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Variational model for collapsed graphene wrinkles

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Abstract

Various configurations are commonly observed in graphene grown by chemical vapour deposition including ripples and wrinkles. Standing self-adhered graphene wrinkles may fold over after reaching a certain height and lead to collapsed graphene wrinkles. We employ a continuous approximation to predict the morphology of collapsed graphene wrinkles supported by various metal substrates. Our model is based on a balance between the elastic bending and the van der Waals (vdW) interaction energies. We partition the geometry of the wrinkle into three constituent parts and express the total energy of the system as the sum of these three independent energy components. Variational calculus is utilised to minimise each energy component and derive parametric solutions for the shape of the corresponding part. We apply the 6–12 Lennard–Jones potential to model the strengths of the graphene–substrate vdW interactions. While we take into account two potential conformations for collapsed wrinkles, our analysis reveals that the folded bilayer is always followed by a flat region. This model also predicts the critical height of the self-adhered wrinkle providing consistent results with previous experimental and theoretical data with regards to this transition height.

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Acknowledgements

Mr. Aljedani is pleased to acknowledge King Abdulaziz University for the provision of a fully funded scholarship to help making this work achievable at the University of Adelaide.

Funding

This research was conducted under a fully funded scholarship provided by King Abdulaziz University for Jabr Aljedani

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Authors and Affiliations

  1. The Applied College, King Abdulaziz University, Jeddah, Makkah, 21589, Saudi Arabia

    Jabr Aljedani

  2. School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia

    Jabr Aljedani, Michael J. Chen & Barry J. Cox

Authors
  1. Jabr Aljedani
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  2. Michael J. Chen
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  3. Barry J. Cox
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Contributions

All authors conceive and plan this study. Jabr Aljedani performs the calculations, analyses the results, and creates all figures under the supervision of Michael Chen and Barry Cox. The paper is initially designed and written by Jabr Aljedani, and the final version of the paper is reviewed, edited, and approved by Michael Chen and Barry Cox.

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Correspondence to Jabr Aljedani.

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Aljedani, J., Chen, M.J. & Cox, B.J. Variational model for collapsed graphene wrinkles. Appl. Phys. A 127, 886 (2021). https://doi.org/10.1007/s00339-021-05000-y

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