Modeling Graphene Deformations Induced by Bucky-Ball and Bucky-Bowl Interactions

Nonplanar hydrocarbon structures, such as corannulene and sumanene, are of particular interest due to their bowl-shaped structures. These molecules can be conceptualized as truncated versions of a bucky-ball C₆₀, where the curvature is reduced and the boundary is hydrogenated. The ability to catalyze the inversion of these bowl-shaped structures using 2D materials like graphene has stimulated significant research into the interaction of these structures with graphene and the catalytic effect of graphene, reducing the energy barrier for bowl-to-bowl inversion. While it has been observed in simulations that the interaction with nonplanar structures can generate a dimple-shaped deformation in graphene sheet, no mathematical model has been formulated to determine such deformation profile. As such, this article proposes a model based on calculus of variational approach to study a dimple-shaped deformation in the graphene sheet induced by fullerenes and bowl-shaped structures. The dimple shapes are shown to depend on the orientations and configurations of fullerene, corannulene, and sumanene when facing graphene sheet. The results indicate that fullerene produces the deepest dimple profile in graphene, followed by corannulene and sumanene, respectively. These results are also consistent with findings found using density functional theory.