The effect of intrinsic crumpling on the mechanics of free-standing graphene

Free-standing graphene is inherently crumpled in the out-of-plane direction due to dynamic flexural phonons and static wrinkling. We explore the consequences of this crumpling on the effective mechanical constants of graphene.We develop a sensitive experimental approach to probe stretching of graphene membranes under low applied stress at cryogenic to room temperatures. We find that the in-plane stiffness of graphene is 20 100Nm–1 at room temperature, much smaller than 340Nm–1 (the value expected for flat graphene). Moreover, while the in-plane stiffness only increases moderately when the devices are cooled down to 10 K, it approaches 300Nm–1 when the aspect ratio of graphene membranes is increased. These results indicate that softening of graphene at temperatures o400 K is caused by static wrinkling, with only a small contribution due to flexural phonons. Overall, these results explain the large variation in reported mechanical constants of graphene devices and pave the way towards controlling their mechanical properties.