Unified application of the coupling model to segmental, Rouse, and terminal dynamics of entangled polymers

The temperature dependence and relaxation function breadth of segmental dynamics (α-relaxation) for 1,2-polybutadiene and 1,4-polybutadiene are used to predict their respective temperature-dependent terminal relaxation times by unified application of the Ngai coupling model. Literature results for the terminal flow of near-monodisperse linear polybutadienes having widely varying molecular weights are successfully represented using the coupling model by variation of only a single parameter, C, which is the proportionality constant between the longest Rouse relaxation time and the primitive relaxation time which underlies the cooperative segmental process. The value of C varies with molecular weight (M) according to C ∝ Mb where b is found to range from 1.8 to 2.1, in close agreement with the expected exponent of 2. Contrary to experimental data and coupling model predictions, reptation theory predicts identical influences of temperature on Rouse and terminal relaxation processes; we suggest that invoking a temperature dependence for contour length fluctuations, and hence number of effective entanglements per chain, may resolve this deficiency of the tube model.