Non-Hookean statistical mechanics of clamped graphene ribbons

Mark J. Bowick, Andrej Košmrlj, David R. Nelson, Rastko Sknepnek

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


Thermally fluctuating sheets and ribbons provide an intriguing forum in which to investigate strong violations of Hooke's Law: Large distance elastic parameters are in fact not constant but instead depend on the macroscopic dimensions. Inspired by recent experiments on free-standing graphene cantilevers, we combine the statistical mechanics of thin elastic plates and large-scale numerical simulations to investigate the thermal renormalization of the bending rigidity of graphene ribbons clamped at one end. For ribbons of dimensions W×L (with L≥W), the macroscopic bending rigidity κR determined from cantilever deformations is independent of the width when W<th, where th is a thermal length scale, as expected. When W>th, however, this thermally renormalized bending rigidity begins to systematically increase, in agreement with the scaling theory, although in our simulations we were not quite able to reach the system sizes necessary to determine the fully developed power law dependence on W. When the ribbon length L>p, where p is the W-dependent thermally renormalized ribbon persistence length, we observe a scaling collapse and the beginnings of large scale random walk behavior.

Original languageEnglish (US)
Article number104109
JournalPhysical Review B
Issue number10
StatePublished - Mar 22 2017

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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