Determining the Dilution Exponent for Entangled 1,4-Polybutadienes Using Blends of Near-Monodisperse Star with Unentangled, Low Molecular Weight Linear Polymers

We determine experimentally the "dilution exponent" α for entangled polymers from the scaling of terminal crossover frequency with entanglement density from the linear rheology of three 1,4-polybutadiene star polymers that are blended with low-molecular-weight, unentangled linear 1,4-polybutadiene at various star volume fractions, η _s . Assuming that the rheology of monodisperse stars depends solely on the plateau modulus G _N (η _s ) ≈ ηs1+α, the number of entanglements per chain M _e (η _s ) ≈ ηs-α, and the tube-segment frictional Rouse time τ _e (η _s ) ≈ ηs-2α, we show that only an α = 1 scaling superposes the M _e (η _s ) dependence of the terminal crossover frequency ω _x,t of the blends with those of pure stars, not α = 4/3. This is the first determination of α for star polymers that does not rely on any particular tube model implementation. We also show that a generalized tube model, the "Hierarchical model", using the "Das" parameter set with α = 1 reasonably predicts the rheological data of the melts and blends featured in this paper.