Linear correlation between binding energy and Young's modulus in graphene nanoribbons

Graphene nanoribbons (GNRs) have been suggested as a promising material for its use as nanoelectromechanical reasonators for highly sensitive force, mass, and charge detection. Therefore the accurate determination of the size-dependent elastic properties of GNRs is desirable for the design of graphene-based nanoelectromechanical devices. In this study we determine the size-dependent Young's modulus and carbon-carbon binding energy in a homologous series of GNRs, C-4n(2)+6n+2H(6n+4) (n=2-12), with the use of all electron first principles computations. An unexpected linearity between the binding energy and Young's modulus is observed, making possible the prediction of the size-dependent Young's modulus of GNRs through a single point energy calculation of the GNR ground state. A quantitative-structure-property relationship is derived, which correlates Young's modulus to the total energy and the number of carbon atoms within the ribbon. In the limit of extended graphene sheets we determine the value of Young's modulus to be 1.09 TPa, in excellent agreement with experimental estimates derived for graphite and suspended graphene sheets.