Two- and three-dimensional self-folding of free-standing graphene by liquid evaporation

Two-dimensional (2-D) atomically thin graphene has exhibited overwhelming excellent properties over its bulk counterpart graphite, yet the broad applications and explorations of its unprecedented properties require a diversity of its geometric morphologies, beyond its inherently planar structures. In this study, we present a self-folding approach for converting 2-D planar free-standing graphene to 2-D and 3-D folded structures through the evaporation of its liquid solutions. This approach involves competition between the surface energy of the liquid, and the deformation energy and van der Waals energy of graphene. An energy-based theoretical model is developed to describe the self-folding process during liquid evaporation by incorporating both graphene dimensions and surface wettability. The critical elastocapillary length by liquid evaporation is extracted and exemplified by investigating three typical graphene geometries with rectangular, circular and triangular shapes. After the complete evaporation of the liquid, the critical self-folding length of graphene that can enable a stable folded pattern by van der Waals energy is also obtained. In parallel, full-scale molecular dynamics (MD) simulations are performed to monitor the evolution of deformation energies and folded patterns with liquid evaporation. The simulation results demonstrate the formation of 2-D folded racket-like and 3-D folded cone-like patterns and show remarkable agreement with theoretical predictions in both energy variations and folded patterns. This work offers quantitative guidance for controlling the self-folding of graphene and other 2-D materials into complex structures by liquid evaporation.