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Forensics of polymer networks


Our lives cannot be imagined without polymer networks, which range widely, from synthetic rubber to biological tissues. Their properties—elasticity, strain-stiffening and stretchability—are controlled by a convolution of chemical composition, strand conformation and network topology. Yet, since the discovery of rubber vulcanization by Charles Goodyear in 1839, the internal organization of networks has remained a sealed ‘black box’. While many studies show how network properties respond to topology variation, no method currently exists that would allow the decoding of the network structure from its properties. We address this problem by analysing networks’ nonlinear responses to deformation to quantify their crosslink density, strand flexibility and fraction of stress-supporting strands. The decoded structural information enables the quality control of network synthesis, comparison of targeted to actual architecture and network classification according to the effectiveness of stress distribution. The developed forensic approach is a vital step in future implementation of artificial intelligence principles for soft matter design.

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Fig. 1: Forensics methodology.
Fig. 2: Forensics of phantom networks.
Fig. 3: Elasticity and percolation transition.
Fig. 4: Forensics of brush network elasticity.
Fig. 5: Network topology classification.

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All data supporting the findings are provided as figures and accompanying tables in the article and Supplementary Information. Data files for all figures are available from the corresponding authors on request.


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This work was supported by the National Science Foundation under grants DMR 1921835 (S.S.S., M.M.), DMR 1921923 (A.V.D., M.J.), DMR 2049518 (A.V.D., Y.T., M.J.) and DMR 2004048 (S.S.S., F.V.). E.A.N. and D.A.I. acknowledge the Ministry of Science and Higher Education of the Russian Federation for financial support in the frame of state contract no. 075-15-2022-1117 from June 30, 2022. A.V.D. and S.S.S. are grateful to E. Samulski for the critical reading of the manuscript and numerous stimulating discussions. We acknowledge the contribution of B. J. Morgan and A. N. Keith to the synthesis of well-defined PBA elastomers and linear–bottlebrush–linear copolymers, reported previously. E.A.N. and D.A.I. acknowledge the European Synchrotron Radiation Facility for provision of synchrotron beamtime at the ID02 beamline and thank the staff of the European Synchrotron Radiation Facility and E. A. Bersenev for assistance.

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Authors and Affiliations



A.V.D. developed the concept and theoretical foundation; F.V. and M.M. performed the synthesis, characterization and mechanical testing of brush networks; Y.T. analysed correlations between the network structure and mechanical properties; M.J. and Y.T. performed molecular dynamics simulations of polymer networks and analysed their properties; E.A.N. and D.A.I. performed X-ray scattering measurements; and A.V.D. and S.S.S. were the primary writers of the manuscript and the principal investigators. All authors discussed the results and provided feedback on the manuscript.

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Correspondence to Andrey V. Dobrynin or Sergei S. Sheiko.

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Supplementary Figs. 1–13, Tables 1–5, equations (1)–(21) and network synthesis and experimental protocols.

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Dobrynin, A.V., Tian, Y., Jacobs, M. et al. Forensics of polymer networks. Nat. Mater. 22, 1394–1400 (2023).

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