Skip to main content
Log in

Exploring the Interplay between Local Chain Structure and Stress Distribution in Polymer Networks

  • Research Article
  • Published:
Chinese Journal of Polymer Science Aims and scope Submit manuscript

Abstract

The mechanical behavior of polymer networks is intrinsically correlated with the local chain topology and chain connectivity. In this study, we delve into this relationship through the lens of coarse-grained molecular dynamics (CG-MD) simulations. Our aim is to illuminate the intricate interplay between local topology and stress distribution within polymer monomers, cross-linkers, and various components with distinct cross-link connections, thereby elucidating their collective impact on the mechanical properties of polymer networks. We mainly focus on how specific local structures contribute to the overall mechanical response of the network. In particular, we employ local stress analysis to unravel the mechanics of these structures. Our findings reveal the diverse responses of individual components, such as junctions, strands, cross-linkers between junctions, and dangling chain ends, when subjected to stretching. Notably, we observe that these components exhibit varying degrees of deformation tolerance, underscoring the significance of their roles in determining the mechanical characteristics of the network. Our investigations highlight junctions as primary contributors to stress accumulation, and particles with higher local stress showing a stronger correlation between stress and Voronoi volume. Moreover, our results indicate that both strands and cross-linkers between junctions exhibit heightened stress levels as strand lengths decrease. This study enhances our understanding of the multifaceted factors governing the mechanical attributes of cross-linked polymer systems at the microstructural level.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request. The authors’ contact information: huangxianbo@Kingfa.com.cn (X.B.H.), zysun@ciac.ac.cn (Z.Y.S.)

References

  1. Ducrot, E.; Creton, C. Characterizing large strain elasticity of brittle elastomeric networks by embedding them in a soft extensible matrix. Adv. Funct. Mater. 2016, 26, 2482–2492.

    Article  CAS  Google Scholar 

  2. Ducrot, E.; Chen, Y.; Bulters, M.; Sijbesma, R. P.; Creton, C. Toughening elastomers with sacrificial bonds and watching them break. Science 2014, 344, 186–189.

    Article  ADS  CAS  PubMed  Google Scholar 

  3. Li, M. X.; Chen, L. L.; Li, Y. R.; Dai, X. B.; Jin, Z. K.; Zhang, Y. C.; Feng, W. W.; Yan, L. T.; Cao, Y.; Wang, C. Superstretchable, yet stiff, fatigue-resistant ligament-like elastomers. Nat. Commun. 2022, 13, 2279.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  4. Wang, Y. J.; Liu, S. J.; Yu, W. Functionalized graphene oxide-reinforced chitosan hydrogel as biomimetic dressing for wound healing. Macromol. Biosci. 2021, 21, 2000432.

    Article  CAS  Google Scholar 

  5. Gong, J. P. Materials both tough and soft. Science 2014, 344, 161–162.

    Article  ADS  CAS  PubMed  Google Scholar 

  6. Sun, J. Y.; Zhao, X. H.; Illeperuma, W. R. K.; Chaudhuri, O.; Oh, K. H.; Mooney, D. J.; Vlassak, J. J.; Suo, Z. G. Highly stretchable and tough hydrogels. Nature 2012, 489, 133–136.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  7. Hagen, R.; Salmén, L.; Stenberg, B. Effects of the type of crosslink on viscoelastic properties of natural rubber. J. Polym. Sci., Part B: Polym. Phys. 1996, 34, 1997–2006.

    Article  ADS  CAS  Google Scholar 

  8. Cui, X.; Jiang, N. F.; Shao, J. Y.; Zhang, H. D.; Yang, Y. L.; Tang, P. Linear and nonlinear viscoelasticities of dissociative and associative covalent adaptable networks: discrepancies and limits. Macromolecules 2023, 56, 772–784.

    Article  ADS  CAS  Google Scholar 

  9. Zhang, W.; Cui, X.; Zhang, H. D.; Yang, Y. L.; Tang, P. Linear viscoelasticity, nonlinear rheology and applications of polyethylene terephthalate vitrimers. J. Polym. Sci. 2023, 61, 2010–2024.

