Principles of centerband-only detection of exchange in solid-state nuclear magnetic resonance, and extension to four-time centerband-only detection of exchange

Abstract

Theoretical principles and experimental details of the centerband-only detection of exchange (CODEX) nuclear magnetic resonance (NMR) experiment for characterizing slow segmental dynamics in solids are described. The experiment, which is performed under magic-angle spinning, employs recoupling of the chemical-shift anisotropy before and after a long mixing time during which molecular reorientations may occur. By an analysis in terms of the difference tensor of the chemical shifts before and after the mixing time, the dependence on the reorientation angle is obtained analytically for uniaxial interactions, and a relation to two-dimensional exchange NMR patterns is established; the same theory can also be applied for analyzing stimulated-echo and pure-exchange NMR data. A favorable linear dependence is derived generally for small rotations, which makes the experiment suitable for detecting small-amplitude motions. Quantification is excellent because the peaks are narrow and intense, unlike the broad powder or sideband spectra that are characteristic of all previous NMR experiments for probing slow segmental rotations. We also introduce and demonstrate a four-time CODEX experiment that yields information previously obtained only in 3D (three-dimensional) and reduced 4D (four-dimensional) exchange NMR experiments, such as the number of orientational sites accessible to the mobile groups. Chemical-shift anisotropies required in the CODEX analysis of motional amplitudes can be estimated using a closely related chemical-shift recoupling experiment. The implementation of total suppression of sidebands before detection is also explained. The experiments are demonstrated on dimethylsulfone, isotactic polypropylene, and poly(methyl methacrylate), PMMA. In isotactic poly(1-butene), the signals of the amorphous and interfacial regions have been observed selectively by using pure-exchange CODEX near the glass transition. The four-time CODEX experiment confirms that in the β-relaxation process of glassy PMMA, fewer than half of the sidegroups perform jumps between two orientations.