Universal Relaxation Behavior of Entangled 1,4-Polybutadiene Melts in the Transition Frequency Region

Linear viscoelastic G' and G '' master curves for linear, star, H, and comb 1,4-polybutadienes from the literature are compared and found to agree well in the transition frequency region, where G' and G '' exceed the plateau modulus, irrespective of molecular weight and branching structures. A value of tau(e) = (3-.7 +/- 0.93) x 10(-7) s for the equilibration time at T = 25 degrees C can therefore-be determined from fitting Rouse predictions to the transition frequency data, after subtracting effects of glassy modes represented by the Kohlrausch-Williams-Watts (KWW) expression. Good agreement among multiple data sets was obtained in the transition region despite large variations in low-temperature shift factors, evidently due to small sample-to-sample variations in 1,2 content. These variations in 1,2 content can also cause small changes the plateau modulus G(N)(0), and the entanglement molecular weight M-e, which should have only a small effect On linear polymers but for long-chain branched polymers could lead to large variations in terminal relaxation time predicted by tube models. The small variations in G(N)(0) can, however, be inferred from the dependence of shift factor on temperature, allowing all three tube model parameters tau(e), G(N)(0), and M-e to be Obtained from high-frequency data for 1,4-polybutadienes, thus in principle removing these as parameters that can be adjusted to fit specific data sets for linear or branched 1,4-polybutadienes.