Nanoindentation of graphene membranes using atomic force microscopy and molecular dynamics simulations

Abstract

This study focuses on the mechanical properties of graphene – a carbon allotrope consisting of a single layer of atoms arranged in a two-dimensional hexagonal lattice. Given the massive scientific research interest that graphene generated during the last few years, work directed at fully understanding its material properties and in turn its expected behaviour under different conditions has proved key to its wider utilisation. Specifically, understanding the mechanical response of graphene under different loads is deemed central in the design of graphene-based devices such as filtration membranes. This work focuses on the measurement of the elastic modulus of graphene, particularly for pristine and defective membranes using point-loading nanoindentation via atomic force microscopy. Few-layer and multi-layer graphene membranes prepared in-house via mechanical exfoliation as well as single-layer CVD-grown graphene membranes deposited on pre-fabricated microsieves were considered. Atomic force microscopy was the primary tool used to indent the graphene membranes and thereby measure the elastic modulus of graphene. While generally nanoindentation is considered a suitable technique for accurate modulus determination, this work reveals that testing parameters such as the spring constant of the cantilever used and the depth to which the membranes are indented affect the measurements obtained. The work presented emphasises the dependency of the measurements obtained on the exact methodology adopted. This points towards the need for an established set of guidelines to be followed such that the results across multiple research groups and testing platforms can be comparable. This work provides preliminary guidelines for this scope. Some applications, such as graphene-based filtration devices, exploit the presence of defects in the crystalline lattice of graphene to tailor its performance. In this work, gallium ion irradiation was used to introduce defects in the graphene membrane. Similar nanoindentation of the treated membranes revealed no clear trend as to whether the elastic modulus is affected by the applied treatment when compared to the untreated material. Finally, molecular dynamics simulations were performed to support and provide insight to the experimental work carried out. The results confirm the ability for simulations to replicate experimental results. As a significant contribution, this work highlights the limitations of the mathematical model used to calculate the elastic modulus from the obtained indentation curves. The use of mathematical methods to ascertain whether experimental results obtained are accurate is suggested.