2014-Sustainable Industrial Processing Summit
SIPS 2014 Volume 7: Energy Production, Environmental & Multiscale
| Editors: | Kongoli F |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2014 |
| Pages: | 528 pages |
| ISBN: | 978-1-987820-09-6 |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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From REBO Potentials to a mechanical model of graphene under a combination of bending and stretching loads
Nicola Pugno1; Antonino Favata1; Paolo Podio-Guidugli2;1UNIVERSITY OF TRENTO, Trento, Italy; 2UNIVERSITY OF ROME TORVERGATA, Roma, Italy;
Type of Paper: Regular
Id Paper: 350
Topic: 18
Abstract:
It is shown in [1] by a DFT-based calculation that in-plane stretching induces softening of the bending rigidity of graphene. In this contribution, working in the framework of discrete structure mechanics, we develop a model that predicts and allows to estimate softening effects in graphene monolayers.
To keep our developments as simple as possible, we restrict attention to bending+traction problems in the armchair (A) and zigzag directions (Z) and for symmetrical load distributions.
Given a REBO potential V(y), with y a string of internal variables such as bond lengths, bond angles, and dihedral angles, we express y in terms of a string x of suitable Lagrangian coordinates, and we write the total energy functional of the system in the form W(x)=V(y(x))-fad(x), where the load potential is the inner product of d, a string of generalized displacement parameters, and the dual string of dead loads f. As usual in structure mechanics, the system's equilibrium shapes are obtained by setting to zero the first gradient of W with respect to x; their stability is assessed by checking the positivity of the Hessian of W. These nonlinear equilibrium equations are given a precise mechanical interpretation in terms of stresses and prestresses; a representative numerical solution is given for V the second-generation Brenner potential [3], that is, for the most common empirical potential, used to perform MD simulations for carbon-based materials.
Whatever V, we give an analytical necessary and sufficient condition for softening of the bending rigidity of graphene in case of the coupled bending-traction problems we study. We also show that such a condition is satisfied by the second-generation Brenner potential - a result consistent with the DFT calculations of [1].
We also argue that the same approach can be used to analyze some delicate issues in the mechanics of carbon nanotubes, such as their exact geometry, prestress level, and zipping-unzipping energy. In connection with the last of these issues, we recall from [2] that a technique to produce nanoribbons is based on an oxidative unzipping process that discloses the presence of a latent energy in the nanotubes one starts off with; our formulation yields both a justification and a quantitative evaluation of that energy.