Component Relaxation Times in Entangled Binary Blends of Linear Chains: Reptation/CLF along Partially or Fully Dilated Tube

Abstract

Recent dielectric analysis suggested that entangled linear cis-polyisoprene (PI) chains in monodisperse bulk exhibit, in the terminal relaxation regime, reptation/contour length fluctuation (CLF) along a partially dilated tube with its diameter being determined by the constraint release (CR) activated tension equilibration along the chain backbone (Matsumiya et al. Macromolecules 2013, 46, 6067). In relation to this finding, we re-examined the dielectric and viscoelastic terminal relaxation times of components in linear PI blends having various component molecular weights and volume fractions, Mi and υi (i = 1 and 2 for the short and long components). In entangling blends with M2 ≫ M1 and large υ2 (>critical volume fraction υ2e for the onset of long−long entanglement), the relaxation time τ2,b of the long chain decreases with decreasing υ2 but stayed considerably larger than τ2,soln of the same long chain in a solution having the same υ2. This result suggested that the CR-activated tension equilibration retards the reptation/CLF motion of the long chain in such blends. A simple “solution model” considering this retardation due to the CR relaxation of short−long entanglements was formulated. Utilizing data for the CR relaxation time τdil‑2,CR of dilute long chains (with υ2 υ2e very well. Nevertheless, this model could not apply to the cases where M2 and M1 are rather narrowly separated and the short−long entanglements considerably survive in the time scale of the long chain relaxation. For this case, a “blend model” was formulated to consider self-consistently, though in an approximate way, the CR relaxation of all species of entanglements (short−short, short−long, long−short, and long−long entanglements) thereby mimicking coupled relaxation of the long and short chains. The component relaxation times deduced from this model (again on the basis of the τdil‑2,CR data) were surprisingly close to the data, not only for the PI/PI blend having narrowly separated M2 and M1 but also for those with M2 ≫ M1 (the latter being described satisfactorily also with the solution model), suggesting that reptation/CLF of the components in the terminal relaxation regime occurs along partially dilated tube with the diameter being determined by the CR-activated tension equilibration. Furthermore, the “blend model” worked satisfactory also for literature data for polystyrene blends having various M2/M1 ratios. These results demonstrate the importance of CR-activated tension equilibration in the blends, which is consistent with the finding for monodisperse bulk.