Adhesion mechanics of graphene on textured substrates

Graphene, the 2D form of carbon, has excellent mechanical, electrical and thermal properties and a variety of potential applications including NEMS, 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 analyze the adhesion mechanics of graphene on 1 and 2D periodic corrugations. We carried out molecular statics simulations and found the results to be in good agreement with our theory. We modeled adhesive interactions surface forces described by Lennard-Jones 6-12 potential in both our analysis and simulations and in principle can be extended to any other interaction potential. The results show that graphene adheres conformally to substrates with large curvatures. We showed in principal that the theory developed here can be extended to substrates of arbitrary shapes that can be represented by a Fourier series. In the second part, we study the mechanics of peeling of graphene ribbons from 1D 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 2D materials like MoS2, BN etc and different kinds of interaction potentials.