Ergodicity and efficiency of cross-polarization in NMR of static solids

Cross-polarization transfer is employed in virtually every solid-state NMR experiment to enhance magnetization of low-gamma spins. Theory and experiment is used to assess the magnitude of the final quasistationary magnetization amplitude. The many-body density matrix equation is solved for relatively large (up to N=14) spin systems without the spin-temperature assumption for the final spin states. Simulations show that about 13% of the thermodynamic limit is still retained within the proton bath. To test this theoretical prediction, a combination of a reverse cross-polarization experiment and multiple contacts is employed to show that the thermodynamic limit of magnetization cannot be transferred from high- to low-gamma nuclei in a single contact. Multiple contacts, however, fully transfer the maximum magnetization. A simple diffusion on a cone model shows that slow dynamics can affect the build up profile for the transferred magnetization.     

Localized cross-polarization in solids

Single quantum heteronuclear cross-polarization in solids is strongly sensitive to resonance offsets. In the presence of main field- or radio-frequency field gradients, the cross-polarization efficiency, therefore, shows a strong spatial dependence, which represents a new principle for localized NMR in solids. Since slices-selective excitation is achieved simultaneously to cross-polarization, the suggested pulse sequences avoid the use of shaped pulses, the application of which is problematic with solid. The dependence of the localization efficiency on experimental and sample parameters is analyzed theoretically for a spin-1/2 system in the presence of a static or a radio-frequency magnetic field gradient. The resulting slice profiles and the calculated dependence of the slice thickness on the parameters of the basic cross-polarization procedures are discussed and confirmed experimentally on the example of¹H-³C spin systems.     

Oxygen-17 cross-polarization nmr spectroscopy of inorganic solids

We have obtained ¹⁷O nuclear magnetic resonance spectra of a variety of ¹⁷O-labeled solids (Mg(OH)₂, Ca(OH)₂, boehmite (AlO(OH)), talc (Mg₃Si₄O₁₀(OH)₂), (C₆H₅)₃SiOH, and amorphous SiO₂) using high-field static and “magic-angle” sample spinning techniques, together with ¹H cross polarization and dipolar decoupling. Our results show that large cross-polarization enhancements can be obtained and that reliable second-order quadrupolar powder lineshapes can be observed under cross-polarization conditions. We have also investigated the dynamics of cross polarization for several samples, including measurements of cross-relaxation rates and ¹H and ¹⁷O rotating-frame spin-lattice relaxation times. We show that rapid ¹⁷O rotating-frame spin-lattice relaxation reduces the cross-polarization enhancement in some cases and that differences in cross-relaxation rates can be used to “edit” spectra by selectively enhancing protonated oxygen resonances (in general, hydroxide versus oxide ions, in inorganic solids). When applied to high surface area metal oxides such as amorphous silica, this selectivity enables the observation of resonances from surface hydroxyl groups that are difficult to detect by conventional ¹⁷O NMR. Overall, the cross-polarization approach appears to have considerable utility for aiding in the interpretation of ¹⁷O NMR spectra of complex inorganic solids.     

Spin-state-selective excitation in gradient-selected heteronuclear cross-polarization NMR experiments

Several heteronuclear coherence transfer mechanisms involved in proton-detected heteronuclear J-cross-polarization (HCP) NMR experiments have been theoretically derived and experimentally verified in isotropic solution. It is shown that in-phase and/or anti-phase heteronuclear coherence transfer can take place separately or simultaneously during the HCP process as a function of the relative phase between the HCP mixing sequence and the corresponding input magnetization. As the more important consequence, clean coherence-order and spin-state selective (S3) excitation with maximum sensitivity can be achieved from gradient-enhanced HCP experiments by proper co-addition/subtraction of in-phase and anti-phase magnetizations, offering an attractive alternative to widely used HSQC-type experiments.     

Indirect covariance NMR spectroscopy of through-bond homo-nuclear correlations for quadrupolar nuclei in solids under high-resolution

Indirect covariance NMR spectroscopy is demonstrated in solids, and we show that it can be used to obtain through-bond 2D homo-nuclear correlation spectra for quadrupolar nuclei under high-resolution. These spectra, generated with indirect covariance from a hetero-nuclear correlation spectrum, are equivalent to those recorded with the through-bond homo-nuclear hetero-nuclear single-quantum correlation (H-HSQC) method very recently proposed. However, the indirect covariance method can save a lot of experiment time, compared to the H-HSQC experiments, which allows introducing a high-resolution quadrupolar filter, thus providing a much better resolution, even on medium-field spectrometers. The covariance concept can be used to generate many different "indirectly-detected" high-resolution homo-nuclear correlation spectra with through-space or through-bond correlations for spin 1/2 or quadrupolar nuclei. We also propose a simple method that decreases the noise in all (direct or indirect) covariance methods.     

