A double-quantum solid-state NMR technique for determining torsion angles in polymers

This paper introduces a double-quantum solid-state NMR experiment for determining torsion angles in unoriented polymers which contain segments with pairs of C-13-labeled sites separated by only one or two bonds. By double-quantum excitation and evolution, two-dimensional spectra are obtained in which the first dimension displays the sum of the anisotropic chemical shifts. As a consequence, the two-dimensional spectral patterns depend on the relative orientation of the coupled sites and thus on the torsion angle. The double-quantum approach achieves homonuclear dipolar decoupling in the first dimension without multiple-pulse sequences and removes the natural-abundance background signal. The experiment is demonstrated on polyethylene isotopically labeled with dilute (similar to 4%) C-13-C-13 spin pairs and confirms the all-trans structure in the crystalline regions. In polypeptides, it will be applicable to the determination of the backbone torsion angle psi in a doubly C-13-labeled amino acid residue, with a sensitivity to analyze one residue in a repeat unit comprising up to 20 residues.