Dipolar couplings and internuclear distances by double-quantum nuclear magnetic resonance spectroscopy of solids

The analysis of high-resolution double-quantum nuclear magnetic resonance spinning sidebands for measuring dipolar couplings and internuclear distances in dipolar solids is described. For this purpose, the response of a dipolar-coupled spin system in a rigid solid is investigated with respect to high-resolution multiple-quantum experiments using rotor-frequency synchronized pulse sequences. For isolated, magnetically equivalent spin-1/2 pairs, exact expressions for the double-quantum spinning-sideband patterns are derived. These patterns show spinning sidebands only at odd numbers of the rotor frequency. For longer excitation/reconversion cycles, the double-quantum spinning sidebands are sensitive to changes in the internuclear distances. Using this technique, the dipolar couplings for ${}^{13}\mathrm{C}$ spin pairs in double-labeled polyethylene were measured in crystalline and amorphous domains, respectively. In the former the dipolar coupling reflects the carbon–carbon distance, in the latter it is reduced due to molecular dynamics. The possibility to use multiple-quantum pulse sequences as a dipolar filter for the rigid domains is also shown.