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Computational prediction of the molecular configuration of three-dimensional network polymers

Nature Materials volume 20, pages 1422–1430 (2021)Cite this article

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Abstract

The three-dimensional arrangement of natural and synthetic network materials determines their application range. Control over the real-time incorporation of each building block and functional group is desired to regulate the macroscopic properties of the material from the molecular level onwards. Here we report an approach combining kinetic Monte Carlo and molecular dynamics simulations that chemically and physically predicts the interactions between building blocks in time and in space for the entire formation process of three-dimensional networks. This framework takes into account variations in inter- and intramolecular chemical reactivity, diffusivity, segmental compositions, branch/network point locations and defects. From the kinetic and three-dimensional structural information gathered, we construct structure–property relationships based on molecular descriptors such as pore size or dangling chain distribution and differentiate ideal from non-ideal structural elements. We validate such relationships by synthesizing organosilica, epoxy–amine and Diels–Alder networks with tailored properties and functions, further demonstrating the broad applicability of the platform.

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Fig. 1: Network materials in decreasing order of their 3D structural configuration.
Fig. 2: Concepts of the framework exemplified for organosilica synthesis using TEOS; matrix-based kMC and MD simulations are interconnected to visualize the incorporation, building block by building block, of each FG at any t.
Fig. 3: Framework application for organosilica network synthesis with TEOS.
Fig. 4: Structure–property relationships for two network chemistries other than the organosilica case.
Fig. 5: Relevance of non-idealities for 3D Diels–Alder-based network structures (chemistry 3).

Data availability

Source data are provided with this paper. The remaining data that support the findings of this study are included within the manuscript and its supplementary files and available from the corresponding authors upon request.

Code availability

The software used to access the molecular configuration of 3D network polymers in this paper is freely accessible via https://lammps.sandia.gov. Representative input and processing scripts are available at https://github.com/ldkeer/NatMater_dekeer_2021.

References

  1. Flory, P. J. Network topology and the theory of rubber elasticity. Br. Polym. J. 17, 96–102 (1985).

    Article  CAS  Google Scholar 

  2. Kryven, I. Bond percolation in coloured and multiplex networks. Nat. Commun. 10, 404 (2019).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  4. Sheiko, S. S. & Dobrynin, A. V. Architectural code for rubber elasticity: from supersoft to superfirm materials. Macromolecules 52, 7531–7546 (2019).

    Article  CAS  Google Scholar 

  5. LLorca, J. On the quest for the strongest materials. Science 360, 264–265 (2018).

    Article  CAS  Google Scholar 

  6. Berman, D., Erdemir, A. & Sumant, A. V. Graphene: a new emerging lubricant. Mater. Today 17, 31–42 (2014).

    Article  CAS  Google Scholar 

  7. Anderson, M. W. & Klinowski, J. Direct observation of shape selectivity in zeolite ZSM-5 by magic-angle-spinning NMR. Nature 339, 200–203 (1989).

    Article  CAS  Google Scholar 

  8. Rimer, J. D. Rational design of zeolite catalysts. Nat. Catal. 1, 488–489 (2018).

    Article  CAS  Google Scholar 

  9. Boerjan, W., Ralph, J. & Baucher, M. Lignin biosynthesis. Annu. Rev. Plant Biol. 54, 519–546 (2003).

    Article  CAS  Google Scholar 

  10. Burg, J. A. & Dauskardt, R. H. Elastic and thermal expansion asymmetry in dense molecular materials. Nat. Mater. 15, 974–980 (2016).

    Article  CAS  Google Scholar 

  11. Owens, G. J. et al. Sol–gel based materials for biomedical applications. Prog. Mater. Sci. 77, 1–79 (2016).

    Article  CAS  Google Scholar 

  12. Loccufier, E. et al. Silica nanofibrous membranes for the separation of heterogeneous azeotropes. Adv. Funct. Mater. 28, 1804138 (2018).

    Article  CAS  Google Scholar 

  13. Caló, E. & Khutoryanskiy, V. V. Biomedical applications of hydrogels: a review of patents and commercial products. Eur. Polym. J. 65, 252–267 (2015).

