Terminal relaxation and diffusion of entangled three‐arm star polymers: Temperature and molecular weight dependencies

Abstract

Recent experimental investigation of the terminal relaxation in high molecular weight polyisoprenes by dynamic mechanical measurements (C. A. Bero and C. M. Roland, Macromolecules, 29, 1562) has found the terminal relaxation times to be more sensitive to changes in temperature for three-arm stars than for the linear polyisoprenes. Moreover, these measurements, carried out with significantly higher molecular weight samples than heretofore, show that the molecular weight dependence of the terminal relaxation times for three-arm star polyisoprenes is much weaker than the exponential dependence previously proposed (L. J. Fetters, et al., Macromolecules, 26, 647 (1993)). Tracer diffusion of labeled linear and three-arm star polyethylenelike diffusant molecules in a highly entangled linear polyethylene matrix exhibit temperature and molecular weight dependencies similar to those observed spectroscopically from bulk polymers. Both the temperature and molecular weight dependencies for the star-branched polymers are at variance with the predictions of the reptation model. It is shown here, however, that these observations can be reconciled through application of the coupling model of relaxation.

Rheological Behavior of Entangled Polystyrene−Polyhedral Oligosilsesquioxane (POSS) Copolymers

“…There are several theoretical models to explain the effects of branches on the temperature dependence of terminal relaxation time. According to the coupling model, − the dynamics of polymer chains can be described by the coupling parameter n (0 < n < 1), where the value of n is closely related to the topological constraints of the entangled system. The surrounding environment experienced by a single macromolecular chain is the key factor of this parameter.…”

“…More specifically, branched polymers are expected to have stronger “coupling” that acts to increase n , resulting in broadening of the relaxation function and increasing activation energy of the rheological properties. Usually, this model is valid for branched polymers for which the molecular weight of branches exceeds the entanglement molecular weight, M e . − However, only a few studies have been reported for branched polystyrene. − Ferri et al prepared randomly branched polystyrene by copolymerization of styrene (St) and divinylbenzene (DVB) and studied the melt rheology of linear and randomly branched polystyrene (LPS ad RBPS), where the RBPS featured entangled branches ( M br / M e > 4). They found that, while the shift factors ( a T ) of LPS were similar to those of RBPS, the activation energy slightly increased with degree of branching.…”

Vertex Group Effects in Entangled Polystyrene−Polyhedral Oligosilsesquioxane (POSS) Copolymers

“…Our results revealed increasing activation energy with POSS incorporation (POSS branching) consistent with those observed in the randomly branched polystyrene. 45 There are several theoretical models to explain the effects of branches on the temperature dependence of terminal relaxation time, including coupling models [49][50][51] and the reptation theory. 52 Their predictions are consistent with our observations in the random copolymers of styrene with styryl-POSS, although they are applicable to the polymers with polymeric coil branches.…”

Rheology of Star-Branched Polyisobutylene

“…The coupling model of relaxation , offers an alternative approach to the effect long branches have on the rheology. According to this model, , entangled arms will enhance intermolecular cooperativity and thus always result in more temperature-sensitive rheological properties. This prediction, which is independent of the trans/gauche conformational energies, appears to be at odds with our PIB data.…”