Abstract
This paper compares simple interatomic potentials for carbon nanostructures with hexagonal lattice, by investigating the in-plane and the out-of-plane tensile behaviour of single-layer graphene sheets. Attention is given both to potentials already considered in the literature and to a new one, which we call the damped DREIDING potential, in which damping functions are added to the DREIDING potential. For each potential, a calibration of its parameters and a focus on its performance are carried out in the in-plane context, by comparison with ab initio results of the rigidities and of the tensile limit properties, under periodic conditions. In addition, the damped DREIDING potential is used to perform in-plane tensile tests on both pristine and perforated single-layer graphene sheets of finite size. In the out-of-plane context, the calibration from ab initio results is only possible with reference to the rigidity. For the damped DREIDING potential, a sensitivity analysis, applied to a nanoindentation problem, on a pristine single-layer graphene sheet of finite size is provided. In doing so, a narrow range of value of the force needed to remove an atom from a sheet is given.
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Notes
The Stillinger–Weber potential is the only potential in which the inner forces are not directly zero when \(r_{ij} = {\bar{r}}\).
The zigzag and armchair test nomenclature is borrowed from the tensile tests on the ribbons: by the term zigzag or armchair we mean the arrangement of the side on which the traction is applied.
This constraint is managed by condensation of one of the two variables.
References
Nguyen, B.H., Nguyen, V.H.: Promising applications of graphene and graphene-based nanostructures. Nanosci. Nanotechnol. 7, 023002 (2016)
Sun, C., Wen, B., Bai, B.: Recent advances in nanoporous graphene membrane for gas separation and water purification. Sci. Bull. 60, 1807–1823 (2015)
Aïssa, B., Memon, N.K., Ali, A., Khraisheh, M.K.: Recent progress in the growth and applications of graphene as a smart material: a review. Front. Mater. 2, 58 (2015)
Kumar, R., Singh, R., Hui, D., Feo, L., Fraternali, F.: Graphene as biomedical sensing element: state of art review and potential engineering applications. Compos. B Eng. 134, 193–206 (2018)
Kudin, K.N., Scuseria, G.E., Yakobson, B.I.: \(C_2 \, F\), \(BN\), and \(C\) nanoshell elasticity from ab initio computations. Phys. Rev. B 64, 235406 (2001)
Liu, F., Ming, P., Li, J.: Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys. Rev. B 76, 064120 (2007)
Reddy, C.D., Rajendran, S., Liew, K.M.: Equilibrium configuration and continuum elastic properties of finite sized graphene. Nanotechnology 17, 864–870 (2006)
Zhang, Y.Y., Wang, C.M., Xiang, Y.: A molecular dynamics investigation of the torsional responses of defective single-walled carbon nanotubes. Carbon 48, 4100–4108 (2010)
Silvestre, N., Faria, B., Lopes, J.N.C.: A molecular dynamics study on the thickness and post-critical strength of carbon nanotubes. Compos. Struct. 94, 1352–1358 (2012)
Gamboa, A., Vignoles, G.L., Leyssale, J.-M.: On the prediction of graphene’s elastic properties with reactive empirical bond order potential. Carbon 89, 176–187 (2015)
Berinskii, I.E., Borodich, F.M.: Elastic in-plane properties of 2D linearized models of graphene. Mech. Mater. 62, 60–68 (2013)
Favata, A., Micheletti, A., Podio-Guidugli, P.: A nonlinear theory of prestressed elastic stick-and-spring structures. Int. J. Eng. Sci. 80, 4–20 (2014)
Korobeynikov, S.N., Alyokhin, V.V., Annin, B.D., Babichev, A.V.: Quasi-static buckling simulation of single-layer graphene sheets by the molecular mechanics method. Math. Mech. Solids 20, 836–870 (2015)
Genoese, A., Genoese, A., Rizzi, N.L., Salerno, G.: On the derivation of the elastic properties of lattice nanostructures: the case of graphene sheets. Compos. B Eng. 115, 316–329 (2017)
Korobeynikov, S.N., Alyokhin, V.V., Babichev, A.V.: Simulation of mechanical parameters of graphene using the DREIDING force field. Acta Mech. 229, 2343–2378 (2018)
