Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Original Article
  • Published:

Viscoelastic properties of comb-shaped ring polystyrenes

Polymer Journal volume 54, pages 1267–1277 (2022)Cite this article

Subjects

Abstract

In this study, we examined the viscoelastic properties of a series of comb-shaped ring (RC) polystyrene samples with different branch chain lengths, i.e., the molecular weights of the ring backbone Mbb (≃ 4Me where Me is the entanglement molecular weight) and branch chains Mbr (≃ Me, 2Me, and 4Me). Even for the RC sample with the shortest branch chains, a plateau region was observed for the dynamic modulus G*(ω) in the middle angular frequency ω region, suggesting that intermolecular branch chain entanglement occurred. In the ω region between the plateau and terminal regions, G*(ω) was observed with a weaker ω dependence than the terminal relaxation. This behavior was more pronounced for RC samples with shorter branch chains and for the corresponding linear comb (LC) samples than for the RC ones. The molecular weight dependence of the zero-shear viscosity η0 and the steady-state recoverable compliance Jeo of the RC and LC samples was evaluated, and the effects of different backbone molecular structures (i.e., ring or linear) on the terminal relaxation behavior was discussed. Moreover, the G*(ω) data were analyzed with two models: the comb-Rouse model, in which the structures of the RC/LC molecules are taken into account by graph theory, and the Milner-McLeish model for entangled star-shaped polymers. The former model qualitatively described the terminal relaxation behavior of G*(ω) at low ω but failed to reproduce the plateau in the middle ω range. Conversely, the latter model described the entanglement plateau in the middle ω range, but the difference in the terminal relaxation regime for the RC/LC samples seen in the data and the comb-Rouse model disappeared.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Ferry JD. Viscoelastic properties of polymers. New York: John Wiley and Sons; 1980.

  2. Doi M, Edwards SF. The theory of polymer dynamics. Oxford: Clarendon; 1986.

  3. Watanabe H. Viscoelasticity and dynamics of entangled polymers. Prog Polym Sci. 1999;24:1253–403.

    Article  CAS  Google Scholar 

  4. McLeish TCB. Tube theory of entangled polymer dynamics. Adv Phys. 2002;51:1379–527.

    Article  CAS  Google Scholar 

  5. Graessley WW. Polymeric liquids and network: dynamics and rheology. New York: Garland Science; 2004.

  6. Roovers J. Melt properties of ring polystyrenes. Macromolecules. 1985;18:1359–61.

    Article  CAS  Google Scholar 

  7. Kawaguchi D. Direct observation and mutual diffusion of cyclic polymers. Polym J. 2013;45:783–9.

    Article  CAS  Google Scholar 

  8. Vlassopoulos D. Molecular topology and rheology: beyond the tube model. Rheol Acta. 2016;55:613–32.

    Article  CAS  Google Scholar 

  9. Richter D, Goossen S, Wischnewski A. Celebrating Soft Matter’s 10th anniversary: topology matters: structure and dynamics or ring polymers. Soft Matter. 2015;11:8535–49.

    Article  CAS  PubMed  Google Scholar 

  10. Doi Y. Rheological properties of ring polymers and their derivatives. Nihon Reoroji Gakkaishi (J Soc Rheol Jpn). 2022;50:57–62.

    Article  CAS  Google Scholar 

  11. Obukhov SP, Rubinstein M, Duke T. Dynamics of a ring polymer in a gel. Phys Rev Lett. 1994;73:1263–6.

    Article  CAS  PubMed  Google Scholar 

  12. Ge T, Panyukov S, Rubinstein M. Self-similar conformations and dynamics in entangled melts and solutions of nonconcatenated ring polymers. Macromolecules. 2016;49:708–22.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Doi Y, Takano A, Takahashi Y, Matsushita Y. Melt rheology of tadpole-shaped polystyrenes. Macromolecules. 2015;48:8667–74.

    Article  CAS  Google Scholar 

  14. Doi Y, Takano A, Takahashi Y, Matsushita Y. Melt rheology of tadpole-shaped polystyrenes with different ring sizes. Soft Matter. 2020;16:8720–4.

    Article  CAS  PubMed  Google Scholar 

  15. Xia Y, Boydston AJ, Grubbs RH. Synthesis and direct imaging of ultrahigh molecular weight cyclic brush polymers. Angew Chem Int Ed. 2011;50:5882–5.

