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 20-100 N m(-1) at room temperature, much smaller than 340 N m(-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 300 N m(-1) when the aspect ratio of graphene membranes is increased. These results indicate that softening of graphene at temperatures <400 K is caused by static wrinkling, with only a small contribution due to flexural phonons. Together, these results explain the large variation in reported mechanical constants of graphene devices and pave the way towards controlling their mechanical properties.