Basic theory of solid state NMR

There are several excellent texts and articles covering both introductory [215, 216] and advanced solid state NMR [217, 218], but a brief explanation of some of the more important theoretical and technical issues are given here. 

In solution, molecules are generally free to undergo translational and rotational movement such that their orientation with respect to each other and the static magnetic field is effectively random. This results in the averaging of any interaction that is dependent on the orientation of the magnetic field. However, solids usually have a well organised structure in which the relative positions of atoms have a defined mutual relationship. The spins of NMR active nuclei in solids are thus held in distinct environments and can interact with each other in a way that is not motionally averaged. These interactions are manifest in the very broad, often featureless NMR spectra of solids. 

The direct magnetic interaction between two spins of magnetogyric ratio and (the dipole-dipole interaction - D) depends on their distance apart and the angle (0) between their inter-nuclear vector and the static Bq field in the following way  

The geometric term in Equation 4.5 vanishes when =54°44 the magic angle. The dipolar interaction (also referred to as dipolar coupling) should average to zero if the sample is spun at this angle with respect to the static field. However, to completely eliminate the dipolar interactions the speed of rotation must be several times the static linewidth, typically several lOOkHz which is not currently possible. Most commercial MAS systems are capable of rotating 4mm sample rotors at a speed of 10-15 kHz or so. 

Spinning at the magic angle also accomplishes line-width reduction arising by another mechanism. This is the chemical shift anisotropy (CSA), and is a reflection of the fact that in a solid, it is not possible to ignore the orientational dependance of nuclear shielding. 

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