    Article  CAS  Google Scholar 

  14. D’hooge, D. R., Van Steenberge, P. H. M., Reyniers, M.-F. & Marin, G. B. The strength of multi-scale modeling to unveil the complexity of radical polymerization. Prog. Polym. Sci. 58, 59–89 (2016).

    Article  CAS  Google Scholar 

  15. Matyjaszewski, K. Advanced materials by atom transfer radical polymerization. Adv. Mater. 30, 1706441 (2018).

    Article  CAS  Google Scholar 

  16. Van Steenberge, P. H. M. et al. Visualization and design of the functional group distribution during statistical copolymerization. Nat. Commun. 10, 3641 (2019).

    Article  CAS  Google Scholar 

  17. Di Lorenzo, F. & Seiffert, S. Nanostructural heterogeneity in polymer networks and gels. Polym. Chem. 6, 5515–5528 (2015).

    Article  CAS  Google Scholar 

  18. Gu, Y., Zhao, J. & Johnson, J. A. Polymer networks: from rubbers and gels to porous frameworks. Angew. Chem. Int. Ed. 59, 5022–5049 (2020).

    Article  CAS  Google Scholar 

  19. Sandakov, G. I., Smirnov, L. P., Sosikov, A. I., Summanen, K. T. & Volkova, N. N. NMR analysis of distribution of chain lengths between crosslinks of polymer networks. J. Polym. Sci. Polym. Phys. 32, 1585–1592 (1994).

    Article  CAS  Google Scholar 

  20. Mathur, A. M. & Scranton, A. B. Characterization of hydrogels using nuclear magnetic resonance spectroscopy. Biomaterials 17, 547–557 (1996).

    Article  CAS  Google Scholar 

  21. Tripathi, A. K., Neenan, M. L., Sundberg, D. C. & Tsavalas, J. G. Influence of n-alkyl ester groups on efficiency of crosslinking for methacrylate monomers copolymerized with EGDMA: experiments and Monte Carlo simulations of reaction kinetics and sol–gel structure. Polymer 96, 130–145 (2016).

    Article  CAS  Google Scholar 

  22. Kryven, I., Duivenvoorden, J., Hermans, J. & Iedema, P. D. Random graph approach to multifunctional molecular networks. Macromol. Theor. Simul. 25, 449–465 (2016).

    Article  CAS  Google Scholar 

  23. Van Steenberge, P. H. M. et al. Linear gradient quality of ATRP copolymers. Macromolecules 45, 8519–8531 (2012).

    Article  CAS  Google Scholar 

  24. D’hooge, D. R. In silico tracking of individual species accelerating progress in macromolecular engineering and design. Macromol. Rapid Commun. 39, 1800057 (2018).

    Article  CAS  Google Scholar 

  25. Fierens, S. K. et al. Model-based design to push the boundaries of sequence control. Macromolecules 49, 9336–9344 (2016).

    Article  CAS  Google Scholar 

  26. Buback, M., Feldermann, A., Barner-Kowollik, C. & Lacik, I. Propagation rate coefficients of acrylate–methacrylate free-radical bulk copolymerizations. Macromolecules 34, 5439–5448 (2001).

    Article  CAS  Google Scholar 

  27. Burg, J. A. et al. Hyperconnected molecular glass network architectures with exceptional elastic properties. Nat. Commun. 8, 1019 (2017).

    Article  CAS  Google Scholar 

  28. Schwab, F. K. & Denniston, C. Reaction and characterisation of a two-stage thermoset using molecular dynamics. Polym. Chem. 10, 4413–4427 (2019).

    Article  CAS  Google Scholar 

  29. Zanjani, M. B. et al. Computational investigation of the effect of network architecture on mechanical properties of dynamically cross-linked polymer materials. Macromol. Theor. Simul. 28, 1900008 (2019).

    Article  CAS  Google Scholar 

  30. Oliver, M. S., Dubois, G., Sherwood, M., Gage, D. M. & Dauskardt, R. H. Molecular origins of the mechanical behavior of hybrid glasses. Adv. Funct. Mater. 20, 2884–2892 (2010).

