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Flow-Driven Stretch Fluctuations Govern the Nonlinear Viscoelasticity of Elongating Associative Polymer Networks
Phys. Rev. Lett. 135, 098101 – Published 28 August, 2025
DOI: https://doi.org/10.1103/kgrd-8gkb
Abstract
We use nonequilibrium molecular dynamics simulations to verify recent tube-model predictions that associative polymer networks exhibit broad stretch fluctuations during elongational flow. Simulations further show that these fluctuating dynamics give rise to the rate-dependent extensional viscosity measured in filament stretching experiments on H-bonding networks. Simulations model bivalent associative networks with a reactive bead-spring model for varying association strength and extensional strain rate. We observe that stretch fluctuations are driven by a new form of chain tumbling, where chains continually collapse and elongate as their associations break and reform within the advecting network. This produces a broad, nearly uniform distribution of chain stretch over a wide range of strain rates, manifesting as a rate-independent plateau in the extensional stress. Our results show that the nonlinear viscoelasticity of associative networks is dominated by large fluctuations in molecular response, which cannot be captured by current mean-field models.
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References (49)
- S. Wu and Q. Chen, Advances and new opportunities in the rheology of physically and chemically reversible polymers, Macromolecules 55, 697 (2022).
- Z. Zhang, Q. Chen, and R. H. Colby, Dynamics of associative polymers, Soft Matter 14, 2961 (2018).
- W. H. Binder and R. Zirbs, Supramolecular polymers and networks with hydrogen bonds in the main- and side-chain, Adv. Polym. Sci. 207, 1 (2006).
- A. M. Wemyss, C. Ellingford, Y. Morishita, C. Bowen, and C. Wan, Dynamic polymer networks: A new avenue towards sustainable and advanced soft machines, Angew. Chem., Int. Ed. Engl. 60, 13725 (2021).
- M. J. Webber and M. W. Tibbitt, Dynamic and reconfigurable materials from reversible network interactions, Nat. Rev. Mater. 7, 541 (2022).
- C. Guo, C. Li, X. Mu, and D. L. Kaplan, Engineering silk materials: From natural spinning to artificial processing, Appl. Phys. Rev. 7, 011313 (2020).
- V. Volkov, A. V. Ferreira, and A. Cavaco-Paulo, On the routines of wild-type silk fibroin processing toward silk-inspired materials: A review, Macromol. Mater. Eng. 300, 1199 (2015).
- L. G. Baxandall, Dynamics of reversibly cross-linked chains, Macromolecules 22, 1982 (1989).
- L. Leibler, M. Rubinstein, and R. H. Colby, Dynamics of reversible networks, Macromolecules 24, 4701 (1991).
- M. Rubinstein and A. N. Semenov, Dynamics of entangled solutions of associating polymers, Macromolecules 34, 1058 (2001).
- I. Mahmad Rasid, J. Ramirez, B. D. Olsen, and N. Holten-Andersen, Understanding the molecular origin of shear thinning in associative polymers through quantification of bond dissociation under shear, Phys. Rev. Mater. 4, 055602 (2020).
- A. Shabbir, H. Goldansaz, O. Hassager, E. Van Ruymbeke, and N. J. Alvarez, Effect of hydrogen bonding on linear and nonlinear rheology of entangled polymer melts, Macromolecules 48, 5988 (2015).
- C. R. López-Barrón, J. Lu, J. A. Throckmorton, H. Passino, and M. Gopinadhan, Microstructure, viscoelasticity, and extensional rheology of ethylene-propylene copolymer vitrimers, Macromolecules 57, 2729 (2024).
- C. R. López-Barrón, J. A. Throckmorton, and T.-P. Lin, Extensional rheology and flow-induced crystal alignment in polypropylene ionomers, J. Rheol. 66, 657 (2022).
- S. Wu, X. Cao, Z. Zhang, Q. Chen, Y. Matsumiya, and H. Watanabe, Molecular design of highly stretchable ionomers, Macromolecules 51, 4735 (2018).
- A. Shabbir, Q. Huang, G. P. Baeza, D. Vlassopoulos, Q. Chen, R. H. Colby, N. J. Alvarez, and O. Hassager, Nonlinear shear and uniaxial extensional rheology of polyether-ester-sulfonate copolymer ionomer melts, J. Rheol. 61, 1279 (2017).
- G. H. Ling, Y. Wang, and R. A. Weiss, Linear viscoelastic and uniaxial extensional rheology of alkali metal neutralized sulfonated oligostyrene ionomer melts, Macromolecules 45, 481 (2012).
- Q. Huang, When polymer chains are highly aligned: A perspective on extensional rheology, Macromolecules 55, 715 (2022).
- S. Costanzo, Q. Huang, G. Ianniruberto, G. Marrucci, O. Hassager, and D. Vlassopoulos, Shear and extensional rheology of polystyrene melts and solutions with the same number of entanglements, Macromolecules 49, 3925 (2016).
- C. Schaefer and T. C. McLeish, Power law stretching of associating polymers in steady-state extensional flow, Phys. Rev. Lett. 126, 057801 (2021).
- C. Schaefer, P. R. Laity, C. Holland, and T. C. McLeish, Stretching of Bombyx mori silk protein in flow, Molecules 26, 1 (2021).
