Non-uniform Self-Folding of Impure Graphene

Planar graphene with extreme flexibility folds into three-dimension structures, holding promises in quantum- and nano-electronics with interesting geometries and properties. However, it is challenging to synthesize high-quality and uniform graphene on a large scale. The inevitable inhomogeneity, such as geometry variation and material impurity, yields imperfect graphene and tunable folded structures. This enables the diverse design of nanostructures with targeted configurations and engineered performances. The mechanics of non-uniform self-folding of impure graphene is explored through a finite-deformation varying-section beam model, the critical folding conditions, folded profiles, and maximum strains dependent on the non-uniform half-length are theoretically determined. Molecular dynamics (MD) simulations are performed to verify theoretical solutions. Our study is helpful for the design of programmable quantum- and nano-electronics to achieve desired properties.