Solid-state nuclear magnetic resonance

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Solid-state 900 MHz (21.1 Tesla) NMR spectrometer at the Canadian National Ultrahigh-field NMR Facility for Solids.

Solid-state NMR (SSNMR) spectroscopy is a kind of nuclear magnetic resonance (NMR) spectroscopy, characterized by the presence of anisotropic (directionally dependent) interactions.

Contents

1 Introduction
2 Nuclear spin interactions in the solid phase

2.1 Chemical shielding
2.2 J-coupling (scalar coupling)
2.3 Dipolar coupling
2.4 Other interactions

3 History
4 Modern solid-state NMR spectroscopy

4.1 Basic example
4.2 Decoupling
4.3 Recoupling

5 Applications

5.1 Material Science
5.2 Biology
5.3 Chemistry

6 References

6.1 Suggested readings for beginners
6.2 Advanced readings
6.3 General

Introduction

Basic concepts A nuclear spin can interact with a magnetic or electric field. Spatial proximity and/or a chemical bond between two atoms can give rise to interactions between nuclei. In general, these interactions are orientation dependent. In media with no or little mobility (e.g. crystals powders, large membrane vesicles, molecular aggregates), anisotropic interactions have a substantial influence on the behaviour of a system of nuclear spins. In contrast, in a classical solution-state NMR experiment, Brownian motion leads to an averaging of anisotropic interactions. In such cases, these interactions can be neglected on the time-scale of the NMR experiment.

Examples of anisotropic nuclear interactions Two directionally dependent interactions commonly found in solid-state NMR are the chemical shift anisotropy (CSA) and the internuclear dipolar coupling. Many more such interactions exist, such as the anisotropic J-coupling in NMR, or in related fields, such as the g-tensor in electron spin resonance. In mathematical terms, all these interactions can be described using the same formalism.

Experimental background Anisotropic interactions modify the nuclear spin energy levels (and hence the resonance frequency) of all sites in a molecule, and are often attributed to a line-broadening effect in NMR spectra. However, there is a range of situations when their presence can either not be avoided, or is even particularly desired, as they encode structural parameters, such as orientation information, on the molecule of interest.

High-resolution conditions in solids (in a wider sense) can be established using magic angle spinning (MAS), macroscopic sample orientation, combinations of both of these techniques, enhancement of mobility by highly viscous sample conditions, and a variety of radio frequency (RF) irradiation patterns. While the latter allows decoupling of interactions in spin space, the others facilitate averaging of interactions in real space. In addition, line-broadening effects from microscopic inhomogeneities can be reduced by appropriate methods of sample preparation.

Under decoupling conditions, isotropic interactions can report on the local structure, e.g. by the isotropic chemical shift. In addition, decoupled interactions can be selectively re-introduced (recoupling"), and used, for example, for controlled de-phasing or transfer of polarization, which allows to derive a number of structural parameters.

Solid-state NMR line widths The residual line width (full width at half max) of ¹³C nuclei under MAS conditions at 5–15 kHz spinning rate is typically in the order of 0.5–2 ppm, and may be comparable to solution-state NMR conditions. Even at MAS rates of 20 kHz and above, however, ¹H–¹H dipolar interactions can only be suppressed partially, leading to line widths of 0.5 ppm and above, which is considerably more than in optimal solution state NMR conditions.

Anisotropic interactions in solution-state NMR From the perspective of solution-state NMR, it can be desirable to reduce motional averaging of dipolar interactions by alignment media. The order of magnitude of these residual dipolar couplings (RDCs) are typically of only a few rad/Hz, but do not destroy high-resolution conditions, and provide a pool of information, in particular on the orientation of molecular domains with respect to each other.

Dipolar truncation The dipolar coupling between two nuclei is inversely proportional to the cube of their distance. This has the effect that the polarization transfer mediated by the dipolar interaction is cut off in the presence of a third nucleus (all of the same kind, e.g. ¹³C) close to one of these nuclei. This effect is commonly referred to as dipolar truncation. It has been one of the major obstacles in efficient extraction of internuclear distances, which are crucial in the structural analysis of biomolecular structure. By means of labeling schemes or pulse sequences, however, it has become possible to circumvent this problem in a number of ways.

Nuclear spin interactions in the solid phase

Magnitude of interaction...

Chemical shielding

The chemical shielding is a local property of each nucleus, and depends on the external magnetic field.

Specifically, the external magnetic field induces currents of the electrons in molecular orbitals. These induced currents create local magnetic fields that often vary across the entire molecular framework such that nuclei in distinct molecular environments usually experience unique local fields from this effect.

Under sufficiently fast magic angle spinning, or in solution-state NMR, the directionally dependent character of the chemical shielding is removed, leaving the isotropic chemical shift.

J-coupling (scalar coupling)

The J-coupling or scalar coupling describes the interaction of nuclear spins through chemical bonds.

