Paper Number
PM9 

Session
Polymer Melts: From Molecular Rheology to Processing

Title
Determining the dilution exponent for 1,4-polybutadienes using blends of entangled monodispersed star with unentangled, low molecular weight linear polymers

Presentation Date and Time
October 16, 2018 (Tuesday) 2:45

Track / Room
Track 2 / Plaza I

Authors (Click on name to view author profile)

1. Hall, Ryan (University of Michigan, Macromolecular Science and Engineering Program)
2. Kang, Beomgoo (Princeston University, Department of Chemical and Biological Engineering)
3. Lee, Sanghoon (Pohang University of Science and Technology, Chemistry)
4. Chang, Taihyun (Pohang University of Science and Technology, Chemistry)
5. Venerus, David (Illinois Institute of Science and Technology, Chemical and Biological Engineering)
6. Hadjichristidis, Nikos (King Abdullah University of science and Technology, KAUST, Physical Sciences and Engineering Division)
7. Mays, Jimmy (University of Tennessee)
8. Larson, Ronald G. (University of Michigan, Department of Chemical Engineering)

Author and Affiliation Lines (in printed abstract book)
Ryan Hall¹, Beomgoo Kang², Sanghoon Lee³, Taihyun Chang³, David Venerus⁴, Nikos Hadjichristidis⁵, Jimmy Mays², and Ronald G. Larson^6
1Macromolecular Science and Engineering Program, University of Michigan, Ann Arbor, MI 48197; ²University of Tennessee, Knoxville, TN; ³Chemistry, Pohang University of Science and Technology, Pohang, Republic of Korea; ⁴Chemical and Biological Engineering, Illinois Institute of Science and Technology, Chicago, IL; ⁵Physical Sciences and Engineering Division, King Abdullah University of science and Technology, KAUST, Thuwal, Saudi Arabia; ⁶Department of Chemical Engineering, University of Michigan, Ann Arbor, MI

Speaker / Presenter 
Larson, Ronald G.

Text of Abstract
We determine experimentally the “dilution exponent” α for entangled polymers from the scaling of terminal time with entanglement density from the linear rheology of three well characterized 1,4-polybutadiene 4-arm star polymers. These stars are blended with low-molecular-weight, unentangled linear 1,4-polybutadiene at various star volume fractions, φ_s. Assuming only that the rheology of monodisperse stars depends solely on the plateau modulus G⁰_N(φ_s)∝φ_s^1+α; the number of entanglements per chain M_e(φ_s)∝ φ_s^−α; and the tube-segment frictional Rouse time τ_e(φ_s)∝^−2α, we show that only an α=1 scaling superposes the M_e(φ_s)-dependence of the terminal cross-over frequency ω_x,t of the blends with those of pure stars, while an order-of-magnitude deviation between these dependencies is found if one takes α=4⁄3. The nearly exponential dependence of ω_x,t on M_e(φ_s) is strong enough to clearly distinguish the value of the dilution exponent α , which is not possible from the weaker dependence of the low-frequency cross-over modulus G_x,t on M_e(φ_s). We show that this conclusion holds when accounting for experimental uncertainties in arm molecular weights. This is the first clear rheological determination of α that does not rely on the use of any particular tube model, but only on the dependence of rheology on the above three parameters. We also show that a generalized tube model, the “Hierarchical model”, using the “Das” parameter set with α=1 performs reasonably in predicting the terminal and plateau regions of the melts and blends featured here.