A Comparison of Models and Model Parameters for the Interpretation of Carbon-13 Relaxation in Common Polymers

Abstract

A brief survey of models for the interpretation of spin relaxation in polymers suggests models based on the occurrence of the three-bond jump on a tetrahedral lattice are capable both of accounting for observations and providing some physical insight. The lattice model of Valeur, Jarry, Geny and Monnerie is compared with the more recent revisions of Jones and Stockmayer, and Bendler and Yaris. Since it is found that all three lattice models have comparable interpretive ability and produce very similar descriptions of the spectral density when applied to the same data, one model, the Jones and Stockmayer version, was used to interpret several well studied polymers. The resulting characterization of motions in dissolved polyethylene, polyisobutylene, polystyrene and poly(phenylene oxide) are reviewed for trends in time scale, apparent activation energy and the extent of cooperative motion. Time scales varied from picoseconds to nanoseconds, the activation energies for backbone rearrangements are all about 20kJ, and the length of chain involved in cooperative motion is only 5 to 15 bonds. Spin relaxation in four solid polymers was also interpreted with the model. Amorphous polyethylene and polyisobutylene rubber undergo motion nearly as rapid as dissolved polymers and the segment length for cooperative motion is not appreciably longer either. Cis-polyisoprene and cis-polybutadiene are also very mobile as solid rubbers but the apparent segment length for cooperative motion is much longer than for simple dissolved polymers. Of course, a tetrahedral lattice model is not strictly applicable to these last two polymers, and interchain cooperativity was not properly considered for any of the solid polymers.