▎ 摘　　要

Graphene is an ideal membrane for selective separation because of its unique properties and single-layer structure. Considerable efforts have been made to alter the permeability of graphene. In this study, we investigate the pathways for an oxygen atom to pass through graphene sheets. We also identify the effect of the ripple's curvature in graphene sheets on the energy barrier of permeation through density functional theory calculations. Results show that oxygen atoms can easily pass through the concave side of graphene ripples with a large curvature. The analysis of transition states reveals that the space where an oxygen atom passes through keeps an almost identical structure with similar bond lengths regardless of the curvature. We find that the Cu(111) substrate may draw out the C-C bond lengths of graphene at the Cu(111) surface because of the strong interaction between the graphene edge and copper atoms. Consequently, the energy barrier of the permeation of oxygen atoms through graphene is reduced. These results suggest that the rippling of graphene significantly affects its permeation.