Buckled circular monolayer graphene: a graphene nano-bowl

TL;DR

This study uses molecular dynamics simulations to analyze the buckling behavior of circular monolayer graphene under radial load, comparing results with elasticity theory and estimating free energy differences.

Contribution

It provides a combined atomistic and theoretical analysis of graphene buckling, including free energy calculations and the prediction of optimal buckling radius.

Findings

Graphene buckles into a bowl shape after ~0.4% strain.

Young's modulus matches experimental data.

Theoretical buckling threshold agrees with simulations.

Abstract

We investigate the stability of circular monolayer graphene subjected to a radial load using non-equilibrium molecular dynamics simulations. When monolayer graphene is radially stressed, after some small circular strain ($\sim 0.4%$) it buckles and bends into a new bowl like shape. Young's modulus is calculated from the linear relation between stress and strain before the buckling threshold, which is in agreement with experimental results. The prediction of elasticity theory for the buckling threshold of a radially stressed plate is presented and its results are compared to the one of our atomistic simulation. Jarzynski equality is used to estimate the difference between the free energy of the non-compressed states and the buckled states. From a calculation of the free energy we obtain the optimum radius for which the system feels the minimum boundary stress.