    Article  CAS  Google Scholar 

  31. Kilic, K. I. & Dauskardt, R. H. Design of ultrastiff organosilicate hybrid glasses. Adv. Funct. Mater. 29, 1904890 (2019).

    Article  CAS  Google Scholar 

  32. Talati, M., Albaret, T. & Tanguy, A. Atomistic simulations of elastic and plastic properties in amorphous silicon. Europhys. Lett. 86, 66005 (2009).

    Article  CAS  Google Scholar 

  33. Kawamoto, K., Zhong, M. J., Wang, R., Olsen, B. D. & Johnson, J. A. Loops versus branch functionality in model click hydrogels. Macromolecules 48, 8980–8988 (2015).

    Article  CAS  Google Scholar 

  34. Dušek, K. & Patterson, D. Transition in swollen polymer networks induced by intramolecular condensation. J. Polym. Sci. Polym. Phys. 6, 1209–1216 (1968).

    Article  Google Scholar 

  35. Panyukov, S. Loops in polymer networks. Macromolecules 52, 4145–4153 (2019).

    Article  CAS  Google Scholar 

  36. Mita, I. & Horie, K. Diffusion-controlled reactions in polymer systems. J. Macromol. Sci. Polym. Rev. 27, 91–169 (1987).

    Article  Google Scholar 

  37. Pouxviel, J. C., Boilot, J. P., Beloeil, J. C. & Lallemand, J. Y. NMR study of the sol/gel polymerization. J. Non-Cryst. Solids 89, 345–360 (1987).

    Article  CAS  Google Scholar 

  38. Tang, J., Chen, Z., Fu, A. W. & Cheung, D. W. Capabilities of outlier detection schemes in large datasets, framework and methodologies. Knowl. Inf. Syst. 11, 45–84 (2007).

    Article  Google Scholar 

  39. Xia, B. et al. Preparation of silica coatings with continuously adjustable refractive indices and wettability properties via sol–gel method. RSC Adv. 8, 6091–6098 (2018).

    Article  Google Scholar 

  40. Yang, J., Lin, G.-S., Mou, C.-Y. & Tung, K.-L. Mesoporous silica thin membrane with tunable pore size for ultrahigh permeation and precise molecular separation. ACS Appl. Mater. Interfaces 12, 7459–7465 (2020).

    Article  CAS  Google Scholar 

  41. Daelemans, L., Van Paepegem, W., D’hooge, D. R. & De Clerck, K. Excellent nanofiber adhesion for hybrid polymer materials with high toughness based on matrix interdiffusion during chemical conversion. Adv. Funct. Mater. 29, 1807434 (2019).

    Article  CAS  Google Scholar 

  42. Li, J. & Mooney, D. J. Designing hydrogels for controlled drug delivery. Nat. Rev. Mater. 1, 16071 (2016).

    Article  CAS  Google Scholar 

  43. Oehlenschlaeger, K. K. et al. Adaptable hetero Diels–Alder networks for fast self-healing under mild conditions. Adv. Mater. 26, 3561–3566 (2014).

    Article  CAS  Google Scholar 

  44. Zhou, J. et al. Thermally reversible Diels–Alder-based polymerization: an experimental and theoretical assessment. Polym. Chem. 3, 628–639 (2012).

    Article  CAS  Google Scholar 

  45. Zhou, J., Yu, G. & Huang, F. Supramolecular chemotherapy based on host–guest molecular recognition: a novel strategy in the battle against cancer with a bright future. Chem. Soc. Rev. 46, 7021–7053 (2017).

    Article  CAS  Google Scholar 

  46. Harada, A., Takashima, Y. & Nakahata, M. Supramolecular polymeric materials via cyclodextrin–guest interactions. Acc. Chem. Res. 47, 2128–2140 (2014).

    Article  CAS  Google Scholar 

  47. Chakma, P. & Konkolewicz, D. Dynamic covalent bonds in polymeric materials. Angew. Chem. Int. Ed. 58, 9682–9695 (2019).

    Article  CAS  Google Scholar 

  48. Zou, W., Dong, J., Luo, Y., Zhao, Q. & Xie, T. Dynamic covalent polymer networks: from old chemistry to modern day innovations. Adv. Mater. 29, 1606100 (2017).