Ordering in nematic liquid crystals from NMR cross-polarization studies

The measurement of dipolar couplings between nuclei is a convenient way of obtatining directly liquid crystalline ordering through NMR since the coupling is dependent on the average orientation of the dipolar vector in the magnetic field which also aligns the liquid crystal. However, measurement of the dipolar coupling between a pair of selected nuclei is beset with problems that require special solutions. In this article the use of cross polarization for measuring dipolar couplings in liquid crystals is illustrated. Transient oscillations observed during cross polarization provide the dipolar couplings between essentially isolated nearest neighbour spins which can be extracted for several sites simultaneously by employing two-dimensional NMR techniques. The use of the method for obtaining heteronuclear dipolar couplings and hence the order parameters of liquid crystals is presented. Several modifications to the basic experiment are considered and their utility illustrated. A method for obtaining proton-proton dipolar couplings, by utilizing cross polarization from the dipolar reservoir, is also presented.     

NMR imaging in solids

The use of NMR imaging for the study of solids is demonstrated. A modified version of the convolution algorithm is used to construct the images. The modification removes the NMR linebroadening as the image is formed. Examples are presented using the mixed ionic conductor (Na_1?x, K_x) β-alumina.     

Indirect detection of nitrogen-14 in solids via protons by nuclear magnetic resonance spectroscopy

This Communication describes the indirect detection of 14N nuclei (spin I=1) in solids by nuclear magnetic resonance (NMR) spectroscopy. The two-dimensional correlation method used here is closely related to the heteronuclear multiple quantum correlation (HMQC) experiment introduced in 1979 to study molecules in liquids, which has recently been used to study solids spinning at the magic angle. The difference is that the coherence transfer from neighboring 1H nuclei to 14N is achieved via a combination of J couplings and residual dipolar splittings (RDS). Projections of the two-dimensional correlation spectra onto the 14N dimension yield powder patterns which reflect the 14N quadrupolar interaction. In contrast to the indirect detection of 14N via 13C nuclei that was recently demonstrated [Gan, J. Am. Chem. Soc. 128 (2006) 6040; Cavadini et. al., J. Am. Chem. Soc., 128 (2006) 7706], this approach may benefit from enhanced sensitivity, and does not require isotopic enrichment in 13C, although the 1H line-widths may have to be reduced upon selective deuteration.     

Hadamard NMR spectroscopy in solids

The duration of 2D and 3D NMR experiments in solids can be reduced by several orders of magnitude by using frequency domain Hadamard encoding with long selective pulses. We demonstrate Hadamard encoded experiments in (13)C enriched solids samples. To avoid multiple quantum interferences, the Hadamard encoding pulses are applied sequentially rather than simultaneously in this study. Among other possible applications, dipolar assisted rotational resonance experiments and measurement of NOESY type build-up rates in proton driven spin diffusion are demonstrated.     

Long-lived NMR echoes in solids

A new type of long-lived NMR echo in solids with homogeneously broadened dipolar spectra is discussed. The echo can be generated by a simple two-pulse Hahn sequence in solid samples, where dipolar-coupled nuclei have different chemical shifts. We present general considerations and simple theoretical models which explain some features of this phenomenon.     

Multiple-quantum cross-polarization and two-dimensional MQMAS NMR of quadrupolar nuclei

Cross-polarization from (1)H to the multiple-quantum coherences of a quadrupolar nucleus is used in combination with the two-dimensional multiple-quantum magic angle spinning (MQMAS) NMR experiment in order to extract high-resolution CPMAS NMR spectra. The technique is demonstrated on (23)Na (S = 3/2), (17)O, (27)Al (both S = 5/2), and (45)Sc (S = 7/2) nuclei, showing the applicability of multiple-quantum cross-polarization to systems with differing spin quantum number, gyromagnetic ratio, and relative nuclide abundance. The utility of this two-dimensional MAS NMR experiment for spectral editing and site-specific measurement of cross-polarization intensities is demonstrated. The possibility of direct cross-polarization to higher order multiple-quantum coherences is also considered and three-, five-, and seven-quantum cross-polarized (45)Sc MAS NMR spectra are presented.     

Spectral editing in MAS NMR of aprotic solids P---Cd cross-polarization and heteronuclear double-quantum filtering studies in II-IV-V2 semiconductor alloys

Magic-angle-spinning NMR spectra of aprotic solids, ceramics and glasses frequently suffer from poor site resolution due to wide chemical shift distribution effects. In such cases, cross-polarization and heteronuclear double-quantum filtering experiments involving nuclei other than ¹H offer unique spectral editing capabilities. The utility of such assignment techniques for examining site populations in semiconductor alloys is demonstrated for the chalcopyrite systems CdGeAs_2−xP_x, CdSiAs_2−xP_x and Zn_xCd_1−xGeP₂. The results permit a distinction between local and non-local effects on experimental chemical shift trends and reveal that compositional dependences observed in these alloys are dominated by non-local chemical shift contributions.     

