TY - JOUR
T1 - Determining the Dilution Exponent for Entangled 1,4-Polybutadienes Using Blends of Near-Monodisperse Star with Unentangled, Low Molecular Weight Linear Polymers
AU - Hall, Ryan
AU - Kang, Beom Goo
AU - Lee, Sanghoon
AU - Chang, Taihyun
AU - Venerus, David C.
AU - Hadjichristidis, Nikos
AU - Mays, Jimmy
AU - Larson, Ronald G.
N1 - Funding Information:
R.H. and R.G.L. gratefully acknowledge the support of the National Science Foundation under Grants DMR 1403335 and 1707640. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF). N.H. gratefully acknowledges the support of the King Abdullah University of Science and Technology (KAUST).
Publisher Copyright:
© 2019 American Chemical Society.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/2/26
Y1 - 2019/2/26
N2 - 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.
AB - 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.
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U2 - 10.1021/acs.macromol.8b01828
DO - 10.1021/acs.macromol.8b01828
M3 - Article
AN - SCOPUS:85061894337
SN - 0024-9297
VL - 52
SP - 1757
EP - 1771
JO - Macromolecules
JF - Macromolecules
IS - 4
ER -