    Article  CAS  Google Scholar 

  16. Schappacher M, Deffieux A. Atomic force microscopy imaging and dilute solution properties of cyclic and linear polystyrene combs. J Am Chem Soc. 2008;130:14684–9.

    Article  CAS  PubMed  Google Scholar 

  17. Doi Y, Iwasa Y, Watanabe K, Nakamura M, Takano A, Takahashi Y. Synthesis and characterization of comb-shaped ring polystyrenes. Macromolecules. 2016;49:3109–15.

    Article  CAS  Google Scholar 

  18. Zhang S, Tezuka Y, Zhang Z, Li NA, Zhang W, Zhu L. Recent advances in the construction of cyclic grafted polymers and their potential applications. Polym Chem. 2018;9:677–86.

    Article  CAS  Google Scholar 

  19. Roovers J, Graessley WW. Melt rheology of some model comb polystyrenes. Macromolecules. 1981;14:766–73.

    Article  CAS  Google Scholar 

  20. Daniels DR, McLeish TCB, Crosby BJ, Young RN, Fernyhough CM. Molecular rheology of comb polymer melts. 1. linear viscoelastic response. Macromolecules. 2001;34:7025–33.

    Article  CAS  Google Scholar 

  21. Kapnistos M, Vlassopoulos D, Roovers J, Leal LG. Linear rheology of architecturally complex macromolecules: comb polymers with linear backbones. Macromolecules. 2005;38:7852–62.

    Article  CAS  Google Scholar 

  22. Inkson NJ, Graham RS, McLeish TCB, Groves DJ, Fernyhough CM. Viscoelasticity of monodisperse comb polymer melts. Macromolecules. 2006;39:4217–27.

    Article  CAS  Google Scholar 

  23. Kirkwood KM, Leal LG, Vlassopoulos D, Driva P, Hadjichristidis N. Stress relaxation of comb polymers with short branches. Macromolecules. 2009;42:9592–608.

    Article  CAS  Google Scholar 

  24. Iwawaki H, Inoue T, Nakamura Y. Rheo-optical study on bottlebrush-like polymacromonomer consisting of polystyrene. Macromolecules. 2011;44:5414–9.

    Article  CAS  Google Scholar 

  25. Iwawaki H, Urakawa O, Inoue T, Nakamura Y. Rheo-optical study on dynamics of bottlebrush-like polymacromonomer consisting of polystyrene. II. Side chain length dependence on dynamical stiffness of main chain. Macromolecules. 2012;45:4801–8.

    Article  CAS  Google Scholar 

  26. McLeish TCB. Hierarchical relaxation in tube models of branched polymers. Europhys Lett. 1988;6:511–6.

    Article  CAS  Google Scholar 

  27. Milner ST, McLeish TCB. Parameter-free theory for stress relaxation in star polymer melts. Macromolecules. 1997;30:2159–66.

    Article  CAS  Google Scholar 

  28. Rouse PE. A Theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J Chem Phys. 1953;21:1272–80.

    Article  CAS  Google Scholar 

  29. Ham JS. Viscoelastic theory of branched and cross-linked polymers. J Chem Phys. 1957;26:625–33.

    Article  CAS  Google Scholar 

  30. Nitta K. A Graph-theoretical approach to statics and dynamics of treelike molecules. J Math Chem. 1999;25:133–43.

    Article  CAS  Google Scholar 

  31. Nitta K. Graph-theoretical method for Rouse-Ham dynamics. Nihon Reoroji Gakkaishi (J Soc Rheol Jpn). 2002;30:49–54.

    Article  Google Scholar 

  32. Zoller P, Walsh D. Standard pressure-volume-temperature data for polymers. Technomic Pub; Lancaster, 1995.

  33. Doi Y, Takano A, Takahashi Y, Matsushita Y. Viscoelastic properties of dumbbell-shaped polystyrenes in bulk and solution. Macromolecules. 2020;54:1366–74.

    Article  Google Scholar 

  34. Doi Y, Matsubara K, Ohta Y, Nakano T, Kawaguchi D, Takahashi Y, et al. Melt rheology of ring polystyrenes with ultrahigh purity. Macromolecules. 2015;48:3140–7.

