Abstract
Various configurations are commonly observed in graphene grown by chemical vapour deposition including ripples and wrinkles. Standing self-adhered graphene wrinkles may fold over after reaching a certain height and lead to collapsed graphene wrinkles. We employ a continuous approximation to predict the morphology of collapsed graphene wrinkles supported by various metal substrates. Our model is based on a balance between the elastic bending and the van der Waals (vdW) interaction energies. We partition the geometry of the wrinkle into three constituent parts and express the total energy of the system as the sum of these three independent energy components. Variational calculus is utilised to minimise each energy component and derive parametric solutions for the shape of the corresponding part. We apply the 6-12 Lennard-Jones potential to model the strengths of the graphene-substrate vdW interactions. While we take into account two potential conformations for collapsed wrinkles, our analysis reveals that the folded bilayer is always followed by a flat region. This model also predicts the critical height of the self-adhered wrinkle providing consistent results with previous experimental and theoretical data with regards to this transition height.