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

Hall, Ryan, Kang, Beom-Goo, Lee, Sanghoon, Chang, Taihyun, Venerus, David C., Hadjichristidis, Nikos, Mays, Jimmy, Larson, Ronald G.
Macromolecules 2019 v.52 no.4 pp. 1757-1771
melting, models, molecular weight, polymers, rheology
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, ϕₛ. Assuming that the rheology of monodisperse stars depends solely on the plateau modulus GN(ϕₛ) ∝ ϕₛ¹⁺ᵅ, the number of entanglements per chain Mₑ(ϕₛ) ∝ ϕₛ–ᵅ, and the tube-segment frictional Rouse time τₑ(ϕₛ) ∝ ϕₛ–²ᵅ, we show that only an α = 1 scaling superposes the Mₑ(ϕₛ) dependence of the terminal crossover frequency ωₓ,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.