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Aging of ring polymeric topological glass formers via thermal quench

Arabinda Behera1,2,*, Projesh Roy3,†, Pinaki Chaudhuri1,2,‡, and Satyavani Vemparala1,2,§

  • *Contact author: arabindab@imsc.res.in
  • †Contact author: projesh@nitt.edu
  • ‡Contact author: pinakic@imsc.res.in
  • §Contact author: vani@imsc.res.in
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Phys. Rev. Research 8, 033019 – Published 6 July, 2026

DOI: https://doi.org/10.1103/tdfs-l7fw

Abstract

We investigate the nonequilibrium glassy dynamics of dense, topologically constrained ring-polymer systems subjected to instantaneous thermal quenches, using large-scale molecular dynamics simulations. We show that the onset of dynamical arrest is strongly controlled by polymer stiffness, with increasing rigidity enhancing configurational constraints and shifting the estimated glass transition temperature to higher values. Below this threshold temperature, the system exhibits clear aging behavior, manifested through the waiting-time dependence of two-time correlation functions, with the corresponding structural relaxation approximately displaying a simple aging scenario. A key feature of these systems is the emergence of long-lived threaded rings, upon quenching, which act as persistent topological constraints, and the threading relaxation is shown to be correlated with aging dynamics. At the collective level, persistent threading leads to pronounced spatial heterogeneity, manifested as clustering of centers of mass of the rings. Cluster formation is maximized near the glass transition and is enhanced by polymer stiffness, while aging primarily affects the kinetics of cluster participation rather than their characteristic size. Overall, our study establishes a direct connection between polymer stiffness, topological constraints, spatial heterogeneity, and aging dynamics in ring-polymer glasses.

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References (56)

