▎ 摘　　要

Superior flexibility of the planar graphene allotropes containing pentagons and heptagons was demonstrated by evaluating the bending modulus through first-principles calculations. The bending moduli of planar graphene allotropes depend closely on the geometry and bending direction. Compared with pristine graphene, incorporation of pentagons and heptagons will change the bond length, planar carbon density and geometric contribution of carbon atoms, which further degrade the bending moduli of graphene allotropes. Generally, the longer the average bond length is, the lower bending modulus will be. While large planar carbon density and geometric contribution of the hexagons result in high bending modulus. Meanwhile, bending direction depended bending modulus suggests the mechanical anisotropy of the graphene allotropes. Our calculations not only provide a general approach to understand the flexibility of graphene allotropes, but also give an important clue to design high-performance flexible devices.