Effective Value of the Dynamic Dilution Exponent in Bidisperse Linear Polymers: From 1 to 4/3

We revisit previously published dielectric and viscoelastic data of binary blends of linear cis-polyisoprene [Watanabe, H; Ishida, S.; Matsumiya, Y.; Inoue, T. Macromolecules 2004, 37, 6619] in order to test the validity of the dynamic tube dilution (DTD) picture and to determine the most appropriate value of the dilution exponent a. We conclude that the DTD picture with alpha = 1 is more appropriate at short times, while at longer time, a larger exponent of alpha = 4/3 gives a better description of the experiments. Furthermore, between these two time regions, a broad crossover zone is found, going from an effective alpha = 1 to an effective alpha = 4/3. On the basis of this result, we propose to consider a new relaxation process, which is combined with the classical DTD picture ith alpha = 1 to give the experimentally observed effective alpha = 4/3 at long times. This extra relaxation process results from the tension equilibration along the long chains, which takes place thanks to the blinking feature of release/reformation of the long-short entanglements and leads to a partial disorientation of the primitive path itself within the dilated tube. We have formulated the relaxation function considering this tension equilibration and demonstrated its validity for description of the experiments in the entire range of time.