    Article  CAS  Google Scholar 

  10. Mukherji, D.; Abrams, C. F. Mechanical behavior of highly cross-linked polymer networks and its links to microscopic structure. Phys. Rev. E 2009, 79, 061802.

    Article  ADS  Google Scholar 

  11. Liao, X. J.; Dulle, M.; de Souza e Silva, J. M.; Wehrspohn, R. B.; Agarwal, S.; Förster, S.; Hou, H. Q.; Smith, P.; Greiner, A. High strength in combination with high toughness in robust and sustainable polymeric materials. Science 2019, 366, 1376–1379.

    Article  ADS  CAS  PubMed  Google Scholar 

  12. Martinez, R. V.; Glavan, A. C.; Keplinger, C.; Oyetibo, A. I.; Whitesides, G. M. Soft actuators and robots that are resistant to mechanical damage. Adv. Funct. Mater. 2014, 24, 3003–3010.

    Article  CAS  Google Scholar 

  13. Yang, Y.; Wu, Y. X.; Li, C.; Yang, X. M.; Chen, W. Flexible actuators for soft robotics. Adv. Intell. Syst. 2020, 2, 1900077.

    Article  Google Scholar 

  14. Rogers, J. A.; Someya, T.; Huang, Y. Materials and mechanics for stretchable electronics. Science 2010, 327, 1603–1607.

    Article  ADS  CAS  PubMed  Google Scholar 

  15. Wang, C. F.; Wang, C. H.; Huang, Z. L.; Xu, S. Materials and structures toward soft electronics. Adv. Mater. 2018, 30, 1801368.

    Article  Google Scholar 

  16. Zhang, J.; Wang, W.; Wang, Y. B.; Qiu, C. L.; Mao, C. L.; Deng, S. W.; Wang, J. G. Effect of cross-linked structures on mechanical properties of styrene-butadiene rubber via molecular dynamics simulation. Macromol. Theory Simul. 2022, 31, 2100054.

    Article  CAS  Google Scholar 

  17. Bermejo, J. S.; Ugarte, C. M. Influence of cross-linking density on the glass transition and structure of chemically cross-linked PVA: a molecular dynamics study. Macromol. Theory Simul. 2009, 18, 317–327.

    Article  CAS  Google Scholar 

  18. Lee, K. Y.; Rowley, J. A.; Eiselt, P.; Moy, E. M.; Bouhadir, K. H.; Mooney, D. J. Controlling mechanical and swelling properties of alginate hydrogels independently by cross-linker type and crosslinking density. Macromolecules 2000, 33, 4291–4294.

    Article  ADS  CAS  Google Scholar 

  19. Wu, B.; Chassé, W.; Peters, R.; Brooijmans, T.; Dias, A. A.; Heise, A.; Duxbury, C. J.; Kentgens, A. P. M.; Brougham, D. F.; Litvinov, V. M. Network structure in acrylate systems: effect of junction topology on cross-link density and macroscopic gel properties. Macromolecules 2016, 49, 6531–6540.

    Article  ADS  CAS  Google Scholar 

  20. Lei, Z. X.; Zhang, Z. Z.; Wang, J.; Xu, L.; Li, J.; Zhu, Z. C.; Liu, Y. H. New strategy to construct mechanically strong and tough phenolic networks by considering the effect of curing reactions and physical states on the cross-linking density and cross-linking inhomogeneity. Ind. Eng. Chem. Res. 2022, 61, 8858–8870.

    Article  CAS  Google Scholar 

  21. Shen, J. X.; Lin, X. S.; Liu, J.; Li, X. Effects of cross-link density and distribution on static and dynamic properties of chemically cross-linked polymers. Macromolecules 2019, 52, 121–134.

    Article  ADS  CAS  Google Scholar 

  22. Seitz, J. T. The estimation of mechanical properties of polymers from molecular structure. J. Appl. Polym. Sci. 1993, 49, 1331–1351.