Genoese, A., Genoese, A., Rizzi, N.L., Salerno, G.: Force constants of BN, SiC, AlN and GaN sheets through discrete homogenization. Meccanica 53, 593–611 (2018)
Genoese, A., Genoese, A., Salerno, G.: Elastic constants of achiral single-wall CNTs: analytical expressions and a focus on size and small scale effects. Compos. B Eng. 147, 207–226 (2018)
Genoese, A., Genoese, A., Rizzi, N.L., Salerno, G.: On the in-plane failure and post-failure behaviour of pristine and perforated single-layer graphene sheets. Math. Mech. Solids 24, 3418–3443 (2019)
Genoese, A., Genoese, A., Salerno, G.: On the nanoscale behaviour of single-wall C, BN and SiC nanotubes. Acta Mech. 230, 1105–1128 (2019)
Genoese, A., Genoese, A., Rizzi, N.L., Salerno, G.: Buckling analysis of single-layer graphene sheets using molecular mechanics. Front. Mater. 6, 26 (2019)
Georgantzinos, S.K., Giannopoulos, G.I., Anifantis, N.K.: Numerical investigation of elastic properties of graphene structures. Mater. Des. 31, 4646–4654 (2010)
Sakharova, N.A., Pereira, A.F.G., Antunes, J.M., Brett, C.A.M., Fernandes, J.V.: Mechanical characterization of single-walled carbon nanotubes: numerical simulation study. Compos. Part B Eng. 75, 73–85 (2015)
Korobeynikov, S.N., Alyokhin, V.V., Babichev, A.V.: On the molecular mechanics of single layer graphene sheets. Int. J. Eng. Sci. 133, 109–131 (2018)
Arroyo, M., Belytschko, T.: Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy–Born rule. Phys. Rev. B 69, 115415 (2004)
Cohen-Tanugi, D., Grossman, J.C.: Water desalination across nanoporous graphene. Nano Lett. 12, 3602–3608 (2012)
Hollerer, S.: Numerical validation of a concurrent atomistic-continuum multiscale method and its application to the buckling analysis of carbon nanotubes. Comput. Methods Appl. Mech. Eng. 270, 220–246 (2014)
Ghaffari, R., Duong, T.X., Sauer, R.A.: A new shell formulation for graphene structures based on existing ab-initio data. Int. J. Solids Struct. 135, 37–60 (2018)
Singh, S., Patel, B.P.: A computationally efficient multiscale finite element formulation for dynamic and postbuckling analyses of carbon nanotubes. Comput. Struct. 195, 126–144 (2018)
Schneider, G.F., Kowalczyk, S.W., Calado, V.E., Pandraud, G., Zandbergen, H.W., et al.: DNA translocation through graphene nanopores. Nano Lett. 10, 3163–3167 (2010)
Jiang, D., Cooper, V.R., Dai, S.: Porous graphene as the ultimate membrane for gas separation. Nano Lett. 9, 4019–4024 (2009)
Cohen-Tanugi, D., Grossman, J.C.: Mechanical strength of nanoporous graphene as a desalination membrane. Nano Lett. 14, 6171–6178 (2014)
Belytschko, T., Xiao, S.P., Schatz, G.C., Ruoff, R.S.: Atomistic simulations of nanotube fracture. Phys. Rev. B 65, 235430 (2002)
Duan, W.H., Chang, T., Liew, K.M., He, X.Q.: Molecular mechanics modeling of carbon nanotube fracture. Carbon 11, 1769–1776 (2007)
Stillinger, F.H., Weber, T.A.: Computer simulation of local order in condensed phases of silicon. Phys. Rev. B 31, 5262–5271 (1985)
Rappé, A.K., Casewit, C.J., Colwell, K.S., Goddard III, W.A., Skiff, W.M.: UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J. Am. Chem. Soc. 114, 10024–10035 (1992)
Mayo, S.L., Olafson, B.D., Goddard III, W.A.: DREIDING: a generic force field for molecular simulations. J. Phys. Chem. 94, 8897–8909 (1990)
Dyck, O., Kim, S., Kalinin, S.V., Jesse, S.: Placing single atoms in graphene with a scanning trasmission electron miscroscope. Appl. Phys. Lett. 111, 113104 (2017)
Acknowledgements
We are very grateful to the University “Roma Tre” for cofunding the research contract of PhD Alessandra Genoese and to the Italian Ministry of University, Research and Education for cofunding the research contract of PhD Andrea Genoese.
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Genoese, A., Genoese, A. & Salerno, G. In-plane and out-of-plane tensile behaviour of single-layer graphene sheets: a new interatomic potential. Acta Mech 231, 2915–2930 (2020). https://doi.org/10.1007/s00707-020-02680-0
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DOI: https://doi.org/10.1007/s00707-020-02680-0