Continuum Plate Theory and Atomistic Modeling to Find the Flexural Rigidity of a Graphene Sheet Interacting with a Substrate

Abstract

Using a combination of continuum modeling, atomistic simulations, and numerical optimization, we estimate the flexural rigidity of a graphene sheet. We consider a rectangular sheet that is initially parallel to a rigid substrate. The sheet interacts with the substrate by van der Waals forces and deflects in response to loading on a pair of opposite edges. To estimate the flexural rigidity, we model the graphene sheet as a continuum and numerically solve an appropriate differential equation for the transverse deflection. This solution depends on the flexural rigidity. We then use an optimization procedure to find the value of the flexural rigidity that minimizes the difference between the numerical solutions and the deflections predicted by atomistic simulations. This procedure predicts a flexural rigidity of 0.26 nN<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>nm</mml:mtext><mml:mo>=</mml:mo><mml:mn>1.62</mml:mn></mml:mrow></mml:math> eV.