Nonmonotonic Stress Overshoot in Entangled Polymer Melts under Two-step Shear

Yong-Jin Ruan; Ya-Qing Chang; Jiang-Yang Mo; Bai-Cheng Mei

doi:10.1007/s10118-025-3481-9

Your Location：

Home >

Browse articles >

Nonmonotonic Stress Overshoot in Entangled Polymer Melts under Two-step Shear

RESEARCH ARTICLE | Updated：2026-01-13

- Nonmonotonic Stress Overshoot in Entangled Polymer Melts under Two-step Shear
- Chinese Journal of Polymer Science Vol. 44, Issue 1, Pages: 268-277(2026)
- Affiliations：
  
  a.State Key Laboratory of Polymer Science and Technology, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China
  b.School of Science, Changchun Institute of Technology, Changchun 130012, China
  c.Shandong Key Laboratory of Biophysics, Institute of Biophysics, Dezhou University, Dezhou 253023, China
  d.Beijing Key Laboratory of Construction Tailorable Advanced Functional Materials and Green Applications, School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China
- Author bio：
  
  yjruan@ciac.ac.cn
- Funds：
- DOI：10.1007/s10118-025-3481-9
  CLC：
- Received：12 September 2025，
  
  Accepted：13 October 2025，
  
  Online First：18 December 2025，
  
  Published：15 January 2026
- Accepted：
Scan QR Code
Ruan, Y. J.; Chang, Y. Q.; Mo, J. Y.; Mei, B. C. Nonmonotonic stress overshoot in entangled polymer melts under two-step shear. Chinese J. Polym. Sci. 2026, 44, 268–277

Yong-Jin Ruan, Ya-Qing Chang, Jiang-Yang Mo, et al. Nonmonotonic Stress Overshoot in Entangled Polymer Melts under Two-step Shear[J]. Chinese Journal of Polymer Science, 2026, 44(1): 268-277.
Ruan, Y. J.; Chang, Y. Q.; Mo, J. Y.; Mei, B. C. Nonmonotonic stress overshoot in entangled polymer melts under two-step shear. Chinese J. Polym. Sci. 2026, 44, 268–277 DOI： 10.1007/s10118-025-3481-9.

Yong-Jin Ruan, Ya-Qing Chang, Jiang-Yang Mo, et al. Nonmonotonic Stress Overshoot in Entangled Polymer Melts under Two-step Shear[J]. Chinese Journal of Polymer Science, 2026, 44(1): 268-277. DOI： 10.1007/s10118-025-3481-9.

摘要

Molecular dynamics simulations uncover the microscopic origin of the second stress overshoot

2max

in two-step shear. The nonmonotonic

2max

results from coupled variations of tube orientation and entanglement number

highlighting the need for a unified theoretical framework.

Abstract

Shear stress overshoot in entangled polymer rheology is a hallmark of transient dynamics

but its microscopic origin remains under debate. Using molecular dynamics simulations

we investigate a two-step shear protocol consisting of successive startup shears separated by a waiting period

with the first shear interrupted before the overshoot. In the homogeneous flow

the GLaMM theory captures the stress response during the first shear

but fails to reproduce the nonmonotonic dependence of the second stress overshoot (

2max

) on the waiting time. Contrary to the prediction of a nonmonotonic normal stress component

during the waiting period

our simulations show that

like the tube segment orientation (

)

the contour length of the primitive chain (

)

and the entanglement number per chain (

)

relaxes monotonically toward equilibrium. At the strain corresponding to

2max

both the tube segment orientation and the entanglement number per chain exhibit a nonmonotonic dependence on the waiting time that closely mirrors the behavior of

2max

indicating that both factors play significant roles in governing

2max

. Our findings are consistent with the interpretation of Ianniruberto and Marrucci [

ACS Macro. Lett.

2014

552

]

for orientation effects and with the viewpoint of Wang

et al

. [

Macromolecules

2013

3147

]

for entanglement effects

although the two explanations are rooted in distinct physical pictures. These results provide new insights into the stress responses of entanglement polymer fluids and underscore the need for a more unified theoretical framework.

关键词

Keywords

references

[Doi, M.; Edwards, S. F. Dynamics of concentrated polymer systems. Part 3.-the constitutive equation. J. Chem. Soc., Faraday Trans. 2 1978, 74 , 1818−1832..

