title: Elastic coupling between layers in two-dimensional materials.
abstract: 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.
authors.affiliation: 1] School of Physics, Georgia Institute of Technology, 837 State Street Atlanta, Georgia 30332-0430, USA [2] Advanced Science Research Center and City College New York, City University of New York, 85 St Nicholas Terrace New York, New York 10031, USA.
authors.forename: Yang
authors.initials: Y
authors.lastname: Gao
authors.affiliation: Department of Applied Physics, Hanyang University, Ansan 426-791, South Korea.
authors.forename: Suenne
authors.initials: S
authors.lastname: Kim
authors.affiliation: School of Physics, Georgia Institute of Technology, 837 State Street Atlanta, Georgia 30332-0430, USA.
authors.forename: Si
authors.initials: S
authors.lastname: Zhou
authors.affiliation: Department of Physics, National Taiwan Normal University, 88, Sec.4, Ting-Chou Road Taipei 116, Taiwan.
authors.forename: Hsiang-Chih
authors.initials: HC
authors.lastname: Chiu
authors.affiliation: Université de Lyon, CNRS, INSA-Lyon, LaMCoS UMR5259, Villeurbanne F69621, France.
authors.forename: Daniel
authors.initials: D
authors.lastname: Nélias
authors.affiliation: 1] School of Physics, Georgia Institute of Technology, 837 State Street Atlanta, Georgia 30332-0430, USA [2] Institut Néel, Université Grenoble Alpes-CNRS, BP 166 38042 Grenoble, France.
authors.forename: Claire
authors.initials: C
authors.lastname: Berger
authors.affiliation: 1] School of Physics, Georgia Institute of Technology, 837 State Street Atlanta, Georgia 30332-0430, USA [2] King Abdulaziz University, Department of Physics, Jeddah 21589, Saudi Arabia.
authors.forename: Walt
authors.initials: W
authors.lastname: de Heer
authors.affiliation: L-NESS, Department of Physics, Politecnico di Milano, Via Anzani 42 22100 Como, Italy.
authors.forename: Laura
authors.initials: L
authors.lastname: Polloni
authors.affiliation: L-NESS, Department of Physics, Politecnico di Milano, Via Anzani 42 22100 Como, Italy.
authors.forename: Roman
authors.initials: R
authors.lastname: Sordan
authors.affiliation: 1] School of Physics, Georgia Institute of Technology, 837 State Street Atlanta, Georgia 30332-0430, USA [2] Department of Chemistry, College of Staten Island, City University of New York, New York, New York 10314, USA.
authors.forename: Angelo
authors.initials: A
authors.lastname: Bongiorno
authors.affiliation: 1] School of Physics, Georgia Institute of Technology, 837 State Street Atlanta, Georgia 30332-0430, USA [2] Advanced Science Research Center and City College New York, City University of New York, 85 St Nicholas Terrace New York, New York 10031, USA.
authors.forename: Elisa
authors.initials: E
authors.lastname: Riedo