Intrinsic ripples in graphene.

By A. Fasolino, J. H. Los, M. Katsnelson. Nature Materials, 2007

1,586 citations recorded by the source corpus.

The stability of two-dimensional (2D) layers and membranes is the subject of a long-standing theoretical debate. According to the so-called Mermin-Wagner theorem, long-wavelength fluctuations destroy the long-range order of 2D crystals. Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled. These fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes meaning that a 2D membrane can exist but will exhibit strong height fluctuations. The discovery of graphene, the first truly 2D crystal, and the recent experimental observation of ripples in suspended graphene make these issues especially important. Besides the academic interest, understanding the mechanisms of the stability of graphene is crucial for understanding electronic transport in this material that is attracting so much interest owing to its unusual Dirac spectrum and electronic properties. We address the nature of these height fluctuations by means of atomistic Monte Carlo simulations based on a very accurate many-body interatomic potential for carbon. We find that ripples spontaneously appear owing to thermal fluctuations with a size distribution peaked around 80 A which is compatible with experimental findings (50-100 A). This unexpected result might be due to the multiplicity of chemical bonding in carbon.

Subfields: Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/349327d24907b2fc0743270d3a9bd1d83e9b01a5

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In Materials Chemistry

1. N. M. R. Peres
2. K. Novoselov
3. Rui Huang
4. E. Hwang
5. E. Rossi
6. Francisco Guinea
7. S. Adam
8. A.K. Geim

Citations in the corpus

• Polymer Nanocomposites—A Comparison between Carbon Nanotubes, Graphene, and Clay as Nanofillers (2016, background): “Nanofillers can be categorized on the basis of their dimensions—one dimensional which include nanotubes and nanowires [3,4], two dimensional such as nanoclays [5] and graphene [6], and three dimensional such as spherical [7] and cubical nanoparticles [8].”
• Alignment of graphene nanoribbons by an electric-field (2009, background): “Thus, the edge disorder effects on structural [33] and mechanical properties [24] of graphene were neglected.”
• NONLINEAR MECHANICS OF SINGLE-ATOMIC-LAYER GRAPHENE SHEETS (2009, background): “C) interatomic distance (∼0.142nm) even for very large graphene sheets [Fasolino et al., 2007].”
• A review on mechanics and mechanical properties of 2D materials—Graphene and beyond (2016, background): “Theoretically, thermal rippling is inevitable [89], which may have profound effects on thermomechanical properties of graphene [10,11], including thermal expansion and temperature-dependent elastic modulus.”