The sensitivity of Graphene 'Snap-through' to substrate geometry

We study theoretically the deposition of Few Layer Graphene sheets onto a grooved substrate incorporating adhesion between substrate and sheet. We develop a model to understand the equilibrium of the sheet allowing for partial conformation of sheet to substrate. This model gives new insight into recent observations of 'snap-through' from flat to conforming states and emphasizes the crucial role of substrate shape in determining the nature of this transition. Our analytical results are consistent with numerical simulations using a van der Waals-like interaction . Finally we propose a novel substrate shape that should exhibit a continuous, rather than 'snap-through', transition.