Conformation of graphene folding around single-walled carbon nanotubes

  • Tom Dyer
  • Ngamta Thamwattana
  • Barry Cox
Original Paper


The low bending rigidity of graphene facilitates the formation of folds into the structure. This curvature change affects the reactivity and electron transport of the sheet. One novel extension of this is the intercalation of small molecules into these folds. We construct a model incorporating a single-walled carbon nanotube into a sheet of folded graphene. Variational calculus techniques are employed to determine the minimum energy structure and the resulting curves are shown to agree well with molecular dynamics study.

Graphical Abstract

Using calculus of variations, the elastic bending energy and van der Waals energy are minimised giving rise to Euler-Lagrange equation for which analytical solutions are derived to determine the optimal curved sturctures of graphene wrapped around carbon nanotubes . Overall agreement between the analytical solutions (with different values of bending rigidities) and results from molecular dynamics simulations (grey) is shown here for (6,6), (8,8) and (10,10) armchair nanotubes, respectively.


Carbon nanotubes Graphene Calculus of variations Elastic energy van der Waals force 



The authors are grateful to A/Prof. James McCoy (University of Newcastle) for many helpful comments and suggestions. Thamwattana also acknowledges the support from the School of Mathematics and Applied Statistics at the University of Wollongong.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Applied StatisticsUniversity of WollongongWollongongAustralia
  2. 2.School of Mathematical and Physical SciencesUniversity of NewcastleCallaghanAustralia
  3. 3.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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