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Energetics of graphene origami and their “spatial resolution”

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Abstract

The extreme thinness of graphene combined with its tensile strength made it a material appealing for discussing and even making complex cut-kirigami or folded-only origami. In the case of origami, its stability is mainly defined by the positive energy of the single- or double-fold curvature deformation counterbalanced by the energy reduction due to favorable van der Waals contacts. These opposite sign contributions also have notably different scaling with the size L of the construction, the contacts contributing in proportion to area ~ L2, single folds as ~ L, and highly strained double-fold corners as only ~ L0 = const. Computational analysis with realistic atomistic-elastic representation of graphene allows one to quantify these energy contributions and to establish the length scale, where a single fold is favored (7 nm < L < 21 nm) or a double fold becomes sustainable (L > 21 nm), defining the size of the smallest possible complex origami designs as L ≫ 21 nm.

Impact statement

The flexibility and foldability of graphene are some of its attractive properties inspiring the designs of origami structures with potential use in flexible electronics and electromechanical nanodevices. The aesthetics, precision, and ease of folding and stability, however, have limitations at the nanoscale. Here, by means of large-scale atomistic calculations and continuum models, it is quantified how the dimensions determine the relative robustness of the elementary folds of graphene (a single fold and a double-folded graphene forming a single order-four vertex), thereby mapping the spatial resolution limits and providing important guidance for graphene nano-origami realizations.

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Acknowledgments

This work was supported by the US Department of Defense: Air Force Office of Scientific Research (AFOSR), Grant #FA9550-17-1-0262. Z.Z. and Z.H. at NUAA were supported by the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (No. MCMS-E-0420K01). Computer resources were provided by XSEDE, which is supported by National Science Foundation (NSF) Grant #OCI-1053575, under allocation TG-DMR100029, and the NOTS cluster at Rice University acquired with funds from NSF Grant #CNS-1338099.

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Authors and Affiliations

  1. Department of Materials Science and NanoEngineering, Rice University, Houston, TX, USA

    Yang Yang, Evgeni S. Penev & Boris I. Yakobson

  2. State Key Laboratory of Mechanics and Control of Mechanical Structures, Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, Institute of Nano Science, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Zhuhua Zhang & Zhili Hu

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  1. Yang Yang
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  2. Zhuhua Zhang
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  3. Zhili Hu
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  4. Evgeni S. Penev
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  5. Boris I. Yakobson
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Correspondence to Boris I. Yakobson.

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Yang, Y., Zhang, Z., Hu, Z. et al. Energetics of graphene origami and their “spatial resolution”. MRS Bulletin 46, 481–486 (2021). https://doi.org/10.1557/s43577-020-00018-8

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  • DOI: https://doi.org/10.1557/s43577-020-00018-8

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