Two-dimensional materials, such as graphene and MoS2, are films of a few atomic layers in thickness with strong in-plane bonds and weak interactions between the layers. The in-plane elasticity has been widely studied in bending experiments where a suspended film is deformed substantially; however, little is known about the films’ elastic modulus perpendicular to the planes, as the measurement of the out-of-plane elasticity of supported 2D films requires indentation depths smaller than the films’ interlayer distance. Here, we report on sub-ångström-resolution indentation measurements of the perpendicular-to-the-plane elasticity of 2D materials. Our indentation data, combined with semi-analytical models and density functional theory, are then used to study the perpendicular elasticity of few-layer-thick graphene and graphene oxide films. We find that the perpendicular Young’s modulus of graphene oxide films reaches a maximum when one complete water layer is intercalated between the graphitic planes. This non-destructive methodology can map interlayer coupling and intercalation in 2D films.
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Y.G., S.K., H-C.C. and E.R., acknowledge the support of the Office of Basic Energy Sciences of the US Department of Energy (DE-FG02-06ER46293). S.Z. and A.B. acknowledge the support of the National Science Foundation (NSF) grant CMMI 1436375. S.Z., A.B., C.B. and W.d.H. acknowledge the support of the NSF grant DMR-0820382. C.B. acknowledges partial financial support from the European Flagship Graphene. A.B. acknowledges the support of the NSF grant CHE-0946869. R.S. acknowledges the support of the Italian Cariplo Foundation, project No. 2011-0373. We thank J-P. Turmaud for the EG on Si sample.
The authors declare no competing financial interests.
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Gao, Y., Kim, S., Zhou, S. et al. Elastic coupling between layers in two-dimensional materials. Nature Mater 14, 714–720 (2015). https://doi.org/10.1038/nmat4322
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