Mechanics of self-folding of single-layer graphene

The extreme out-of-plane flexibility makes single-layer graphene vulnerable to self-folding, driven by van der Waals interactions. Racket shaped bilayer graphene edges form after self-folding, which can significantly affect the electrical properties of graphenes. To study the self-folding behaviour, a theoretical model based on finite deformation beam theory is established. The critical folding lengths for both metastable and stable self-folding, as well as the edge profile of a folded single-layer graphene, are given. They all agree very well with MD simulations. MD simulations also show that folding directions do not have strong influence on the shape of folded graphene edges.