Tube dilation and reptation in binary blends of monodisperse linear polymers

We extend the Milner-McLeish theory for monodisperse linear polymers to binary blends, where the reptation time of the long chain is set to either the reptation time in the undilated tube or the reptation time in the dilated tube depending on the value of the "Graessley parameter" Gr drop M2Me2/M-1(3), where M-1 is the short chain molecular weight, M-2 is the long chain molecular weight, and M-e is the entanglement molecular weight. We find experimentally that, in blends in which Gr is much smaller than the critical value Gr(c) approximate to 0.064 established by an observed crossover in diffusivity measurements [Green et al. Phys. Rev. Lett. 1984, 26, 2145], the long-chain motion in the binary blend is well predicted by the Milner-McLeish model using reptation in the undilated tube. However, for Gr larger than Gr(c), reptation must to be assumed to occur in a dilated tube to obtain agreement with the experimental data. These results confirm that the crossover behavior observed in diffusivity also occurs in rheology and show that existing tube models can accurately predict linear rheology in both regimes where reptation occurs in a dilated or an undilated tube.