    Article  CAS  Google Scholar 

  49. St John, N. A. & George, G. A. Cure kinetics and mechanisms of a tetraglycidyl-4,4′-diaminodiphenylmethane/diaminodiphenylsulphone epoxy resin using near i.r. spectroscopy. Polymer 33, 2679–2688 (1992).

    Article  Google Scholar 

  50. Stockmayer, W. H. Theory of molecular size distribution and gel formation in branched-chain polymers. J. Chem. Phys. 11, 45–55 (1943).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

L.D.K. acknowledges the research foundation Flanders (FWO; 1S37517N). P.H.M.V.S. and L.D. acknowledge FWO through a postdoctoral fellowship (12C4319N and 12ZR520N). D.R.D acknowledges FWO through G.0H52.16N and Flemish Government and Flanders Innovation & Entrepreneurship (Vlaio) through the Moonshot project P2C (HBC.2019.0114). The computational resources (Stevin Supercomputer Infrastructure) and services used in this work were provided by the Flemish Supercomputer Center, funded by Ghent University, FWO and the Flemish Government, department Economics, Science and Innovation (EWI). The work at Stanford University was supported by the US Department of Energy, Office of Basic Energy Sciences, under contract no. DE-FG02-07ER46391. C.B.-K. acknowledges an Australian Research Council Laureate Fellowship enabling his photochemical research programme as well as the Queensland University of Technology for key support. H.F. acknowledges Australian Research Council funding through a Discovery Early Career Researcher Award (DE200101096). We thank E. Loccufier for discussion regarding the interpretation of the experimental data for the membrane filtration. We thank J. Pelloth for carefully conducting initial kinetic experiments on the Diels–Alder chemistry.

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Authors and Affiliations

  1. Laboratory for Chemical Technology (LCT), Ghent University, Ghent, Belgium

    Lies De Keer, Paul H. M. Van Steenberge, Marie-Françoise Reyniers & Dagmar R. D’hooge

  2. Department of Materials Science and Engineering, Stanford University, Stanford, CA, USA

    Karsu I. Kilic & Reinhold H. Dauskardt

  3. Centre for Textile Science and Engineering (CTSE), Ghent University, Ghent, Belgium

    Lode Daelemans, Karen De Clerck & Dagmar R. D’hooge

  4. Centre for Materials Science, School of Chemistry and Physics, Queensland University of Technology (QUT), Brisbane, Queensland, Australia

    Daniel Kodura, Hendrik Frisch & Christopher Barner-Kowollik

  5. Institute of Nanotechnology (INT), Karlsruhe Institute of Technology (KIT), Eggenstein-Leopoldshafen, Germany

    Christopher Barner-Kowollik

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Contributions

L.D.K, P.H.M.V.S and D.R.D. contributed to the development of matrix-based kMC simulations for network synthesis. L.D.K, P.H.M.V.S., M.-F.R. and D.R.D. focused on the determination of the scale-dependent model parameters of the kMC simulations and contributed to the construction of the associated structure–property relationships. D.R.D. developed the overall framework of the connection of kMC and MD simulations. K.I.K. and R.H.D. contributed to part of the MD simulations and interpretation, as well as the construction of the structure–property relationship for the organosilica case. L.D. and K.D.C. contributed to the experimental part concerning the epoxy–amine curing and the construction of the related structure–property relationship. D.K., H.F. and C.B.-K. conceptualized and conducted the experimental part concerning the Diels–Alder chemistry and the construction of the related structure–property relationships. All authors approved the manuscript and made revisions during its preparation.

Corresponding authors

Correspondence to Reinhold H. Dauskardt or Dagmar R. D’hooge.

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Peer review information Nature Materials thanks Simon Harrisson, Philippe Zinck and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–27, Discussion, Methods and Tables 1–5.

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De Keer, L., Kilic, K.I., Van Steenberge, P.H.M. et al. Computational prediction of the molecular configuration of three-dimensional network polymers. Nat. Mater. 20, 1422–1430 (2021). https://doi.org/10.1038/s41563-021-01040-0

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