Non-Hookean Mechanics of Crystalline Membranes

Abstract

Graphene is the simplest crystalline membrane and therefore the ideal material to test mechanics at the ultimate, atomic thickness limit. It is well known from experiments performed at high stress that graphene is one of the stiffest materials ever studied. At the same time, any thin material is always crumpled. In the case of graphene, crumpling can arise from static wrinkling or thermal fluctuations (flexural phonons). In this dissertation, we experimentally studied the effect of this crumpling on stretching and bending graphene. First, we developed a method to measure the mechanical response of suspended graphene at low stress. We found that the stretching stiffness of graphene is reduced by up to 10 times because of crumpling. We probed the contribution to stretching due to flexural phonons through temperature-dependent measurements. We probed the contribution due to static wrinkling by measuring changes in mechanical response when modifying membrane geometry in-situ. From this, we found that static wrinkles are the dominant source of crumpling. Second, we observed nonlinear stress-strain curves while applying high stress to our suspended graphene samples. We studied this nonlinearity in detail by comparing two complementary measurements of strain obtained from interferometric profilometry and Raman spectroscopy. This allowed us to measure the strength of crumpling and compare our data to recent theory. We found that stress/strain relationship in crumpled in graphene is described by a non-linear Hooke’s law with an exponent of ~0.14, which is good agreement with theory. Finally, we developed process flows to fabricate graphene cantilevers, stable in vacuum and air. We estimated that their bending rigidities are at least 100 times higher than what is expected for flat graphene. It is likely that this increase in the bending rigidity is also associated with crumpling.