Scaling relations for the interactions between curved graphene sheets in water

The effect of curvature and relative orientation between two curved graphene sheets in aqueous media is quantified by calculating the potential of mean force using molecular dynamics simulations and thermodynamic perturbation. The potential of mean force between two curved graphene sheets is found to scale as U_CG ∼ R^0.5d^-4.5, where R is the sheet radius of curvature and d is the inter-sheet distance. Further, a simple analytical calculation based on classical Hamaker theory and the Derjaguin approximation also arrives at the same scaling of interaction energy with respect to R and d. For the case where a misorientation, θ, exists between the two curved graphene sheets, the simulation results strongly suggest an inverse dependence of the potential of mean force on sin θ for θ > 30°. This result is very similar to the scaling predicted by the Derjaguin approximation for two cylinders crossed at an angle θ with respect to each other.