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A computational method for characterizing molecular-scale load transfer in polymer systems with structural heterogeneity

Polymer Journal volume 57, pages 385–394 (2025)Cite this article

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Abstract

Contemporary polymer physics emphasizes polymer material design, which uses nano- and microscale structures to predict and optimize material properties. Despite their importance, predicting the mechanical behavior of polymers remains challenging because of the diverse configurations of their molecular chains. In recent years, quantitative structure‒property relationship modeling based on molecular dynamics (MD) simulations has become increasingly important. MD simulations excel at resolving sub-10-nm-scale morphological features, providing critical insights into network topology, chemical conformation, and molecular transitions. This review highlights recent MD simulation studies that have focused on subcontinuum heterogeneities in polymers from the perspective of their mechanical properties. The theoretical framework for rationally distributing the stress tensor to individual molecular components is revisited, and the key achievements made via this approach are summarized.

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References

  1. Le T, Epa VC, Burden FR, Winkler DA. Quantitative structure–property relationship modeling of diverse materials properties. Chem Rev. 2012;112:2889–919.

    Article  CAS  PubMed  Google Scholar 

  2. Theodorou DN. Understanding and predicting structure–property relations in polymeric materials through molecular simulations. Mol Phys. 2004;102:147–66.

    Article  CAS  Google Scholar 

  3. Afzal MAF, Browning AR, Goldberg A, Halls MD, Gavartin JL, Morisato T, et al. High-throughput molecular dynamics simulations and validation of thermophysical properties of polymers for various applications. ACS Appl Polym Mater. 2020;3:620–30.

    Article  Google Scholar 

  4. Nguyen D, Tao L, Li Y. Integration of machine learning and coarse-grained molecular simulations for polymer materials: physical understandings and molecular design. Front Chem. 2022;9:820417.

    Article  PubMed  PubMed Central  Google Scholar 

  5. Okabe T, Oya Y, Tanabe K, Kikugawa G, Yoshioka K. Molecular dynamics simulation of crosslinked epoxy resins: curing and mechanical properties. Eur Polym J. 2016;80:78–88.

    Article  CAS  Google Scholar 

  6. Bandyopadhyay A, Valavala PK, Clancy TC, Wise KE, Odegard GM. Molecular modeling of crosslinked epoxy polymers: the effect of crosslink density on thermomechanical properties. Polymer. 2011;52:2445–52.

    Article  CAS  Google Scholar 

  7. Varshney V, Patnaik SS, Roy AK, Farmer BL. A molecular dynamics study of epoxy-based networks: cross-linking procedure and prediction of molecular and material properties. Macromolecules. 2008;41:6837–42.

    Article  CAS  Google Scholar 

  8. Park H, Kim B, Choi J, Cho M. Influences of the molecular structures of curing agents on the inelastic-deformation mechanisms in highly-crosslinked epoxy polymers. Polymer. 2018;136:128–42.

    Article  CAS  Google Scholar 

  9. Wick CD, Peters AJ, Li G. Quantifying the contributions of energy storage in a thermoset shape memory polymer with high stress recovery: a molecular dynamics study. Polymer. 2021;213:123319.

    Article  CAS  Google Scholar 

  10. Li C, Strachan A. Evolution of network topology of bifunctional epoxy thermosets during cure and its relationship to thermo-mechanical properties: a molecular dynamics study. Polymer. 2015;75:151–60.

    Article  CAS  Google Scholar 

  11. Zihan W, Peibin K, Tianyu W, Dongli C, Xiaoping Y, Gang S. Atomistic understanding of cross-linking network in different epoxy resin: effect of loop structure. Polymer. 2022;243:124629.

    Article  Google Scholar 

  12. Radue MS, Jensen BD, Gowtham S, Klimek‐McDonald DR, King JA, Odegard GM. Comparing the mechanical response of di‐, tri‐, and tetra‐functional resin epoxies with reactive molecular dynamics. J Polym Sci Part B Polym Phys. 2018;56:255–64.

    Article  CAS  Google Scholar 

  13. Bukowski C, Zhang T, Riggleman RA, Crosby AJ. Load-bearing entanglements in polymer glasses. Sci Adv. 2021;7:eabg9763.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Kim H, Choi J. Subcontinuum interpretation of mechanical behavior for cross-linked epoxy networks. Macromolecules. 2022;55:5916–25.

    Article  CAS  Google Scholar 

  15. Kim Y, Kim H, Choi J. Mechanical origin of shape memory performance for crosslinked epoxy networks. Eur Polym J. 2023;194:112162.

    Article  CAS  Google Scholar 

  16. Kim H, Choi J. Theoretical analysis of phase transition behavior of ALCP/CNT nanocomposites interface by photo and thermal stimulation. Compos A Appl Sci Manuf. 2023;175:107824.

