along the indirect dimension without requiring apodization and Fourier transformation along this dimension. The theoretical treatment of covariance NMR spectroscopy is given for NOESY and TOCSY experiments. It is shown that for a large class of 2D NMR experiments the covariance spectrum and the 2D Fourier transform spectrum can be related to each other by means of Parseval's theorem. A general procedure is presented for the construction of a symmetric spectrum with improved resolution along the indirect frequency domain as compared to the 2D FT spectrum.     

Optically pumped nuclear magnetic resonance of semiconductors

Optically pumped NMR (OPNMR) of direct gap and indirect gap semiconductors has been an area of active research interest, motivated by both basic science and technological perspectives. Proposals to enhance and to spatially localize nuclear polarization have stimulated interest in this area. Recent progress in OPNMR has focused on exploring the experimental parameter space in order to elucidate details of the underlying photophysics of optical pumping phenomena. The focus of this review is on recent studies of bulk samples of GaAs and InP, namely, the photon energy dependence, the magnetic field dependence, and the phase dependence of OPNMR resonances. Models for the development of nuclear polarization are discussed.     

Singlet nuclear magnetic resonance of nearly-equivalent spins

Nuclear singlet states may display lifetimes that are an order of magnitude greater than conventional relaxation times. Existing methods for accessing these long-lived states require a resolved chemical shift difference between the nuclei involved. Here, we demonstrate a new method for accessing singlet states that works even when the nuclei are almost magnetically equivalent, such that the chemical shift difference is unresolved. The method involves trains of 180° pulses that are synchronized with the spin-spin coupling between the nuclei. We demonstrate experiments on the terminal glycine resonances of the tripeptide alanylglycylglycine (AGG) in aqueous solution, showing that the nuclear singlet order of this system is long-lived even when no resonant locking field is applied. Variation of the pulse sequence parameters allows the estimation of small chemical shift differences that are normally obscured by larger J-couplings.     

Nitrogen-14 nuclear magnetic resonance of azine-N-oxides

The ¹⁴N NMR chemical shifts of mono-N-oxides of 1,2-, 1,3-, and 1,4-diazine systems in mono-, bi, and tri-cyclic structures are shown to depend linearly on the π-charge density at the oxide nitrogen atom obtained from SCF-PPP-MO calculations. The ¹⁴N NMR chemical shifts in poly-azine-mono-N-oxides relative to parent structures of mono-azine-N-oxides may be expressed in terms of additivity rules for 1,2-, 1,3-, and 1,4-interactions of azine type nitrogen atoms. Simple additivity rules are also found for an influence of fused ring systems. Nitrogen chemical shifts, hitherto unknown, are predicted for a number of poly-azine-mono-N-oxide structures.     

Gradient elution capillary electrochromatography and hyphenation with nuclear magnetic resonance

Coupling of gradient capillary electrochromatography (gradient CEC) and capillary zone electrophoresis (CZE) with nuclear magnetic resonance spectroscopy (NMR) was performed using a recently developed capillary NMR interface. This technique was applied for the analysis of pharmaceuticals and food. An analgesic was investigated using isocratic and gradient continuous-flow CEC-NMR. Comparison of the results demonstrated the superiority of gradient CEC over isocratic CEC. Aspartame and caffeine, both ingredients of soft beverages, were separated and analyzed by continuous flow CZE-NMR. The order of elution could be reversed by altering the pH. This reversal led to an increased sample concentration in the NMR detection cell, thus allowing the acquisition of a totally correlated spectroscopy (TOCSY) two-dimensional (2-D) spectrum of the synthetic peptide aspartame.     

Near neighbor approximation in nuclear magnetic resonance

A new way to deal with the excitation by multiple effective RF fields with interference is presented using the coherent averaging theory. It significantly simplifies the calculation of the effect of RF interference that occurs in the excitations by periodic pulses and phase-incremented pulses (PIPs). This approach shows that each neighboring RF field contributes to an excitation profile an offset shift, which is termed the Bloch-Siegert offset shift (BSOS). The BSOS depends not only on the strengths of both RF fields that interfere with each other but also on their relative phase between the two RF fields. Consequently, it can be positive, negative, and zero. In addition, the BSOS is also inversely proportional to the frequency separation of the two RF fields. Therefore, only a few near neighbors need to be taken into account in most cases, resulting in a near neighbor approximation (NNA). The BSOS for two multiband excitation profiles, one by a periodic pulse and the other by a PIP, are calculated using the NNA. The results are in good agreement with the computer simulated ones.