High-Precision Determination of NMR Interaction Parameters by Measurement of Single Crystals: A Review of Classical and Advanced Methods

In this review, the process of extracting precise values for NMR interaction tensors from single crystal samples is systematically explored. Starting with a description of the orientation dependence of the considered interactions, i.e., chemical shift, dipolar, and quadrupole interaction, the techniques for acquiring and analysing single-crystal spectra are outlined. This includes the 'classical' approach, which requires the acquisition of three rotation patterns around three rotation axes that are orthogonal to each other, as well as more recent strategies aimed at reducing the number of required NMR spectra. One such strategy is the 'single-rotation method', which exploits the symmetry relations between tensors in the crystal structure to reduce the necessary amount of orientation-dependent data. This concept may be extended to additionally include the orientation of the goniometer axis itself in the data fit, which may be termed the 'minimal-rotation method'. Other, more exotic schemes, such as the use of specialised probe designs or the investigation of single crystals under magic-angle-spinning, are also briefly discussed. Actual values of NMR interaction tensors as determined from the various single-crystal methods have been collected and are provided in tables for spin I=1/2, I=1, and half-integer spins with I>1/2.

In situ solid-state NMR of a magnetically oriented microcrystal suspension

In situ solid-state NMR measurements of a magnetically oriented microcrystal suspension (MOMS) were demonstrated. Under modulated rotation of the static field, or equivalently, of the sample tube, randomly oriented microcrystals in a viscous liquid medium feel a torque arising from the anisotropic bulk susceptibility and eventually aligned in the same direction. In this way, a three-dimensional MOMS (3D-MOMS) was obtained. To apply an elliptically rotating magnetic field to microcrystals in suspension, a probe to rotate the sample tube around an axis perpendicular to the static magnetic field was developed. Single-crystal (SC) rotation patterns were obtained from the 3D-MOMS by solid-state CP measurements triggered in synchronous with the sample-tube rotation. Unlike the traditional SC method, the 3D-MOMS approach presented here does not require the elaborate adjustment of the direction of the reference frame. The process of three-dimensional magnetic alignment was also studied by monitoring the spectral changes during continuous application of the modulated sample rotation.

Accurate determination of chemical shift tensor orientations of single-crystals by solid-state magic angle spinning NMR

An improved implementation of single-crystal magic-angle-spinning (MAS) NMR is presented which gives access to chemical shift tensors both in orientation (relative to the crystal axis system) and principal axis values. For mounting arbitrary crystals inside ordinary MAS rotors, a mounting tool is described which allows to relate the crystal orientation determined by diffraction techniques to the rotor coordinate system. The crystal is finally mounted into a MAS rotor equipped with a special insert which allows a defined reorientation of the single-crystal by 90°. The approach is based on the idea that the dispersive spectra, which are obtained when applying read-pulses at specific rotor-phases, not only yield the size of the eigenvalues but also encode the orientation of the different chemical shift (rank-2) tensors. For this purpose two 2D-data sets with orthogonal crystal orientation are fitted simultaneously. The presented analysis for chemical shift tensors is supported by an analytical formula which allows fast calculation of phase and amplitude of individual spinning side-bands and by a protocol which solves the problem of finding the correct reference phase of the spectrum. Different rotor-synchronized pulse-sequences are introduced for the same reason. Experiments are performed on L-alanine and O-phosphorylethanolamine and the observed errors are analyzed in detail. The experimental data are opposed to DFT-computed chemical shift tensors which have been obtained by the extended embedded ion method.

Submillimeter coils for stimulated-echo spectroscopy of a solid sodium ion conductor by nonselective excitation of MHz broad 23Na quadrupolar satellite spectra

In solids the detection of ionic motion covering the time range of milliseconds and longer is often accomplished using stimulated-echo spectroscopy. For spectral line widths much below or much above 1MHz nonselective or fully selective radio-frequency pulse excitation, respectively, is typically applied in such experiments. To enable the study of samples with quadrupolarly broadened satellite spectra featuring intermediate widths (in the lower MHz range) the present work exploits microcoils. Using such coils, stimulated-echo spectroscopy can be performed under conditions of nonselective excitation for instance with ²³Na as a nuclear probe. Nutation experiments carried out used to assess the coil performance. The impact of second-order quadrupolar interactions is studied using explicit density-matrix calculations. The applicability of the present approach is successfully tested for a sodium orthophosphate based solid ion conductor.

1D Measurement of Sodium Ion Flow in Hydrogel After a Bath Concentration Jump

NMR is used to measure sodium flow driven by a 1D concentration gradient inside poly-acrylamid (pAA) hydrogel. A sodium concentration jump from 0.5 M NaCl to 0 M NaCl is applied at the bottom of a cylindrical pAA sample. The sodium level and hydrogen level are measured as a function of time and position inside the sample for 5 days. Then a reversed step is applied, and ion flow is measured for another 5 days. During the measurement, the cylindrical sample is radially confined and allowed to swell in the axial direction. At the same time, sodium and moisture in the sample are measured on a 1D spatial grid in the axial direction. A quadriphasic mixture model (Huyghe and Janssen in Int J Eng Sci 35:793, 1997) is used to simulate the results and estimate the diffusion coefficient of sodium and chloride. The best fit results were obtained for D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{Na^+} = 1.15\times 10^{-5}$$\end{document}Na+=1.15×10-5 cm²/s and D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{Cl^-} = 2.15\times 10^{-5}$$\end{document}Cl-=2.15×10-5 cm²/s, at 25 degrees centigrade. Different time constants were observed for swelling and deswelling.

Radiofrequency microcoils for magnetic resonance imaging and spectroscopy

Small radiofrequency coils, often termed "microcoils", have found extensive use in many areas of magnetic resonance. Their advantageous properties include a very high intrinsic sensitivity, a high (several MHz) excitation and reception bandwidth, the fact that large arrays can fit within the homogeneous volume of the static magnetic field, and the very high resonance frequencies (several GHz) that can be achieved. This review concentrates on recent developments in the construction of single and multiple RF microcoil systems, and new types of experiments that can be performed using such assemblies.

Microcoils and microsamples in solid-state NMR

Recent reports on microcoils are reviewed. The first part of the review includes a discussion of how the geometries of the sample and coil affect the NMR signal intensity. In addition to derivation of the well-known result that the signal intensity increases as the coil size decreases, the prediction that dilution of a small sample with magnetically inert matter leads to better sensitivity if a tiny coil is not available is given. The second part of the review focuses on the issues specific to solid-state NMR. They include realization of magic-angle spinning (MAS) using a microcoil and harnessing of such strong pulses that are feasible only with a microcoil. Two strategies for microcoil MAS, the piggyback method and magic-angle coil spinning (MACS), are reviewed. In addition, MAS of flat, disk-shaped samples is discussed in the context of solid-state NMR of small-volume samples. Strong RF irradiation, which has been exploited in wide-line spectral excitation, multiple-quantum MAS (MQMAS), and dipolar decoupling experiments, has been accompanied by new challenges regarding the Bloch-Siegert effect, the minimum time resolution of the spectrometer, and the time scale of pulse transient effects. For a possible solution to the latter problem, recent reports on active compensation of pulse transients are described.