  1. K. Binder and W. Kob, Glassy Materials and Disordered Solids: An Introduction to Their Statistical Mechanics (World scientific, Singapore, 2011).
  2. C. A. Angell, Formation of glasses from liquids and biopolymers, Science 267, 1924 (1995).
  3. J.-P. Bouchaud, M. Cates, and M. Evans, Aging in glassy systems: New experiments, simple models, and open questions, in Soft and Fragile Matter: Nonequilibrium Dynamics, Metastability and Flow, edited by M. E. Cates and M. R. Evans (CRC Press, Boca Raton, FL, 2000), Vol. 53, pp. 285–321.
  4. R. Bandyopadhyay, D. Liang, J. L. Harden, and R. L. Leheny, Slow dynamics, aging, and glassy rheology in soft and living matter, Solid State Commun. 139, 589 (2006).
  5. F. Arceri, F. P. Landes, L. Berthier, and G. Biroli, Glasses and aging, a statistical mechanics perspective on, in Statistical and Nonlinear Physics, edited by F. Corberi, G. Gonnela, and A. Lamura (Springer, Cham, 2022), pp. 229–296.
  6. G. Janzen and L. M. Janssen, Aging in thermal active glasses, Phys. Rev. Res. 4, L012038 (2022).
  7. P. G. Debenedetti, T. M. Truskett, C. P. Lewis, and F. H. Stillinger, Theory of supercooled liquids and glasses: Energy landscape and statistical geometry perspectives, Adv. Chem. Eng. 28, 21 (2001).
  8. P. N. Pusey and W. van Megen, Observation of a glass transition in suspensions of spherical colloidal particles, Phys. Rev. Lett. 59, 2083 (1987).
  9. M. Yang, W. Li, X. Liu, H. Wang, Y. Wu, X. Wang, F. Zhang, Q. Zeng, D. Ma, H. Ruan, et al., Configurational entropy effects on glass transition in metallic glasses, J. Phys. Chem. Lett. 13, 7889 (2022).
  10. Z. Lu, H. Tan, S. Ng, and Y. Li, The correlation between reduced glass transition temperature and glass forming ability of bulk metallic glasses, Scr. Mater. 42, 667 (2000).
  11. J. Dudowicz, K. F. Freed, and J. F. Douglas, The glass transition temperature of polymer melts, J. Phys. Chem. B 109, 21285 (2005).
  12. T. Jin, C. W. Coley, A. Alexander-Katz, et al., Molecular signatures of the glass transition in polymers, Phys. Rev. E 106, 014506 (2022).
  13. G. B. McKenna, Mechanical rejuvenation in polymer glasses: Fact or fallacy? J. Phys.: Condens. Matter 15, S737 (2003).
  14. T. C. Hufnagel, C. A. Schuh, and M. L. Falk, Deformation of metallic glasses: Recent developments in theory, simulations, and experiments, Acta Mater. 109, 375 (2016).
  15. N. Gnan and E. Zaccarelli, The microscopic role of deformation in the dynamics of soft colloids, Nat. Phys. 15, 683 (2019).
  16. I. Chubak, C. N. Likos, and S. A. Egorov, Multiscale approaches for confined ring polymer solutions, J. Phys. Chem. B 125, 4910 (2021).
  17. C. N. Likos, Effective interactions in soft condensed matter physics, Phys. Rep. 348, 267 (2001).
  18. R. Nayak, P. Chaudhuri, and S. Vemparala, Glassy dynamics in two-dimensional ring polymers: Size versus stiffness polydispersity, Soft Matter 22, 145 (2025).
  19. A. Rosa and R. Everaers, Ring polymers in the melt state: The physics of crumpling, Phys. Rev. Lett. 112, 118302 (2014).
  20. J. D. Halverson, G. S. Grest, A. Y. Grosberg, and K. Kremer, Rheology of ring polymer melts: From linear contaminants to ring-linear blends, Phys. Rev. Lett. 108, 038301 (2012).
  21. J. D. Halverson, W. B. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. I. Statics, J. Chem. Phys. 134, 204904 (2011).
  22. J. D. Halverson, W. B. Lee, G. S. Grest, A. Y. Grosberg, and K. Kremer, Molecular dynamics simulation study of nonconcatenated ring polymers in a melt. II. Dynamics, J. Chem. Phys. 134, 204905 (2011).
  23. M. Rubinstein, Dynamics of ring polymers in the presence of fixed obstacles, Phys. Rev. Lett. 57, 3023 (1986).
  24. M. Cates and J. Deutsch, Conjectures on the statistics of ring polymers, J. Phys. 47, 2121 (1986).
  25. E. Lee and Y. Jung, Segregated structures of ring polymer melts near the surface: A molecular dynamics simulation study, Soft Matter 11, 6018 (2015).
  26. S. Brown, T. Lenczycki, and G. Szamel, Influence of topological constraints on the statics and dynamics of ring polymers, Phys. Rev. E 63, 052801 (2001).
  27. J. Suzuki, A. Takano, T. Deguchi, and Y. Matsushita, Dimension of ring polymers in bulk studied by Monte-Carlo simulation and self-consistent theory, J. Chem. Phys. 131, 144902 (2009).
  28. E. Lee and Y. Jung, Slow dynamics of ring polymer melts by asymmetric interaction of threading configuration: Monte Carlo study of a dynamically constrained lattice model, Polymers 11, 516 (2019).
  29. T. Deguchi and E. Uehara, Statistical and dynamical properties of topological polymers with graphs and ring polymers with knots, Polymers 9, 252 (2017).
