The Gaussian Stiffness of Graphene deduced from a Continuum Model based on Molecular Dynamics Potentials

Abstract

We consider a discrete model of a graphene sheet with atomic interactions governed by a harmonic approximation of the 2nd-generation Brenner potential that depends on bond lengths, bond angles, and two types of dihedral angles. A continuum limit is then deduced that fully describes the bending behavior. In particular, we deduce for the first time an analytical expression of the Gaussian stiffness, a scarcely investigated parameter ruling the rippling of graphene, for which contradictory values have been proposed in the literature. We disclose the atomic-scale sources of both bending and Gaussian stiffnesses and provide for them quantitative evaluations.

References in corpus (9)

• Finite temperature lattice properties of graphene beyond the quasiharmonic approximation
• Nonlinear elasticity of monolayer graphene
• Breakdown of continuum mechanics for nanometer-wavelength rippling of graphene
• The Influence of Graphene Curvature on Hydrogen Adsorption: Towards Hydrogen Storage Devices
• Graphene's morphology and electronic properties from discrete differential geometry
• Curvature dependent surface energy for a free standing monolayer graphene: some closed form solutions of the nonlinear theory
• Curvature dependent surface energy for free standing monolayer graphene: geometrical and material linearization with closed form solutions
• An analytical benchmark for MD codes: testing LAMMPS on the 2nd generation Brenner potential
• Cavitation of Water by Volume-Controlled Stretching

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• Graphene ground states
• A REBO-potential-based model for graphene bending by $\Gamma$-convergence
• First-principles derived force field for h-BN monolayer nanostructures: Applications to sheets, nanotubes and nanotori
• Elastic Constants and Bending Rigidities from Long-Wavelength Perturbation Expansions