Measuring graphene's bending stiffness

Graphene's unusual combination of in-plane strength and out-of-plane flexibility makes it promising for mechanical applications. A key value is the bending stiffness, which microscopic theories and measurements of phonon modes in graphite put at $\kappa_{\mathrm{0}}=$1.2 eV.$^{\mathrm{1}}$ However, theories of the effects of thermal fluctuations in 2D membranes predict that the bending stiffness at longer length scales could be orders of magnitude higher.$^{\mathrm{2,3}}$ This macroscopic value has not been measured. Here we present the first direct measurement of monolayer graphene's bending stiffness, made by mechanically lifting graphene off a surface in a liquid and observing both motion induced by thermal fluctuations and the deflection caused by gravity's effect on added weights. These experiments reveal a value $\kappa_{\mathrm{eff}}=$12 keV at room temperature --- four orders of magnitude higher than $\kappa_{\mathrm{0}}$. These results closely match theoretical predictions of the effects of thermally-induced fluctuations which effectively thicken the membrane, dramatically increasing its bending stiffness at macroscopic length scales. [1] A. Fasolino et al., Nat. Mater. (2007) [2] D. R. Nelson and L. Peliti, J Physique (1987) [3] F. L. Braghin and N. Hasselmann, Phys Rev B (2010)