[Doi, M.; Edwards, S. F. Dynamics of concentrated polymer systems. Part 4.-rheological properties. J. Chem. Soc., Faraday Trans. 2 1979, 75 , 38−54..

Masubuchi, Y.; Watanabe, H. Origin of stress overshoot under start-up shear in primitive chain network simulation. ACS Macro Lett. 2014 , 3 , 1183−1186..

Dealy, J. M.; Tsang, W. K. W. Structural time dependency in the rheological behavior of molten polymers. J. Appl. Polym. Sci. 1981 , 26 , 1149−1158..

Menezes, E. V.; Graessley, W. W. Nonlinear rheological behavior of polymer systems for several shear-flow histories. J. Polym. Sci. Polym. Phys. Ed. 1982 , 20 , 1817−1833..

Sanchez-Reyes, J.; Archer, L. A. Relaxation dynamics of entangled polymer liquids in steady shear flow. J. Rheol. 2003 , 47 , 469−482..

Roy, D.; Roland, C. M. Reentanglement kinetics in polyisobutylene. Macromolecules 2013 , 46 , 9403−9408..

[Masubuchi, Y.; Doi, Y.; Uneyama, T. Primitive chain network simulations for the interrupted shear response of entangled polymeric liquids. Soft Matter 2020, 16 , 6654-6661..

Dolata, B. E.; Galvani Cunha, M. A.; O’Connor, T.; Hopkins, A.; Olmsted, P. D. Entanglement kinetics in polymer melts are chemically specific. ACS Macro Lett. 2024 , 13 , 896−902..

Wang, S. Q.; Wang, Y.; Cheng, S.; Li, X.; Zhu, X.; Sun, H. New experiments for improved theoretical description of nonlinear rheology of entangled polymers. Macromolecules 2013 , 46 , 3147−3159..

Rouse, P. E. A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 1953 , 21 , 1272−1280..

Wang, Y.; Li, X.; Zhu, X.; Wang, S. Q. Characterizing s tate of chain entanglement in entangled polymer solutions during and after large shear deformation. Macromolecules 2012 , 45 , 2514−2521..

Wang, S. Q.; Ravindranath, S.; Wang, Y.; Boukany, P. New theoretical considerations in polymer rheology: elastic breakdown of chain entanglement network. J. Chem. Phys. 2007 , 127 , 064903..

Graham, R. S.; Henry, E. P.; Olmsted, P. D. Comment on “New experiments for improved theoretical description of nonlinear rheology of entangled polymers”. Macromolecules 2013 , 46 , 9849−9854..

Holroyd, G. A. J.; Martin, S. J.; Graham, R. S. Analytic solutions of the Rolie-Poly model in time-dependent shear. J. Rheol. 2017 , 61 , 859−870..

Likhtman, A. E.; Graham, R. S. Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie-Poly equation. J. Non-Newton. Fluid Mech. 2003 , 114 , 1−12..

[Ianniruberto, G.; Marrucci, G. Do repeated shear startup runs of polymeric liquids reveal structural changes ACS Macro Lett . 2014, 3 , 552-555..

Ruan, Y.; Lu, Y.; An, L.; Wang, Z. G. Shear banding in entangled polymers: Stress plateau, banding location, and lever rule. ACS Macro Lett. 2021 , 10 , 1517−1523..

Graham, R. S.; Likhtman, A. E.; McLeish, T. C. B.; Milner, S. T. Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release. J. Rheol. 2003 , 47 , 1171−1200..

Ruan, Y.; Lu, Y.; An, L.; Wang, Z. G. Nonlinear rheological behaviors in polymer melts after step shear. Macromolecules 2019 , 52 , 4103−4110..

Ruan, Y.; Lu, Y.; An, L.; Wang, Z. G. Multiple entanglements between two chains in polymer melts: an analysis of primitive paths based on Frenet trihedron. Macromolecules 2024 , 57 , 2792−2800..

Shanbhag, S.; Kröger, M. Primitive path networks generated by annealing and geometrical methods: insights into differences. Macromolecules 2007 , 40 , 289 7−2903..

Kröger, M.; Dietz, J. D.; Hoy, R. S.; Luap, C. The Z1+ package: shortest multiple disconnected path for the analysis of entanglements in macromolecular systems. Comput. Phys. Commun. 2023 , 283 , 108567..

