Determining the Gaussian modulus and edge properties of 2D materials: From graphene to lipid bilayers

Matthew Zelisko, Fatemeh Ahmadpoor, Huajian Gao, Pradeep Sharma

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


The dominant deformation behavior of two-dimensional materials (bending) is primarily governed by just two parameters: bending rigidity and the Gaussian modulus. These properties also set the energy scale for various important physical and biological processes such as pore formation, cell fission and generally, any event accompanied by a topological change. Unlike the bending rigidity, the Gaussian modulus is, however, notoriously difficult to evaluate via either experiments or atomistic simulations. In this Letter, recognizing that the Gaussian modulus and edge tension play a nontrivial role in the fluctuations of a 2D material edge, we derive closed-form expressions for edge fluctuations. Combined with atomistic simulations, we use the developed approach to extract the Gaussian modulus and edge tension at finite temperatures for both graphene and various types of lipid bilayers. Our results possibly provide the first reliable estimate of this elusive property at finite temperatures and appear to suggest that earlier estimates must be revised. In particular, we show that, if previously estimated properties are employed, the graphenefree edge will exhibit unstable behavior at room temperature. Remarkably, in the case of graphene, we show that the Gaussian modulus and edge tension even change sign at finite temperatures.

Original languageEnglish (US)
Article number068002
JournalPhysical Review Letters
Issue number6
StatePublished - Aug 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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