Dynamic Dilution Effect in Binary Blends of Linear Polymers with Well-Separated Molecular Weights

We investigate and model the viscoelastic properties of binary blends composed of linear chains. These systems are indeed very suitable to test the validity and the limit of the constraint release (CR) process and dynamic tube dilution and to determine the value of the dynamic dilution exponent alpha. We first focus on binary blends containing barely entangled short chains. In such a case, we show that the tension re-equilibration process previously observed [van Ruymbeke Macromolecules 2012, 45, 2085] can be correctly described as a CR-activated contour length fluctuation (CLF) process, which takes place along the fully dilated tube and is governed by the intrinsic Rouse time of a longlong entanglement segment. In addition, reptation is considered to take place along the fully dilated tube. We also show that this CR-activated CLF process speeds up the relaxation of the long chains, which naturally leads to an effective dilution exponent alpha equal to 4/3, despite the fact that the modeling is based on alpha = 1. This result is in agreement with the experimental data. Then, we analyze the rheological behavior of binary blends containing entangled short chains. In such a case, we show that the CR-activated CLF also takes place, but with a delay time being necessary for the long chain to explore the dilated tube. This approach is tested for several binary blends, showing an improved quality of the predictions compared to previous tube modeling on the same blends. Indeed, by considering the chain motions on two different length scales, a larger fraction of the long chains relax at intermediate frequencies (through the tension re-equilibration) before their reptation, leading to an effective dilution exponent larger than 1 as determined from the low-frequency plateau modulus.