Multi-dimensional1H NMR nuclear Overhauser spectroscopy under magic angle spinning: theory and application to elastomers

Abstract

The process of cross-relaxation between different protons (nuclear Overhauser effect) is investigated in soft solids by 2- and 3-dimensional NMR under the conditions of fast magic-angle spinning. The cross-relaxation rates are found to depend weakly on fast motions in the Larmor frequency range and strongly on slow motions of the order of the spinning frequency W _R. Explicit expressions for the W _R dependent cross-relaxation rates are derived for different motional models. These findings were tested experimentally on elastomers, i.e., on a cross-linking series of styrene-butadiene rubbers where the cross-relaxation was studied as a function of W _R. Short mixing times as are required for extracting the relaxation rates could be realized conveniently using a pulsed magnetic-field gradient for coherence pathway selection. As in solution NMR, relative couplings between chemically resolved spins can be determined from the peak intensities. By combining cross-relaxation measurements with T ₁ measurements, the distribution of correlation times can be probed for slow and fast timescales, respectively. Only the former were found to depend on the crosslink density.