Solid-state nuclear magnetic resonance
Solid-state nuclear magnetic resonance is a spectroscopy technique used to characterize atomic-level structure and dynamics in solid materials. ssNMR spectra are broader due to nuclear spin interactions which can be categorized as dipolar coupling, chemical shielding, quadrupolar interactions, and j-coupling. These interactions directly affect the lines shapes of experimental ssNMR spectra which can be seen in powder and dipolar patterns. There are many essential solid-state techniques alongside advanced ssNMR techniques that may be applied to elucidate the fundamental aspects of solid materials. ssNMR is often combined with magic angle spinning to remove anisotropic interactions and improve the sensitivity of the technique. The applications of ssNMR further extend to biology and medicine.
Nuclear spin interactions
The resonance frequency of a nuclear spin depends on the strength of the magnetic field at the nucleus, which can be modified by isotropic and anisotropic interactions. In a classical liquid-state NMR experiment, molecular tumbling coming from Brownian motion averages anisotropic interactions to zero and they are therefore not reflected in the NMR spectrum. However, in media with no or little mobility, anisotropic local fields or interactions have substantial influence on the behaviour of nuclear spins, which results in the line broadening of the NMR spectra.Chemical shielding
Chemical shielding is a local property of each nuclear site in a molecule or compound, and is proportional to the applied external magnetic field. The external magnetic field induces currents of the electrons in molecular orbitals. These induced currents create local magnetic fields that lead to characteristic changes in resonance frequency. These changes can be predicted from molecular structure using empirical rules or quantum-chemical calculations.In general, the chemical shielding is anisotropic because of the anisotropic distribution of molecular orbitals around the nuclear sites. Under sufficiently fast magic angle spinning, or under the effect of molecular tumbling in solution-state NMR, the anisotropic dependence of the chemical shielding is time-averaged to zero, leaving only the isotropic chemical shift.
Dipolar coupling
Nuclear spins exhibit a magnetic dipole moment, which generates a magnetic field that interacts with the dipole moments of other nuclei. The magnitude of the interaction is dependent on the gyromagnetic ratio of the spin species, the internuclear distance r, and the orientation, with respect to the external magnetic field B, of the vector connecting the two nuclear spins. The maximum dipolar coupling is given by the dipolar coupling constant d,where γ1 and γ2 are the gyromagnetic ratios of the nuclei, is the reduced Planck constant, and is the vacuum permeability. In a strong magnetic field, the dipolar coupling depends on the angle θ between the internuclear vector and the external magnetic field B according to
D becomes zero for. Consequently, two nuclei with a dipolar coupling vector at an angle of θm = 54.7° to a strong external magnetic field have zero dipolar coupling. θm is called the magic angle. Magic angle spinning is typically used to remove dipolar couplings weaker than the spinning rate.
Quadrupolar interaction
Nuclei with a spin quantum number >1/2 have a non-spherical charge distribution and a quadrupole moment. The quadrupole moment is a second rank tensor that couples to the surrounding electric field gradient, another second rank tensor. Nuclear quadrupole coupling is typically the second largest interaction in NMR, comparable in size to the largest interaction called Zeeman interactions. When the nuclear quadrupole coupling is not negligible relative to the Zeeman coupling, higher order corrections are needed to describe the NMR spectrum correctly. In such cases, the first-order correction to the NMR transition frequency leads to a strong anisotropic line broadening of the NMR spectrum. However, all symmetric transitions, between and levels are unaffected by the first-order frequency contribution. The second-order frequency contribution depends on the P4 Legendre polynomial, which has zero points at 30.6° and 70.1°. These anisotropic broadenings can be removed using DOR where you spin at two angles at the same time, or DAS where you switch quickly between the two angles. Both techniques were developed in the late 1980s, and require specialized hardware. Multiple quantum magic angle spinning NMR was developed in 1995 and has become a routine method for obtaining high resolution solid-state NMR spectra of quadrupolar nuclei. A similar method to MQMAS is satellite transition magic angle spinning NMR developed in 2000.J-coupling
The J-coupling or indirect nuclear spin-spin coupling describes the interaction of nuclear spins through chemical bonds. J-couplings are not always resolved in solids owing to the typically large linewdiths observed in solid state NMR.Other interactions
substances are subject to the Knight shift.Solid-state NMR line shapes
Powder pattern
A powder pattern arises in powdered samples where crystallites are randomly oriented relative to the magnetic field so that all molecular orientations are present. In presence of a chemical shift anisotropy interaction, each orientation with respect to the magnetic field gives a different resonance frequency. If enough crystallites are present, all the different contributions overlap continuously and lead to a smooth spectrum.Fitting of the pattern in a static ssNMR experiment gives information about the shielding tensor, which are often described by the isotropic chemical shift, the chemical shift anisotropy parameter, and the asymmetry parameter.
Dipolar pattern
The dipolar powder pattern has a very characteristic shape that arises when two nuclear spins are coupled together within a crystallite. The splitting between the maxima of the pattern is equal to the dipolar coupling constant.:where γ1 and γ2 are the gyromagnetic ratios of the dipolar-coupled nuclei, is the internuclear distance, is the reduced Planck constant, and is the vacuum permeability.
Essential solid-state techniques
Magic angle spinning
Magic angle spinning is a technique routinely used in ssNMR to improve ssNMR spectra resolution. After applying the MAS technique, NMR spectra will be sharper and narrower. This improved resolution results from manipulating a sample's spin interactions with the applied magnetic field. This is achieved by rotating the sample at a certain angle to the magnetic field to fully or partially average out anisotropic nuclear interactions such as dipolar, chemical shift anisotropy, and quadrupolar interactions. This rotation angle is called the magic angle θm. To achieve the complete averaging of these interactions, the sample needs to be spun at a rate that is at least higher than the largest anisotropy.Spinning a powder sample at a slower rate than the largest component of the chemical shift anisotropy results in an incomplete averaging of the interaction, and produces a set of spinning sidebands in addition to the isotropic line, centred at the isotropic chemical shift. Spinning sidebands are sharp lines separated from the isotropic frequency by a multiple of the spinning rate. Although spinning sidebands can be used to measure anisotropic interactions, they are often undesirable and removed by spinning the sample faster or by recording the data points synchronously with the rotor period.
Cross-polarization
if a fundamental RF pulse sequence and a building-block in many solid-state NMR. It is typically used to enhance the signal of a dilute nuclei with a low gyromagnetic ratio by magnetization transfer from an abundant nuclei with a high gyromagnetic ratio, or as a spectral editing method to get through space information.To establish magnetization transfer, RF pulses are simultaneously applied on both frequency channels to produce fields whose strength fulfil the Hartmann–Hahn condition:
where are the gyromagnetic ratios, is the spinning rate, and is an integer. In practice, the pulse power, as well as the length of the contact pulse are experimentally optimised. The power of one contact pulse is typically ramped to achieve a more broadband and efficient magnetisation transfer.
Decoupling
Spin interactions can be removed to increase the resolution of NMR spectra during the detection, or to extend the lifetime of the nuclear magnetization.Heteronuclear decoupling is achieved by radio-frequency irradiation on at the frequency of the nucleus to be decoupled, which is often 1H. The irradiation can be continuous, or a series of pulses that extend the performance and the bandwidth of the decoupling
Homonuclear decoupling is achieved with multiple-pulse sequences, or continuous wave modulation. Dipolar interactions can also be removed with magic angle spinning. Ultra fast MAS is an efficient way to average all dipolar interactions, including 1H–1H homonuclear dipolar interactions, which extends the resolution of 1H spectra and enables the usage of pulse sequences used in solution state NMR.