[Nafar Sefiddashti, M. H.; Edwards, B. J.; Khomami, B. Individual molecular dynamics of an entangled polyethylene melt undergoing steady shear flow: steady-state and transient dynamics. Polymers 2019 , 11 , 476..

Kremer, K.; Grest, G. S. Dynamics of entangled linear polymer melts: a molecular dynamics simulation. J. Chem. Phys. 1990 , 92 , 5057−5086..

Everaers, R.; Sukumaran, S. K.; Grest, G. S.; Svaneborg, C.; Sivasubramanian, A.; Kremer, K. Rheology and microscopic topology of entangled polymeric liquids. Science 2004 , 303 , 823−826..

Auhl, R.; Everaers, R.; Grest, G. S.; Kremer, K.; Plimpton, S. J. Equilibration of long chain polymer melts in computer simulations. J. Chem. Phys. 2003 , 119 , 12718−12728..

Thompson, A. P.; Aktulga, H. M.; Berger, R.; Bolintineanu, D. S.; Brown, W. M.; Crozier, P. S.; in 't Veld, P. J.; Kohlmeyer, A.; Moore, S. G.; Nguyen, T. D.; Shan, R.; Stevens, M. J.; Tranchida, J.; Trott, C.; Plimpton, S. J. LAMMPS — a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 2022 , 271 , 108171..

Ramírez, J.; Sukumaran, S. K.; Vorselaars, B.; Likhtman, A. E. Efficient on the fly calculation of time correlation functions in computer simulations. J. Chem. Phys. 2010 , 133 , 154103..

Boudara, V. A. H.; Read, D. J.; Ramírez, J. Reptate rheology software: Toolkit for the analysis of theories and experiments. J. Rheol. 2020 , 64 , 709−722..

Likhtman, A. E.; McLeish, T. C. B. Quantitative theory for linear dynamics of linear entangled polymers. Macromolecules 2002 , 35 , 6332−6343..

Cheng, S.; Lu, Y.; Liu, G.; Wang, S. Q. Finite cohesion due to chain entanglement in polymer melts. Soft Matter 2016 , 12 , 3340−3351..

Costanzo, S.; Huang, Q.; Ianniruberto, G.; Marrucci, G.; Hassager, O.; Vlassopoulos, D. Shear and extensional rheology of polystyrene melts and solutions with the same number of entanglements. Macromolecules 2016 , 49 , 3925−3935..

[Macosko, C. W. Rheology: principles, measurements, and applications . Wiley-VCH: New York, 1994 , pp. 111−126..

Schweizer, K. S.; Xie, S. J. Physics of the stress overshoot and chain stretch dynamics of entangled polymer liquids under continuous startup nonlinear shear. ACS Macro Lett. 2018 , 7 , 218−222..

Xie, S. J.; Schweizer, K. S. Consequences of delayed chain retraction on the rheology and stretch dynamics of entangled polymer liquids under continuous nonlinear shear deformation. Macromolecules 2018 , 51 , 4185−4200..

Sukumaran, S. K.; Grest, G. S.; Kremer, K.; Everaers, R. Identifying the primitive path mesh in entangled polymer liquids. J. Polym. Sci. B: Polym. Phys. 2005 , 43 , 917−933..

Dolata, B. E.; Olmsted, P. D. A thermodynamically consistent constitutive equation describing polymer disentanglement under flow. J. Rheol. 2022 , 67 , 269−292..

Views

110

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

Sliding Dynamics of Ring Chain on a Rod-Coil Block Copolymer in Rotaxane

Length-dependent Nanopore Transport and Surface-induced Unfolding of Polyglutamine Chains

Simulation of the Specific Contributions of Molecular Weight, Orientation Degree, and Crystallinity to the Tensile Mechanics of Polyethylene Fibers

Special Topic: Chirality in Polymers

End-to-End Neuron-inspired Signal Transduction Using Organic Electrochemical Transistors

Related Author

Si-Yi Yan

Xiang-Hong Wang

Ke Li

Lin-Li He

Mei Feng

Nan Wang

Yan Wang

Bi-Jun Xu

Related Institution

Department of Physics, Wenzhou University

Shanghai Technical Institute of Electronics & Information

College of Electronics and Information Engineering, Shanghai University of Electric Power

Department of Physics, Zhejiang University of Science and Technology

Zhejiang Key Laboratory of Biomedical Intelligent Computing Technology

⁰