    Article  CAS  Google Scholar 

  17. Heyes DM. Pressure tensor of partial-charge and point-dipole lattices with bulk and surface geometries. Phys Rev B Condens Matter. 1994;49:755.

    Article  CAS  PubMed  Google Scholar 

  18. Thompson AP, Plimpton SJ, Mattson W. General formulation of pressure and stress tensor for arbitrary many-body interaction potentials under periodic boundary conditions. J Chem Phys. 2009;131:154107.

  19. Subramaniyan AK, Sun C. Continuum interpretation of virial stress in molecular simulations. Int J Solids Struct. 2008;45:4340–6.

    Article  Google Scholar 

  20. Reda H, Chazirakis A, Behbahani AF, Savva N, Harmandaris V. A methodology for determining the local mechanical properties of model atomistic glassy polymeric nanostructured materials. MethodsX. 2022;9:101931.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Reda H, Chazirakis A, Behbahani AF, Savva N, Harmandaris V. Mechanical properties of glassy polymer nanocomposites via atomistic and continuum models: the role of interphases. Comput Methods Appl Mech Eng. 2022;395:114905.

    Article  Google Scholar 

  22. Barakat M, Reda H, Katsamba P, Shraim H, Harmandaris V. Predicting mechanical heterogeneity in glassy polymer nanocomposites via an inverse computational approach based on atomistic molecular simulations and homogenization methods. Mech Mater. 2024;197:105082.

    Article  Google Scholar 

  23. Elder RM, Mattson WD, Sirk TW. Origins of error in the localized virial stress. Chem Phys Lett. 2019;731:136580.

    Article  CAS  Google Scholar 

  24. Lu J, Lazar EA, Rycroft CH. An extension to Voro++ for multithreaded computation of Voronoi cells. Comput Phys Commun. 2023;291:108832.

    Article  CAS  Google Scholar 

  25. Rycroft C. VORO++: a three-dimensional Voronoi cell library in C++. 2009.

  26. Choi J, Shin H, Yang S, Cho M. The influence of nanoparticle size on the mechanical properties of polymer nanocomposites and the associated interphase region: a multiscale approach. Compos Struct. 2015;119:365–76.

    Article  Google Scholar 

  27. Choi J, Shin H, Cho M. A multiscale mechanical model for the effective interphase of SWNT/epoxy nanocomposite. Polymer. 2016;89:159–71.

    Article  CAS  Google Scholar 

  28. Reda H, Chazirakis A, Behbahani AF, Savva N, Harmandaris V. Revealing the role of chain conformations on the origin of the mechanical reinforcement in glassy polymer nanocomposites. Nano Lett. 2023;24:148–55.

    Article  PubMed  Google Scholar 

  29. Reda H, Chazirakis A, Savva N, Ganghoffer J-F, Harmandaris V. Gradient of mechanical properties in polymer nanocomposites: from atomistic scale to the strain gradient effective continuum. Int J Solids Struct. 2022;256:111977.

    Article  CAS  Google Scholar 

  30. Sahraei AA, Mokarizadeh AH, George D, Rodrigue D, Baniassadi M, Foroutan M. Insights into interphase thickness characterization for graphene/epoxy nanocomposites: a molecular dynamics simulation. Phys Chem Chem Phys. 2019;21:19890–903.

    Article  Google Scholar 

  31. Putz KW, Palmeri MJ, Cohn RB, Andrews R, Brinson LC. Effect of cross-link density on interphase creation in polymer nanocomposites. Macromolecules. 2008;41:6752–6.

    Article  CAS  Google Scholar 

  32. Bortz DR, Heras EG, Martin-Gullon I. Impressive fatigue life and fracture toughness improvements in graphene oxide/epoxy composites. Macromolecules. 2012;45:238–45.

    Article  CAS  Google Scholar 

  33. Kim H, Choi J. Interfacial and mechanical properties of liquid crystalline elastomer nanocomposites with grafted Au nanoparticles: a molecular dynamics study. Polymer. 2021;218:123525.

    Article  CAS  Google Scholar 

  34. Li C, Strachan A. Free volume evolution in the process of epoxy curing and its effect on mechanical properties. Polymer. 2016;97:456–64.

    Article  CAS  Google Scholar 

  35. Sridhar AS. Effect of stoichiometry on crosslinked epoxy resin characteristics: structural heterogeneities, topological defects, properties, free volume and segmental mobility. Soft Matter. 2022;18:2354–72.

    Article  CAS  PubMed  Google Scholar 

  36. Shudo A, Izumi A, Hagita K, Nakao T, Shibayama M. Structure-mechanical property relationships in crosslinked phenolic resin investigated by molecular dynamics simulation. Polymer. 2017;116:506–14.

    Article  CAS  Google Scholar 

  37. Yan C, Li G. A mechanism-based four-chain constitutive model for enthalpy-driven thermoset shape memory polymers with finite deformation. J Appl Mech. 2020;87:061007.