  30. S. Mukhopadhyay and J. Peixinho, Packings of deformable spheres, Phys. Rev. E 84, 011302 (2011).
  31. H. A. Makse, D. L. Johnson, and L. M. Schwartz, Packing of compressible granular materials, Phys. Rev. Lett. 84, 4160 (2000).
  32. V. M. Batista and M. A. Miller, Crystallization of deformable spherical colloids, Phys. Rev. Lett. 105, 088305 (2010).
  33. A. Boromand, A. Signoriello, F. Ye, C. S. O'Hern, and M. D. Shattuck, Jamming of deformable polygons, Phys. Rev. Lett. 121, 248003 (2018).
  34. M. Q. Tu, O. Davydovich, B. Mei, P. K. Singh, G. S. Grest, K. S. Schweizer, T. C. O’Connor, and C. M. Schroeder, Unexpected slow relaxation dynamics in pure ring polymers arise from intermolecular interactions, ACS Polym. Au 3, 307 (2023).
  35. V. Privalko and Y. S. Lipatov, Glass transition and chain flexibility of linear polymers, J. Macromol. Sci. Part B 9, 551 (1974).
  36. H.-P. Hsu and K. Kremer, A coarse-grained polymer model for studying the glass transition, J. Chem. Phys. 150, 091101 (2019).
  37. C. Ness, V. V. Palyulin, R. Milkus, R. Elder, T. Sirk, and A. Zaccone, Nonmonotonic dependence of polymer-glass mechanical response on chain bending stiffness, Phys. Rev. E 96, 030501(R) (2017).
  38. S. P. Obukhov, M. Rubinstein, and T. Duke, Dynamics of a ring polymer in a gel, Phys. Rev. Lett. 73, 1263 (1994).
  39. S. P. Obukhov, M. Rubinstein, and R. H. Colby, Network modulus and superelasticity, Macromolecules 27, 3191 (1994).
  40. F. Guo, K. Li, J. Wu, L. He, and L. Zhang, Effects of topological constraints on penetration structures of semi-flexible ring polymers, Polymers 12, 2659 (2020).
  41. R. Staňo, C. N. Likos, and J. Smrek, To thread or not to thread? Effective potentials and threading interactions between asymmetric ring polymers, Soft Matter 19, 17 (2022).
  42. E. Lee, S. Kim, and Y. Jung, Slowing down of ring polymer diffusion caused by inter-ring threading, Macromol. Rapid Commun. 36, 1115 (2015).
  43. P. K. Roy, P. Chaudhuri, and S. Vemparala, Effect of ring stiffness and ambient pressure on the dynamical slowdown in ring polymers, Soft Matter 18, 2959 (2022).
  44. P. K. Roy, P. Chaudhuri, and S. Vemparala, Bidisperse ring polymers: Topological glass to stacking, Phys. Rev. Mater. 8, 045601 (2024).
  45. W. Kob and H. C. Andersen, Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture I: The van Hove correlation function, Phys. Rev. E 51, 4626 (1995).
  46. L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, and W. van Saarloos, Dynamical Heterogeneities in Glasses, Colloids, and Granular Media (Oxford University Press, Oxford, 2011), Vol. 150.
  47. W. Kob and J.-L. Barrat, Fluctuations, response and aging dynamics in a simple glass-forming liquid out of equilibrium, Eur. Phys. J. B 13, 319 (2000).
  48. D. El Masri, L. Berthier, and L. Cipelletti, Subdiffusion and intermittent dynamic fluctuations in the aging regime of concentrated hard spheres, Phys. Rev. E 82, 031503 (2010).
  49. M. Rubinstein and R. H. Colby, Polymer Physics (Oxford University Press, New York, 2003).
  50. D. Michieletto and M. S. Turner, A topologically driven glass in ring polymers, Proc. Natl. Acad. Sci. USA 113, 5195 (2016).
  51. F. H. Stillinger, Supercooled liquids, glass transitions, and the Kauzmann paradox, J. Chem. Phys. 88, 7818 (1988).
  52. J. Smrek, J. Garamella, R. Robertson-Anderson, and D. Michieletto, Topological tuning of DNA mobility in entangled solutions of supercoiled plasmids, Sci. Adv. 7, eabf9260 (2021).
  53. A. Narros, A. J. Moreno, and C. N. Likos, Effects of knots on ring polymers in solvents of varying quality, Macromolecules 46, 3654 (2013).
  54. M. Ester, H.-P. Kriegel, J. Sander, X. Xu, et al., A density-based algorithm for discovering clusters in large spatial databases with noise, in Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD-96) (AAAI Press, Portland, OR, 1996), Vol. 96, pp. 226–231.
  55. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, et al., Scikit-learn: Machine learning in Python, J. Mach. Learn. Res. 12, 2825 (2011).
  56. J. P. Miranda, E. Locatelli, and C. Valeriani, Self-organized states from solutions of active ring polymers in bulk and under confinement, J. Chem. Theory Comput. 20, 1636 (2024).

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Phys. Rev. Research 8, 033019– Published 6 July, 2026
  • Received 30 April 2025
  • Accepted 25 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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