Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids
Abstract
:1. Introduction
2. Model and Simulation Method
2.1. Kink Dynamics Algorithm
Kink Dynamics Predictions for Entanglement Force
- Under affine motion, immediately after formation of the locally fully extended kinked state, the stress reaches at its final value which does not change during the unraveling of the kinked state to the fully extended state.
- The chain end-to-end distance evolves very similarly under dilute and entangled kink conditions for a specific chain length.
- Using the EKD model, when (a highly entangled system), the tension along the chain at the start of the folded state is almost flat and as the chain unravels, it becomes quadratic after a few Hencky strain units, depending on the length of the chain.
- What is the transition strain () beyond which the EKD results become valid?
- What is the number of kinks for a chain of arbitrary chain length at the transition strain?
- What is the ratio of the number of entangled to free kinks in an entangled sample?
- What is the distribution of strand lengths between the kinks?
2.2. Slip-Spring Simulations
3. Simulation Results and Discussions
3.1. Comparison of Maximum Entanglement Force (MEF), Two-Chain (TC), Affine Motion (AM) Methods
3.2. MEF Results for Chain Conformation
- [18]
- Fraction of entangled kinks:
- Strand length probability distribution:
3.3. Addition of Slip-Link Regeneration and Constraint Release to Slip-Link Model
- Regeneration off—CR off: when a slip-link passes through its chain end, it is destroyed, and no further action is taken for other slip-links on the chain. This results in a continual reduction in the number of slip-links until all of them are gone. This condition has been used to obtain the results in Section 3.2.
- Regeneration off—CR on: when a slip-link passes through its chain end, it is destroyed. Simultaneously, another slip-link on the same chain is randomly chosen and removed to represent constraint release produced by other chains, which are not simulated directly. Since there is no regeneration, slip-springs disappear faster than in Condition 1 above.
- Regeneration on—CR off: If a slip-link passes by the chain end, it is removed and instantaneously recreated at a random location on the chain. Thus, the total number of entanglements stays constant under this condition.
- Regeneration on—CR on: If the chain end passes through a slip-link, the slip-link is destroyed and recreated at a random position on the same chain. Simultaneously, another randomly chosen slip-link is removed and recreated at a random position along the chain. Therefore, the number of slip-links stays constant.
3.4. Comparison of Kink Dynamics Results with Experimental Data
4. Conclusions and Future Directions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Time-Step Size in Slip-Spring Simulations
Condition | Direction of Slip-Spring Jump | |
---|---|---|
i | | |
ii | |
Appendix B
MEF Performance in Unraveling a Kinked Chain
Conformation | |||
---|---|---|---|
1 | 1.22 | 0.61 | 2.00 |
2 | 4.87 | 2.42 | 2.01 |
3 | 2.99 | 1.52 | 1.97 |
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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. https://doi.org/10.3390/polym11030465
Moghadam S, Saha Dalal I, Larson RG. Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids. Polymers. 2019; 11(3):465. https://doi.org/10.3390/polym11030465
Chicago/Turabian StyleMoghadam, Soroush, Indranil Saha Dalal, and Ronald G. Larson. 2019. "Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids" Polymers 11, no. 3: 465. https://doi.org/10.3390/polym11030465
APA StyleMoghadam, S., Saha Dalal, I., & Larson, R. G. (2019). Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids. Polymers, 11(3), 465. https://doi.org/10.3390/polym11030465