# A REBO-potential-based model for graphene bending by $\Gamma$-convergence

## TL;DR

This paper develops a continuum model for graphene bending based on atomistic interactions governed by the REBO potential, deriving the limit energy functional depending on curvature measures.

## Contribution

It introduces a $ ext{Gamma}$-convergence approach to derive a continuum bending model from a REBO-potential-based atomistic description of graphene.

## Key findings

- The $ ext{Gamma}$-limit depends on mean and Gaussian curvatures.
- Neglecting certain atomic interactions leads to a non-local limit.
- The model bridges atomistic interactions and continuum curvature descriptions.

## Abstract

An atomistic to continuum model for a graphene sheet undergoing bending is presented. Under the assumption that the atomic interactions are governed by a harmonic approximation of the 2nd-generation Brenner REBO (reactive empirical bond-order) potential, involving first, second and third nearest neighbors of any given atom, we determine the variational limit of the energy functionals. It turns out that the $\Gamma$-limit depends on the linearized mean and Gaussian curvatures. If some specific contributions in the atomic interaction are neglected, the variational limit is non-local.