Theory of the Relaxation spectra of polymer networks with included hard rodlike particles manifested in NMR

A theory of nuclear magnetic resonance relaxation of¹³C nuclei and nuclear Overhauser effect (NOE) of polymer networks with included rodlike particles is developed for the case when the length of each rod is comparable or greater than the average distance between neighboring crosslinks. The long-scale dynamics of the network is described by means of a regular cubic “coarse-grained” model. The effects of entanglements of long rods in the network are described by a quasi-elastic potential acting between rods and network fragments. The frequency dependences of 1/T _1C and NOE are calculated for the case when the internuclear vector is directed along each rodlike particle. The frequency dependences of 1/T _1C and NOE for rods included into a polymer network are shifted to high frequencies as compared with these dependences for free rods due to quasi-elastic interactions between rods and network fragments. At strongly different viscoelastic parameters of rods and network fragments, the frequency dependences of 1/T_1C and NOE may have two maxima. The high-frequency maximum corresponds to localized motions of rods at immobile network domains. The low-frequency maximum is caused by involving rods in long-scale network motions. The intensity of the low-frequency maximum increases when the degree of interactions between rods and the network increases.