    Article  CAS  Google Scholar 

  38. Fan J, Li G. High enthalpy storage thermoset network with giant stress and energy output in rubbery state. Nat Commun. 2018;9:642.

    Article  PubMed  PubMed Central  Google Scholar 

  39. Kim H, Ahn S-K, Mackie DM, Kwon J, Kim SH, Choi C, et al. Shape morphing smart 3D actuator materials for micro soft robot. Mater Today. 2020;41:243–69.

    Article  CAS  Google Scholar 

  40. Pang X, Lv JA, Zhu C, Qin L, Yu Y. Photodeformable azobenzene‐containing liquid crystal polymers and soft actuators. Adv Mater. 2019;31:1904224.

    Article  CAS  Google Scholar 

  41. Kim H, Lee JA, Ambulo CP, Lee HB, Kim SH, Naik VV, et al. Intelligently actuating liquid crystal elastomer‐carbon nanotube composites. Adv Funct Mater. 2019;29:1905063.

    Article  CAS  Google Scholar 

  42. Bi M, He Y, Wang Y, Yang W, Qin B, Xu J, et al. Photo actuation performance of nanotube sheet incorporated azobenzene crosslinked liquid crystalline polymer nanocomposite. Polymers. 2019;11:735.

    Article  PubMed  PubMed Central  Google Scholar 

  43. Rau H. Photoisomerization of azobenzenes. Photochem. Photophys. 1990;2:119–41.

    Google Scholar 

  44. Heinz H, Vaia R, Koerner H, Farmer B. Photoisomerization of azobenzene grafted to layered silicates: simulation and experimental challenges. Chem Mater. 2008;20:6444–56.

    Article  CAS  Google Scholar 

  45. Choi J, Chung H, Yun J-H, Cho M. Photo-isomerization effect of the azobenzene chain on the opto-mechanical behavior of nematic polymer: A molecular dynamics study. Appl Phys Lett. 2014;105:221906.

  46. Kim H, Kim H, Choi J. Interface mechanics of liquid crystal polymer nanocomposites with high concentrations of MWCNTs. Compos Sci Technol. 2022;222:109376.

    Article  CAS  Google Scholar 

  47. Kim H, Choi J. Mechanical assessment of interfacial stability of LCP/MWCNT nanocomposites during phase transition. Compos A Appl Sci Manuf. 2023;167:107461.

    Article  CAS  Google Scholar 

  48. Choi J, Chung H, Yun J-H, Cho M. Molecular dynamics study on the photothermal actuation of a glassy photoresponsive polymer reinforced with gold nanoparticles with size effect. ACS Appl Mater Interfaces. 2016;8:24008–24.

    Article  CAS  PubMed  Google Scholar 

  49. Choi J, Shin H, Cho M. Multiscale multiphysical analysis of photo-mechanical properties of interphase in light-responsive polymer nanocomposites. Compos Sci Technol. 2018;160:32–41.

    Article  CAS  Google Scholar 

  50. Kim H, Choi J. A lamellar-morphology-based computational modeling for predicting the thermal conductivity of semicrystalline polymers. Int J Mech Sci. 2024;282:109622.

    Article  Google Scholar 

  51. Kim H, Choi J. Influence of crystalline structure on creep resistance capability in semi-crystalline Polymers: a coarse-grained molecular dynamics study. Int J Fatigue. 2024;188:108517.

    Article  CAS  Google Scholar 

  52. Kim H, Won D, Ko SH, Choi J. Thermodynamic mechanism governing the coalescence of conductive particles in PEDOT: PSS under laser irradiation. Macromolecules. 2024;57:2048–56.

    Article  CAS  Google Scholar 

  53. Ma R, Wang Y, Huang H, Zhao X, Li X, Zhang L, et al. Insight into the fracture properties and molecular mechanism of polyurethane. Macromolecules. 2024;57:4484–94.

    Article  CAS  Google Scholar 

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Acknowledgements

This study was supported by a National Research Foundation of Korea (NRF) grant (RS-2023-00210865) funded by the Korean government (MSIT).

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  1. Department of Mechanical Design Engineering, Hanyang University, Seoul, Republic of Korea

    Hongdeok Kim & Joonmyung Choi

  2. Department of Mechanical Engineering, BK21 FOUR ERICA-ACE Center, Hanyang University, Sangnok-gu Ansan, Republic of Korea

    Hongdeok Kim & Joonmyung Choi

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  1. Hongdeok Kim
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Correspondence to Joonmyung Choi.

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Kim, H., Choi, J. A computational method for characterizing molecular-scale load transfer in polymer systems with structural heterogeneity. Polym J 57, 385–394 (2025). https://doi.org/10.1038/s41428-024-00997-4

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