The influence of molecular motion on cross-polarization in cross-linked elastomers

The effect of molecular motion on the heteronuclear cross-polarization rate for the case of the spin-lock procedure was investigated. In applying heteronuclear solid state NMR techniques to mobile elastomer systems the influence of molecular motion cannot be neglected. Starting in the slow motion regime a strong collision model was used for predicting changes of the cross-polarization rate in the dipolar spectral density function of abundant spins. The dipolar correlation time and hence the cross-polarization rate is found to scale with the inverse of the correlation time of the molecular motion. The same behavior is obtained using a second approach valid in the intermediate molecular motion regime. This is based on the effect of the motion on the homonuclear and heteronuclear van-Vleck moments and leads to a linear dependence of the cross-polarization rate on the correlation time of molecular motion. This dependence was verified experimentally by 1H-13C high-resolution cross-polarization measurements on sulfur cross-linked elastomer systems. 13C rotating frame spin-lattice relaxation rate measurements were used to corroborate these data and the approximations used to evaluate the influence of molecular motion on cross-polarization rates. The dependence of these rates on the cross-link density of the elastomer network is analyzed and it is shown that they scale with the cross-link density. The correlation of the 1H-13C cross-polarization rates with the dynamic storage moduli was demonstrated.