    Article  CAS  Google Scholar 

  23. Gehman, S. D. Relationship between molecular structure and physical properties. Ind. Eng. Chem. 1952, 44, 730–739.

    Article  CAS  Google Scholar 

  24. Gu, Y. W.; Zhao, J. L.; Johnson, J. A. Polymer networks: from plastics and gels to porous frameworks. Angew. Chem. Int. Ed. 2020, 59, 5022–5049.

    Article  CAS  Google Scholar 

  25. James, H. M.; Guth, E. Theory of the increase in rigidity of rubber during cure. J. Chem. Phys. 1947, 15, 669–683.

    Article  ADS  CAS  Google Scholar 

  26. Rubinstein, M.; Panyukov, S. Elasticity of polymer networks. Macromolecules 2002, 35, 6670–6686.

    Article  ADS  CAS  Google Scholar 

  27. Rottach, D. R.; Curro, J. G.; Budzien, J.; Grest, G. S.; Svaneborg, C.; Everaers, R. Permanent set of cross-linking networks: comparison of theory with molecular dynamics simulations. Macromolecules 2006, 39, 5521–5530.

    Article  ADS  CAS  Google Scholar 

  28. Davidson, J. D.; Goulbourne, N. C. Nonaffine chain and primitive path deformation in crosslinked polymers. Modell. Simul. Mater. Sci. Eng. 2016, 24, 065002.

    Article  ADS  Google Scholar 

  29. Zhong, M. J.; Wang, R.; Kawamoto, K.; Olsen, B. D.; Johnson, J. A. Quantifying the impact of molecular defects on polymer network elasticity. Science 2016, 353, 1264–1268.

    Article  ADS  CAS  PubMed  Google Scholar 

  30. Lin, T. S.; Wang, R.; Johnson, J. A.; Olsen, B. D. Revisiting the elasticity theory for real gaussian phantom networks. Macromolecules 2019, 52, 1685–1694.

    Article  ADS  CAS  Google Scholar 

  31. Grest, G. S.; Kremer, K. Statistical properties of random crosslinked rubbers. Macromolecules 1990, 23, 4994–5000.

    Article  ADS  CAS  Google Scholar 

  32. Gao, Y. S.; Zhou, D. Z.; Lyu, J.; Sigen, A.; Xu, Q.; Newland, B.; Matyjaszewski, K.; Tai, H. Y.; Wang, W. X. Complex polymer architectures through free-radical polymerization of multivinyl monomers. Nat. Rev. Chem. 2020, 4, 194–212.

    Article  CAS  PubMed  Google Scholar 

  33. Seiffert, S. Origin of nanostructural inhomogeneity in polymer-network gels. Polym. Chem. 2017, 8, 4472–4487.

    Article  CAS  Google Scholar 

  34. Galant, O.; Bae, S.; Silberstein, M. N.; Diesendruck, C. E. Highly stretchable polymers: mechanical properties improvement by balancing intra- and intermolecular interactions. Adv. Funct. Mater. 2020, 30, 1901806.

    Article  CAS  Google Scholar 

  35. Galant, O.; Bae, S.; Wang, F.; Levy, A.; Silberstein, M. N.; Diesendruck, C. E. Mechanical and thermomechanical characterization of glassy thermoplastics with intrachain cross-links. Macromolecules 2017, 50, 6415–6420.

    Article  ADS  CAS  Google Scholar 

  36. Deng, J. X.; Bai, R. X.; Zhao, J.; Liu, G. Q.; Zhang, Z. M.; You, W.; Yu, W.; Yan, X. Z. Insights into the correlation of cross-linking modes with mechanical properties for dynamic polymeric networks. Angew. Chem. Int. Ed. 2023, 62, e202309058.

    Article  CAS  Google Scholar 

  37. Zhao, J.; Zhang, Z. M.; Cheng, L.; Bai, R. X.; Zhao, D.; Wang, Y. M.; Yu, W.; Yan, X. Z. Mechanically interlocked vitrimers. J. Am. Chem. Soc. 2022, 144, 872–882.

