Chain orientation and slow dynamics in elastomers by mixed magic-Hahn echo decays

Abstract

The decays of the mixed H1 echo represented by a combination of the magic and the Hahn echoes was measured in a series of cross-linked elastomers. The mixed echo refocuses the homogeneous and inhomogeneous spin interactions. It allows the investigation of the fluctuation of the dipolar interaction of polymer chains in the slow motion regime. The method accounts for multispin dipolar interactions and eliminates the interference of linear spin interactions due to chemical shielding, magnetic field inhomogeneities, local susceptibility variations, and heteronuclear dipolar interactions. The multispin dipolar correlation functions characterizing the mixed echo decay are derived in the approximation of a single correlation time and for a distribution of correlation times. Based on these dipolar correlation functions the H1 residual second van Vleck moment, correlation times, and parameters of the correlation time distribution are determined for a series of natural rubber samples with different cross-link densities. The segmental order measured by the residual second van Vleck moment was shown to scale with a polynomial dependence on cross-link density or shear modulus. This can be interpreted by considering high-order corrections to a Gaussian distribution of the end-to-end vectors. By assuming a log-Gaussian distribution function for the correlation times and the validity of the Williams–Landel–Ferry equation, the center of gravity and the logarithmic width of the distribution function of the correlation times describing the slow motion of the network chains scale with the degree of topological constraints and the chemical cross-link density by a power-law with exponents 2.85±0.65 and 3.09±0.23, respectively.