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 13 C-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 (∼4%) 13 C− 13 C 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 ψ in a doubly 13 C-labeled amino acid residue, with a sensitivity to analyze one residue in a repeat unit comprising up to 20 residues.