    Article  CAS  PubMed  Google Scholar 

  38. Creton, C.; Ciccotti, M. Fracture and adhesion of soft materials: a review. Rep. Prog. Phys. 2016, 79, 046601.

    Article  ADS  PubMed  Google Scholar 

  39. Slootman, J.; Waltz, V.; Yeh, C. J.; Baumann, C.; Göst, R.; Comtet, J.; Creton, C. Quantifying and mapping covalent bond scission during elastomer fracture, arXiv:2006.09468. arXiv.org ePrint archive. https://arxiv.org/abs/2006.09468.

  40. Gu, Y. W.; Zhao, J. L. and Johnson, J. A. A (macro)molecular-level understanding of polymer network topology. Trends Chem. 2019, 1, 318–334.

    Article  CAS  Google Scholar 

  41. Pei, H. W.; Zhu, Y. L.; Lu, Z. Y.; Li, J. P. and Sun. Z. Y. Automatic multiscale method of building up a cross-linked polymer reaction system: bridging smiles to the multiscale molecular dynamics simulation. J. Phys. Chem. B 2023, 127, 4905–4914.

    Article  CAS  PubMed  Google Scholar 

  42. Zhang, Z. Y.; Wang, Y. C.; Liu, P. L.; Chen, T. L.; Hou, G. Y.; Xu, L.; Wang, X.; Hu, Z. P.; Liu, J.; Zhang, L. Q. Quantitatively predicting the mechanical behavior of elastomers via fully atomistic molecular dynamics simulation. Polymer 2021, 223, 123704.

    Article  CAS  Google Scholar 

  43. Uddin, M. S.; Ju. J. Multiscale modeling of a natural rubber: Bridging a coarse-grained molecular model to the rubber network theory. Polymer 2016, 101, 34–47.

    Article  CAS  Google Scholar 

  44. Bandyopadhyay, A.; Valavala, P. K.; Clancy, T. C.; Wise, K. E.; Odegard, G. M. Molecular modeling of crosslinked epoxy polymers: the effect of crosslink density on thermomechanical properties. Polymer 2011, 52, 2445–2452.

    Article  CAS  Google Scholar 

  45. Bandyopadhyay, A.; Odegard, G. M. Molecular modeling of crosslink distribution in epoxy polymers. Modell. Simul. Mater. Sci. Eng. 2012, 20, 045018.

    Article  ADS  Google Scholar 

  46. Payal, R. S.; Fujimoto, K.; Jang, C.; Shinoda, W.; Takei, Y.; Shima, H.; Tsunoda, K.; Okazaki, S. Molecular mechanism of material deformation and failure in butadiene rubber: insight from allatom molecular dynamics simulation using a bond breaking potential model. Polymer 2019, 170, 113–119.

    Article  CAS  Google Scholar 

  47. Wang, Y. J.; Liu, H. F.; Li, P. P.; Wang, L. B. The effect of cross-linking type on EPDM elastomer dynamics and mechanical properties: a molecular dynamics simulation study. Polymers 2022, 14, 1308.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Wang, R.; Alexander-Katz, A.; Johnson, J. A.; Olsen, B. D. Universal cyclic topology in polymer networks. Phys. Rev. Lett. 2016, 116, 188302.

    Article  ADS  PubMed  Google Scholar 

  49. Kroll, D. M.; Croll, S. G. Influence of crosslinking functionality, temperature and conversion on heterogeneities in polymer networks. Polymer 2015, 79, 82–90.

    Article  CAS  Google Scholar 

  50. Arora, A.; Lin, T. S.; Olsen, B. D. Coarse-grained simulations for fracture of polymer networks: stress versus topological inhomogeneities. Macromolecules 2022, 55, 4–14.

    Article  ADS  CAS  Google Scholar 

  51. Lorenzo, F. D.; Seiffert, S. Nanostructural heterogeneity in hhpolymer networks and gels. Polym. Chem. 2015, 6, 5515–5528.

    Article  Google Scholar 

  52. David, A.; Tartaglino, U.; Raos, G. Towards realistic simulations of polymer networks: tuning vulcanisation and mechanical properties. Phys. Chem. Chem. Phys. 2021, 23, 3496–3510.

    Article  CAS  PubMed  Google Scholar 

  53. Vogiatzis, G. G.; Theodorou, D. N. Local segmental dynamics and stresses in polystyrene–C60 mixtures. Macromolecules 2014, 47, 387–404.