- C. Schaefer and T. C. B. McLeish, Theoretical rheo-physics of silk: Intermolecular associations reduce the critical specific work for flow-induced crystallization, J. Rheol. 66, 515 (2022).
- S. Liu and T. C. O’Connor, A reactive bead-spring model for associative polymer melts in and out of equilibrium, Macromolecules 57, 1403 (2024).
- M. H. Nafar Sefiddashti, B. J. Edwards, and B. Khomami, Individual chain dynamics of a polyethylene melt undergoing steady shear flow, J. Rheol. 59, 119 (2015).
- K. Kremer and G. S. Grest, Dynamics of entangled linear polymer melts: A molecular-dynamics simulation, J. Chem. Phys. 92, 5057 (1990).
- L. A. Moreira, G. Zhang, F. Müller, T. Stuehn, and K. Kremer, Direct equilibration and characterization of polymer melts for computer simulations, Macromol. Theory Simul. 24, 419 (2015).
- H. P. Hsu and K. Kremer, Static and dynamic properties of large polymer melts in equilibrium, J. Chem. Phys. 144 (2016).
- T. Ge, M. O. Robbins, D. Perahia, and G. S. Grest, Healing of polymer interfaces: Interfacial dynamics, entanglements, and strength, Phys. Rev. E 90, 012602 (2014).
- 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).
- M. Dobson, Periodic boundary conditions for long-time nonequilibrium molecular dynamics simulations of incompressible flows, J. Chem. Phys. 141, 184103 (2014).
- D. A. Nicholson and G. C. Rutledge, Molecular simulation of flow-enhanced nucleation in n-eicosane melts under steady shear and uniaxial extension, J. Chem. Phys. 145, 244903 (2016).
- D. J. Evans and G. P. Morriss, Nonlinear-response theory for steady planar Couette flow, Phys. Rev. A 30, 1528 (1984).
- P. J. Daivis and B. D. Todd, A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows, J. Chem. Phys. 124, 194103 (2006).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/kgrd-8gkb for additional figures plotting steady-state statistics for chain conformations, chain tumbling, and the time evolution of network connections during startup flow.
- M. H. Wagner, E. Narimissa, and A. Shabbir, Modelling the effect of hydrogen bonding on elongational flow of supramolecular polymer melts, Rheol. Acta 61, 637 (2022).
- T. C. O’Connor, N. J. Alvarez, and M. O. Robbins, Relating chain conformations to extensional stress in entangled polymer melts, Phys. Rev. Lett. 121, 047801 (2018).
- T. C. O’Connor, A. Hopkins, and M. O. Robbins, Stress relaxation in highly oriented melts of entangled polymers, Macromolecules 52, 8540 (2019).
- C. M. Schroeder, R. E. Teixeira, E. S. Shaqfeh, and S. Chu, Characteristic periodic motion of polymers in shear flow, Phys. Rev. Lett. 95, 018301 (2005).
- A. Vaccaro and G. Marrucci, A model for the nonlinear rheology of associating polymers, J. Non-Newtonian Fluid Mech. 92, 261 (2000).
- F. Tanaka, Viscoelastic properties of physically crosslinked networks part 2. Dynamic mechanical moduli, J. Non-Newtonian Fluid Mech. 43, 273 (1992).
- F. Tanaka and S. F. Edwards, Viscoelastic properties of physically cross-linked networks. Transient network theory, Macromolecules 25, 1516 (1992).
- F. Tanaka and S. F. Edwards, Viscoelastic properties of physically crosslinked networks part 3. Time-dependent phenomena, J. Non-Newtonian Fluid Mech. 43, 289 (1992).
- F. Tanaka and S. F. Edwards, Viscoelastic properties of physically crosslinked networks part 1. Non-linear stationary viscoelasticity, J. Non-Newtonian Fluid Mech. 43, 247 (1992).
- M. K. Sing, Z. G. Wang, G. H. McKinley, and B. D. Olsen, Celebrating soft matter’s 10th anniversary: Chain configuration and rate-dependent mechanical properties in transient networks, Soft Matter 11, 2085 (2015).
- P. C. Cai, B. A. Krajina, and A. J. Spakowitz, Brachiation of a polymer chain in the presence of a dynamic network, Phys. Rev. E 102, 020501(R) (2020).
- S. S. Mohottalalage, M. Senanayake, J. T. Clemmer, D. Perahia, G. S. Grest, and T. O’Connor, Nonlinear elongation flows in associating polymer melts: From homogeneous to heterogeneous flow, Phys. Rev. X 12, 021024 (2022).
- R. S. Graham, A. E. Likhtman, T. C. B. McLeish, and S. T. Milner, Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release, J. Rheol. 47, 1171 (2003).
- S. S. Mohottalalage, A. P. Saab, and A. Maiti, Bead–spring simulation of ionomer melts—Studying the effects of chain-length and associating group fraction on equilibrium structure and extensional flow behavior, Polymers 15, 4560 (2023).
- L. Songyue and Thomas C. O’Connor, 2025, Simulation files and plotted data are freely available at https://github.com/OConnor-Lab/APN_Flow_Liu_PRL_2025.