Elastic Bending Modulus of Monolayer Graphene

TL;DR

This paper derives an analytical formula for the elastic bending modulus of monolayer graphene, identifying physical origins and validating predictions with simulations and ab initio calculations.

Contribution

It introduces a new analytical expression for graphene's bending modulus based on empirical potentials, linking microscopic bond effects to macroscopic properties.

Findings

Analytical formula closely matches ab initio calculations.

Bending modulus shows slight nonlinearity and anisotropy.

Coupling between bending and in-plane strain in nanotubes.

Abstract

A new formula for elastic bending modulus of monolayer graphene is derived analytically from an empirical potential for solid-state carbon-carbon bonds. Two physical origins are identified for the non-vanishing bending modulus of the atomically thin graphene sheet, one due to the bond angle effect and the other resulting from the bond order term associated with dihedral angles. The analytical prediction compares closely with ab initio energy calculations. Pure bending of graphene monolayers are simulated by a molecular mechanics approach, showing slight nonlinearity and anisotropy in the tangent bending modulus as the bending curvature increases. An intrinsic coupling between bending and in-plane strain is noted for graphene monolayers rolled into carbon nanotubes.