Adhesion mechanics of graphene on textured substrates

Abstract

Graphene, the two dimensional form of carbon, has excellent mechanical, electrical and thermal properties and a variety of potential applications including nano-electro-mechanical systems, protective coatings, transparent electrodes in display devices and biological applications. Adhesion plays a key role in many of these applications. In addition, it has been proposed that the electronic properties of graphene can be affected by elastic deformation caused by adhesion of graphene to its substrate. In light of this, we present here a continuum mechanics based theoretical framework to understand the effect of nanoscale morphology of substrates on adhesion and mechanics of graphene. In the first part, we analyzed the adhesion mechanics of graphene on one and two dimensional periodic corrugations. We carried out molecular statics simulations and found the results to be in good agreement with our theory. We modeled adhesive interactions as surface forces due to a Lennard–Jones 6–12 potential in both our analysis and simulations and in principle any other interaction potential can be used with our methodology. The results show that graphene adheres conformally to substrates with large curvatures. We showed in principle that the theory developed here can be extended to substrates with arbitrary textures that can be represented by a Fourier series.In the second part, we study the mechanics of peeling of graphene ribbons from one dimensional sinusoidally textured substrates. In the molecular statics simulations, we observed two key features in the peel mechanics of the ribbons - the ribbons slide over the substrate and undergo adhesion and peeling near the crack front in an oscillatory manner, the frequency of which reveals the wavelength of the underlying substrate. Our theory qualitatively captures these features of the peel mechanics and is general enough that it can be extended to other two dimensional materials like Molybdenum Disulphide (MoS2), Boron Nitride (BN) or other thin films and different kinds of interaction potentials.