Line shapes of multiple quantum NMR coherences in one-dimensional quantum spin chains in solids

General formulae for intensities of multiple quantum (MQ) NMR coherences in systems of nuclear spins coupled by the dipole-dipole interactions are derived. The second moments of the MQ coherences of zero- and second orders are calculated for infinite linear chains in the approximation of the nearest neighbor interactions. Supercomputer simulations of intensities of MQ coherences of linear chains are performed at different times of preparation and evolution periods of MQ NMR experiments. The second moments obtained from the developed theory are compared with the results of the supercomputer analysis of MQ NMR dynamics. The linewidth information in MQ NMR experiments is discussed.     

Signal identification in NMR spectra with coupled evolution periods

Novel multidimensional NMR experiments rely on modified time-domain sampling schemes to provide significant savings of experimental time. Several approaches are based on the coupling of evolution times resulting in a reduction of the dimensionality of the recorded spectra, and a concomitant saving of experimental time. We present a consistent and general tool, called EVOCOUP, for the analysis of these reduced dimensionality spectra. The approach is flexible in the sense that the input can consist of various forms of reduced dimensionality spectra, that any piece of information can be removed (provided enough information is left), e.g., signals undetectable due to poor signal-to-noise or covered by artifacts, and that it can be applied to spectra involving any number of nuclei. The use of a general optimization procedure and an appropriate target function provides for a robust approach with well-defined results and ensures optimal use of redundant information normally present in the input. Spectral overlap in the directly detected dimension is resolved in a fully automated manner, avoiding the assessment of signal quality and its use in combinatorial trials. The positions of all peaks in a corresponding full-dimensional spectrum are obtained without need for reconstruction of this spectrum. In a systematic analysis of a complete spectrum recorded for the 14 kDa protein azurin and involving five different nuclei, only four spin systems were missed and no false spins systems were detected.     

Sensitivity-enhanced static 15N NMR of solids by 1h indirect detection

A method for enhancing the sensitivity of 15N spectra of nonspinning solids through 1H indirect detection is introduced. By sampling the 1H signals in the windows of a pulsed spin-lock sequence, high-sensitivity 1H spectra can be obtained in two-dimensional (2D) spectra whose indirect dimension yields the 15N chemical shift pattern. By sacrificing the 1H chemical shift information, sensitivity gains of 1.8 to 2.5 for the 15N spectra were achieved experimentally. A similar sensitivity enhancement was also obtained for 2D (15)N-(1)H dipolar and 15N chemical shift correlation spectroscopy, by means of a 3D 1H/15N-1H/15N correlation experiment. We demonstrate this technique, termed PRINS for proton indirectly detected nitrogen static NMR, on a crystalline model compound with long 1H T(1rho) and on a 25-kDa protein with short 1H T(1rho). This 1H indirect detection approach should be useful for enhancing the sensitivity of 15N NMR of oriented membrane peptides. It can also be used to facilitate the empirical optimization of 15N-detected experiments where the inherent sensitivity of the sample is low.     

Photothermoacoustic effect in solids with piezoelectric detection

The photothermoacoustic effect in solids with piezoelectric signal detection is investigated theoretically and experimentally. Analytical expressions are found for the amplitude and phase shift of the photothermoacoustic signal as a function of the thicknesses of the sample and piezoelectric transducer, the modulation frequency, and the material constants of the structure. A method is proposed for detecting the signal using a compound piezoelectric transducer. It is shown for a bilayer piezoelectric transducer that the reduced Young’s modulus and the thermal diffusion coefficient of the experimental object can be found from the amplitude-frequency and phase-frequency curves. Zh. Tekh. Fiz. 69, 1–5 (December 1999)     

13C cross-polarization MAS NMR study of some steroidal sapogenins

Cross-polarization (CP) magic angle spinning (MAS) solid-state 13C NMR spectra of five steroidal sapogenins: tigogenin ((25R)-5alpha-spirostan-3beta-ol), hecogenin (3beta-hydroxy-(25R)-5alpha-spirostan-12-one), diosgenin ((delta5-(25R)-5alpha-spirosten-3beta-ol), sarsasapogenin ((25S)-55beta-spirostan-3beta-ol), and smilagenin ((25R)-5beta-spirostan-3beta-ol) were recorded. The solid-state chemical shifts are almost the same as for solution, which indicate that confirmations of sapogenins are similar in both phases. The doubling of some resonances in the spectra of solid diosgenin shows that there are two molecules in the crystallographic asymmetric unit. The cross-polarization time constants T(CP) and relaxation times in the rotating frame T(1rho)H were obtained from the variable-contact cross-polarization experiments for tigogenin and diosgenin. The values of T(CH) for methyl carbons indicate fast rotation of methyl groups and are close (0.30-0.35 ms), suggesting that the interaction with their intramolecular neighbors is similar. The values of T(1rho)H for carbons of tigogenin are longer than of diosgenin. Very efficient cross-polarization dynamics results in short time required for obtaining a spectrum of sapogenin of remarkably good quality.