Graphene folding on flat substrates

Abstract

We present a combined experimental-theoretical study of graphene folding on flat substrates. The structure and deformation of the folded graphene sheet are experimentally characterized by atomic force microscopy. The local graphene folding behaviors are interpreted based on nonlinear continuum mechanics modeling and molecular dynamics simulations. Our study on self-folding of a trilayer graphene sheet reports a bending stiffness of about 6.57 eV, which is about four times the reported values for monolayer graphene. Our results reveal that an intriguing free sliding phenomenon occurs at the interlayer van der Waals interfaces during the graphene folding process. This work demonstrates that it is a plausible venue to quantify the bending stiffness of graphene based on its self-folding conformation on flat substrates. The findings reported in this work are useful to a better understanding of the mechanical properties of graphene and in the pursuit of its applications.

Topologically confined states at corrugations of gated bilayer graphene

“…These ripples can lead to interesting electronic [38][39][40], magnetic [41], and chemical properties [42], mostly due to the associated charge inhomogeneity and the changes in hybridization. In fact, folding graphene has been put forward as a way to modify its properties [43][44][45]; also, folded ribbons have been proposed as graphene-based electronic connectors between edges or graphene layers [46]. All these schemes are pointing to a novel path to tune the characteristics of graphene-based systems, giving rise to the so-called "origami" graphene [43,44,47].…”

Graphene as a Prototypical Model for Two-Dimensional Continuous Mechanics

“…Whereas the flexural rigidity of graphite flakes with thickness above 2.4 nm has been shown to follow the expected cubic law [36], a controversy exists. In case the atomic planes slip over each other, continuum theory predicts that D for multilayer graphene is proportional to the number of planes, which has been confirmed by some atomistic simulations [37,38]. On the experimental side, atomic force microscopy (AFM) measurement of the deformation of convex-buckled suspended graphene ribbons yielded D = 35.5 eV for bilayer graphene, with relative uncertainty of 50% [39].…”

“…This value is a factor of 8.3 smaller than that given in the last row of Table 1. However, the bending constant D of the self-folded bilayer could be around 3 eV-not 35 eV-if the atomic layers were bending without coupling, as predicted by molecular dynamics [38]. This would bring w b close to the value estimated from the tapering angle.…”

“…However, most of what has been predicted remains qualitatively correct for graphene deposited on a substrate. Of course, the shape of the folded sheet changes from that of Figure 1b to that of Figure 1a due to the underlying material [38]. The case of SiO 2 is very frequent: the driving force for folding is the difference σ gr-gr − σ gr-SiO 2 .…”

Interfacial Interactions in 1D and 2D Nanostructure-Based Material Systems

“…10.3b reveal the respective folding structures of mono-and trilayer graphene, in particular the regions along their folding edges [122]. Figure 10.3c shows an atomic force microscopy (AFM) image of one partially self-folded trilayer graphene sheet on a flat silicon oxide substrate [123]. It can be seen from the AFM topography image that a portion of the graphene sheet (*100 nm in width) is torn and flipped on top of the flat segment on the substrate.…”