Determining graphene adhesion via substrate-regulated morphology of graphene

Understanding the adhesion between graphene and other materials is crucial for achieving more reliable graphene-based applications in electronic devices and nanocomposites. The ultra-thin profile of graphene, however, poses a significant challenge to direct measurement of its adhesion property using conventional approaches. We show that there is a strong correlation between the morphology of graphene on a compliant substrate with patterned surface and the graphene-substrate adhesion. We establish an analytic model to quantitatively determine such a strong correlation. Results show that, depending on the graphene-substrate adhesion, number of graphene layers, and substrate stiffness, graphene exhibits two distinct types of morphology: (I) graphene remains bonded to the substrate and corrugates to an amplitude up to that of the substrate surface patterns; (II) graphene debonds from the substrate and remains flat on top of the substrate surface patterns. The sharp transition between these two types of graphe...