Correlation Between Segmental Order Parameter and Entanglement Length in a Monodisperse Comb Polymer

The motion of a polymer chain within a hypothetical confining tube gives rise to a segmental order parameter S b. This parameter is assessed via multiple-quantum (MQ) NMR experiments, providing a valuable molecule-level rheological observable. In both polymer networks and entangled melts, the order parameter is proportional to the inverse of the number of segments between two covalent cross-links or physical entanglements. In entangled polymer networks, the entanglements have usually been considered as additional but temporary cross-links and the contribution of the physical and chemical constraints are assumed additive. Recent computer simulation results challenged this assumption for lowly cross-linked polymer networks; instead, S b was shown to scale with (N e N c)−1/2, N c and N e being the number of segments between cross-links and entanglements, respectively [Lang, M.; Sommer, J.-U., Phys. Rev. Lett. 2010, 104, 177801]. An experimental confirmation remains elusive due to challenges in distinguishing the contributions of entanglements and cross-links, as well as the long averaging time scales involved. In this study, we assess this correlation by examining chain dynamics in a monodisperse polyisoprene comb, utilized as a model system. To model chain dynamics in this system, the dynamic tube dilation model, originally designed for predicting the rheological behavior of star and branched polymers, has been modified to facilitate its application in the analysis of MQ NMR signals. We also address some of its shortcomings.