Chain order and cross-link density of elastomers as investigated by proton multiple-quantum NMR

We present a quantitative study of local segmental order in vulcanized natural and butadiene rubber far above the glass transition. Network chain order is dependent on the density of cross-links and is here derived from proton homonuclear residual dipolar couplings measured by static multiple-quantum NMR spectroscopy at low field. On the basis of a reasonable model of local chain structure and fast, uniaxially symmetric local motions, spin dynamics simulations are used to investigate the relationship between the experimentally determined residual coupling and the order parameter of the polymer backbone. The model is verified by site-resolved determinations of inter- and intraresonance residual couplings at high field. For both types of rubber, it is found that the distributions of the chain order parameter are rather narrow and in all cases well explained by the local coupling topology, thus excluding distributions of end-to-end separations or network chains lengths as important sources of broadening. This suggests that the NMR-detected order phenomenon cannot simply be captured with single-chain concepts. For natural rubber and poly(dimethylsiloxane), the relationship of the cross-link densities derived from the NMR-determined order parameter and from Flory-Rehner swelling experiments is linear as expected, yet the prefactors differ from the prediction by factors of 2 in different directions. We discuss the implications and the validity of the various models and approximations used for data analysis in light of recent results from computer simulations.