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Polymers 2019, 11(3), 465; https://doi.org/10.3390/polym11030465

Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids

1
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
2
Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
3
Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
Author to whom correspondence should be addressed.
Received: 13 February 2019 / Revised: 2 March 2019 / Accepted: 5 March 2019 / Published: 11 March 2019
(This article belongs to the Special Issue Theory and Simulations of Entangled Polymers)
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Abstract

We combine a slip-spring model with an ‘entangled kink dynamics’ (EKD) model for strong uniaxial extensional flows (with Rouse Weissenberg number W i R 1 ) of long ( M w > 1   Mkg / mol for polystyrene) entangled polymers in solutions and melts. The slip-spring model captures the dynamics up to the formation of a ‘kinked’ or folded state, while the kink dynamics simulation tracks the dynamics from that point forward to complete extension. We show that a single-chain slip-spring model using affine motion of the slip-spring anchor points produces unrealistically high tension near the center of the chain once the Hencky strain exceeds around unity or so, exceeding the maximum tension that a chain entangled with a second chain is able to support. This unrealistic tension is alleviated by pairing the slip links on one chain with those on a second chain, and allowing some of the large tension on one of the two to be transferred to the second chain, producing non-affine motion of each. This explicit pairing of entanglements mimics the entanglement pairing also used in the EKD model, and allows the slip spring simulations to be carried out to strains high enough for the EKD model to become valid. We show that results nearly equivalent to those from paired chains are obtained in a single-chain slip-spring simulation by simply specifying that the tension in a slip spring cannot exceed the theoretical maximum value of ζ ϵ ˙ L 2 / 8 where ζ , ϵ ˙ and L are the friction per unit length, strain rate and contour length of the chain, respectively. The effects of constraint release (CR) and regeneration of entanglements is also studied and found to have little effect on the chain statistics up to the formation of the kinked state. The resulting hybrid model provides a fast, simple, simulation method to study the response of high molecular weight ( M w > 1   Mkg / mol ) polymers in fast flows ( W i R 1 ), where conventional simulation techniques are less applicable due to computational cost. View Full-Text
Keywords: polymer rheology; extensional flows; slip-link simulations; kink dynamics; coil-stretch transition polymer rheology; extensional flows; slip-link simulations; kink dynamics; coil-stretch transition
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Moghadam, S.; Saha Dalal, I.; Larson, R.G. Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids. Polymers 2019, 11, 465.

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