Dipolar coupling

Main article: Dipolar coupling (NMR)

Dipolar coupling vectors

Nuclear spins exhibit a dipole moment, which interacts with the dipole moment of other nuclei (dipolar coupling). The magnitude of the interaction is dependent on the spin species, the internuclear distance, and the orientation of the vector connecting the two nuclear spins with respect to the external magnetic field B (see figure). The maximum dipolar coupling is given by the dipolar coupling constant d,

[ d = \frac \frac ],

where r is the distance between the nuclei, and γ₁ and γ₂ are the gyromagnetic ratios of the nuclei. In a strong magnetic field, the dipolar coupling depends on the orientation of the internuclear vector with the external magnetic field by

[D \propto 3\cos^2\theta - 1].

Consequently, two nuclei with a dipolar coupling vector at an angle of θ_m=54.7° to a strong external magnetic field, which is the angle where D becomes zero, have zero dipolar coupling. θ_m is called the magic angle. One technique for removing dipolar couplings, at least to some extent, is magic angle spinning.

Other interactions

Some nuclei exhibit quadrupolar interactions (spin > 1/2). Paramagnetic substances are subject to the Knight shift...

History

See also: nuclear magnetic resonance or NMR spectroscopy articles for an account on discoveries in NMR and NMR spectroscopy in general.

History of discoveries of NMR phenomena, and the development of solid-state NMR spectroscopy:

Purcell, Torrey and Pound: "nuclear induction" on ¹H in paraffin 1945, at about the same time Bloch et al. on ¹H in water.

Modern solid-state NMR spectroscopy

Methods and techniques

Basic example

CP pulse sequence

A fundamental RF pulse sequences and building-block in most solid-state NMR experiments is cross-polarization (CP) [Pines, 1973]. It can be used to enhance the signal of nuclei with a low gyromagnetic ratio (e.g. ¹³C, ¹⁵N) from a transfer of nuclei with a high gyromagnetic ratio (e.g. ¹H), or as spectral editing method (e.g. directed ¹⁵N→¹³C CP in protein spectroscopy). In order to establish magnetization transfer, the RF pulses applied on the two frequency channels must fulfill the Hartmann–Hahn condition [Hartmann, 1962]. Under MAS, this condition defines a relationship between the voltage through the RF coil and the rate of sample rotation. Experimental optimization of such conditions is one of the routine tasks in performing a (solid-state) NMR experiment.

CP is a basic building block of most pulse sequences in solid-state NMR spectroscopy. Given it's importance, a pulse sequence employing direct excitation of ¹H spin polarization, followed by CP transfer to and signal detection of ¹³C, ¹⁵N) or similar nuclei, is itself often referred to as CP experiment, or, in conjunction with MAS, as CP-MAS [Schaefer and Stejskal, 1976]. It is the typical starting point of an investigation using solid-state NMR spectroscopy.

Decoupling

Sample rotation Nuclear spin interactions need to be removed (decoupled) in order to increase the resolution of NMR spectra, and to isolate spin systems. A technique that can substantially reduce or remove the chemical shift anisotropy, the dipolar coupling is sample rotation (most commonly magic angle spinning, but also off-magic angle spinning).

Heteronuclear RF decoupling

Homonuclear RF decoupling

Recoupling

Recoupling experiments can be used to measure the dipolar coupling between atoms in the crystal lattice. As the dipolar coupling is distance dependent, this may be used to calculate interatomic distances in isotopically labelled molecules. An example of a recoupling experiment is the Rotational Echo DOuble Resonance (REDOR) experiment.

Applications

Material Science

Solid-state NMR spectroscopy can, for example, be used to investigate the molecular structure of polymers.

Biology

Membrane proteins and amyloid fibrils, the latter related to Alzheimer's disease and Parkinson's disease, are two examples of application where solid-state NMR spectroscopy complements solution-state NMR spectroscopy and beam diffraction methods (e.g. X-ray crystallography, electron microscopy).

Chemistry

Solid-state NMR spectroscopy serves as an analysis tool in organic and inorganic chemistry. SSNMR is also a valuable tool to study local dynamics, kinetics, and thermodynamics of a variety of systems.

References

Advanced readings

Books and major review articles

Mehring, "High Resolution NMR in Solids", 2nd ed.
Slichter, "Principles of Magnetic Resonance", 3rd ed.
Schmidt-Rohr and Spiess: "Multidimensional Solid-State NMR and Polymers", Academic Press, 1994.

General

References to books and research articles

Andrew, E. R., Bradbury, A. and Eades, R. G., "Removal of Dipolar Broadening of Nuclear Magnetic Resonance Spectra of Solids by Specimen Rotation," Nature 183, 1802, (1959)
Ernst, Bodenhausen, Wokaun: "Principles of Nuclear Magnetic Resonance in One and Two Dimensions"
Hartmann S.R., Hahn E.L., "Nuclear Double Resonance in the Rotating Frame" Phys. Rev. 128 (1962) 2042.
Pines A., Gibby M.G., Waugh J.S., "Proton-enhanced NMR of dilute spins in solids" J. Chem. Phys. 59, 569-90, (1973)
Purcell, Torrey and Pound (1945).
Schaefer, J. and Stejskal, E. O., "Carbon-13 Nuclear Magnetic Resonance of Polymers Spinning at the Magic Angle," Journal of the American Chemical Society 98, 1031 (1976).

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