    Article  CAS  Google Scholar 

  35. Roovers J. Viscoelastic properties of polybutadiene rings. Macromolecules. 1988;21:1517–21.

    Article  CAS  Google Scholar 

  36. McKenna GB, Hostetter BJ, Hadjichristidis N, Fetters LJ, Plazek DJ. A study of the linear viscoelastic properties of cyclic polystyrenes using creep and recovery measurements. Macromolecules. 1989;22:1834–52.

    Article  CAS  Google Scholar 

  37. Plazek DJ, O’Rourke VM. Viscoelastic behavior of low molecular weight polystyrene. J Polym Sci Part A-2: Polym Phys. 1971;9:209–43.

    Article  CAS  Google Scholar 

  38. Montfort JP, Marin G, Monge P. Effects of constraint release on the dynamics of entangled linear polymer melts. Macromolecules. 1984;17:1551–60.

    Article  CAS  Google Scholar 

  39. Graessley WW, Roovers J. Melt rheology of four-arm and six-arm star polystyrenes. Macromolecules. 1979;12:959–65.

    Article  CAS  Google Scholar 

  40. Fetters LJ, Kiss AD, Pearson DS, Quack GF, Vitus FJ. Rheological behavior of star-shaped polymers. Macromolecules. 1993;26:647–54.

    Article  CAS  Google Scholar 

  41. Doi Y, Matsumoto A, Inoue T, Iwamoto T, Takano A, Matsushita Y, et al. Re-examination of terminal relaxation behavior of high-molecular-weight ring polystyrene melts. Rheol Acta. 2017;56:567–81.

    Article  CAS  Google Scholar 

  42. Watanabe H, Inoue T, Matsumiya Y. Transient conformational change of bead-spring ring chain during creep process. Macromolecules. 2006;39:5419–26.

    Article  CAS  Google Scholar 

  43. Tsolou GT, Stratikis N, Baig C, Stephanou PS, Marvantzas VG. Melt structure and dynamics of unentangled polyethylene riings: Rouse theory, atomistic molecular dynamics simulation, and comparison with the linear analogues. Macromolecules. 2010;43:10692–713.

    Article  CAS  Google Scholar 

  44. Inoue T, Okamoto H, Osaki K. Birefringence of amorphous polymers. 1. Dynamic measurement on polystyrene. Macromolecules. 1991;24:5670–5.

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge Prof. H. Watanabe at Kyoto University for his valuable suggestions, especially for the Rouse analysis. The authors thank Dr. J. Roovers for his kind provision of rheological data for the star polystyrenes. This work was supported by JSPS Research Fellowships for Young Scientists (No. 14J03393 for YD) and Grant-in-Aids for Scientific Research (No. 21K14682 for YD and 24350056 for AT). This work was partly supported by the Collaborative Research Program of the Institute for Chemical Research, Kyoto University (Grant No. 2015-58), and AT is grateful for the support. This work was also supported by the Program for Leading Graduate Schools at Nagoya University entitled “Integrate Graduate Education and Research Program in Green Natural Sciences”.

Author information

Authors and Affiliations

  1. Department of Materials Physics, Nagoya University, Nagoya, 4648603, Japan

    Yuya Doi, Jinya Kitamura, Takashi Uneyama & Yuichi Masubuchi

  2. Department of Molecular and Macromolecular Chemistry, Nagoya University, Nagoya, 4648603, Japan

    Yuya Doi, Atsushi Takano & Yushu Matsushita

  3. Institute of Materials Chemistry and Engineering, Kyushu University, Kasuga, Fukuoka, 8168580, Japan

    Yoshiaki Takahashi

  4. Toyota Physical and Chemical Research Institute, Nagakute, Aichi, 4801192, Japan

    Yushu Matsushita

Authors
  1. Yuya Doi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinya Kitamura
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Takashi Uneyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuichi Masubuchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Atsushi Takano
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yoshiaki Takahashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yushu Matsushita
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yuya Doi or Atsushi Takano.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Doi, Y., Kitamura, J., Uneyama, T. et al. Viscoelastic properties of comb-shaped ring polystyrenes. Polym J 54, 1267–1277 (2022). https://doi.org/10.1038/s41428-022-00686-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41428-022-00686-0

Search

Advanced search

Quick links