Interdependence of Morphological Parameters in Self-Assembled Twisted Bilayers of Folded Graphene

Previous studies have shown the possibility of obtaining folded twisted bilayer graphene and graphene ribbons through spontaneous self-tearing and peeling from a substrate [1]. Here we investigate the morphology of spontaneously self-grown nanoribbon structures using atomic force microscopy. Data reveals similar twist angle dependence of the width and interlayer separation, as well as a width-dependent fold radius. These observations can be described by an energy minimization model that includes bilayer formation, bending, tearing and substrate peeling processes. The corresponding energy densities are parameters determined by comparison with experimental data, with the bilayer adhesion energy density modeled by a Morse potential. We obtain explicit expressions for the radius-width dependence that are in good agreement with experimental observations. These relations provide further evidence of a strong dependence of the bilayer adhesion energy density on the twist angle.
[1] M. Temmen et al, Beilstein J. Nanotechnol. 4, 625 (2013); J. Annett and G. Cross, Nature 535, 271 (2016).