NMR in rotating solids

TLDR

In spinning solids, NMR free induction decay with anisotropic interactions manifests as a train of rotational spin echoes. The echo shape’s Fourier transform encodes anisotropy information, extracted via moment analysis, while homonuclear spin–spin and second‑order quadrupole couplings transform the isotropic spectrum into characteristic powder patterns. The method yields a sharp, anisotropy‑free spectrum, shows that second‑order level shifts are inadequate for predicting the resulting powder pattern—requiring average Hamiltonian theory—and demonstrates that rotational spin echoes can probe very slow random molecular rotations (τc≲1 s).

Abstract

The NMR free induction decay from a spinning sample having inhomogeneous anisotropic interactions (chemical shifts, first order quadrupole couplings) takes the form of a train of rotational spin echoes. The Fourier transform of the echo envelope is a sharp spectrum from which the effects of anisotropy have been removed. The Fourier transform of the echo shape contains information concerning the anisotropies: This information can be extracted by a moment analysis. The effects of localized homonuclear spin–spin interactions are to convert the ’’isotropic’’ spectrum into a characteristic powder pattern. Second order quadrupole coupling produces a similar effect. It is shown in this case that the usual second-order level shifts cannot be used to calculated this pattern, which must be described by a proper average Hamiltonian theory. Finally it is shown that rotational spin echoes provide a convenient means of studying very slow random molecular rotations (τc≲1 sec).