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  55. Wang, J. L.; O’Connor, T. C.; Grest, G. S.; Ge, T. Superstretchable elastomer from cross-linked ring polymers. Phys. Rev. Lett. 2022, 128, 237801.

    Article  ADS  CAS  PubMed  Google Scholar 

  56. Subramaniyan, A. K.; Sun, C. T. Continuum interpretation of virial stress in molecular simulations. Int. J. Solids Struc. 2008, 45, 4340–4346.

    Article  Google Scholar 

  57. Yang, F.; Zhong, Z. On the energy conservation during the active deformation in molecular dynamics simulations. J. Mech. Phys. Solids 2015, 77, 146–157.

    Article  ADS  MathSciNet  CAS  Google Scholar 

  58. Lion, T. W.; Allen, R. J. Computing the local pressure in molecular dynamics simulations. J. Phys.: Condens. Matter 2012, 24, 284133.

    PubMed  Google Scholar 

  59. Branicio, P. S.; Srolovitz, D. J. Local stress calculation in simulations of multicomponent systems. J. Comput. Phys. 2009, 228, 8467–8479.

    Article  ADS  CAS  Google Scholar 

  60. Rycroft, Chris H. Voro++: a three-dimensional voronoi cell library in C++. Chaos 2009, 19, 041111.

    Article  ADS  PubMed  Google Scholar 

  61. Zhu, Y. L.; Liu, H.; Li, Z. W.; Qian, H. J.; Milano, G.; Lu, Z. Y. GALAMOST: GPU-accelerated large-scale molecular simulation toolkit. J. Comput. Chem. 2019, 34, 2197–2211.

    Article  Google Scholar 

  62. Bae, J.; Kwon, H.; Park, S. R.; Lee, J.; Song, I. Explicit correlation coefficients among random variables, ranks, and magnitude ranks. IEEE Trans. Infor. Theory 2006, 52, 2233–2240.

    Article  MathSciNet  Google Scholar 

  63. Song, H. Y.; Park, S. An analysis of correlation between personality and visiting place using Spearman’s rank correlation coefficient. KSII Transactions on Internet and Information Systems 2020, 14, 1951–1966.

    Google Scholar 

  64. Widmer-Cooper, A.; Harrowell, P. Free volume cannot explain the spatial heterogeneity of Debye-Waller factors in a glass-forming binary alloy. J. Non-Crystalline Solids 2006, 352, 5098–5102.

    Article  ADS  CAS  Google Scholar 

  65. Hocky, G. M.; Coslovich, D.; Ikeda, A.; Reichman, D. R. Correlation of local order with particle mobility in supercooled liquids is highly system dependent. Phys. Rev. Lett. 2014, 113, 157801.

    Article  ADS  PubMed  Google Scholar 

  66. Yao, P.; Feng, L. K.; Guo, H. X. Combined molecular dynamics simulation and rouse model analysis of static and dynamic properties of unentangled polymer melts with different chain architectures. Chinese J. Polym. Sci. 2021, 39, 512–524.

    Article  CAS  Google Scholar 

  67. Wang, F.; Feng, L. K.; Li, Y. D.; Guo, H. X. Statics, dynamics and linear viscoelasticity from dissipative particle dynamics simulation of entangled linear polymer melts. Chinese J. Polym. Sci. 2023, 41, 1392–1409.

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This work was financially supported by the National Key R&D Program of China (No. 2022YFB3707303), and the National Natural Science Foundation of China (Nos. 52293471 and 21833008). We are also grateful to the Network and Computing Center in Changchun Institute of Applied Chemistry for the hardware support.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Xian-Bo Huang or Zhao-Yan Sun.

Ethics declarations

The authors declare no interest conflict.

Electronic Supplementary Material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xue, JT., Bai, Y., Peng, L. et al. Exploring the Interplay between Local Chain Structure and Stress Distribution in Polymer Networks. Chin J Polym Sci (2024). https://doi.org/10.1007/s10118-024-3099-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10118-024-3099-3

Keywords

Navigation