Influence of the Vacancies on the Buckling Behavior of a Single–Layered Graphene Nanosheet

Document Type: Research Paper

Authors

Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

Graphene is a new class of two-dimensional carbon nanostructure, which holds great promise for the vast applications in many technological fields. It would be one of the prominent new materials for the next generation nano-electronic devices. In this paper the influence of various vacancy defects on the critical buckling load of a single-layered graphene nanosheet is investigated. The nanosheet is modeled on the base of structural mechanics approach which covalent bonds between atoms are modeled as equivalent beam elements in a finite element model. The mechanical properties of the nanosheet extracted from the model are in good agreement with those of other research works. Effect of the number of vacancies and their positions on the critical buckling load is investigated in the present work. Our results show that the location of the vacancy has a significant role in the amount of critical buckling load. Furthermore, as the density of the vacancies increases, the value of critical buckling load decreases and the relationship is approximately linear.                        

Keywords


[1] Sakhae-pour A., Ahmadian M.T., Naghdabadi R., 2008, Vibrational analysis of single-layered graphene sheets, Nanotechnology 19: 085702.
[2] Li C.Y., Chou T.W., 2004, Mass detection using carbon nanotube-based nanomechanical resonators, Applied Physics Letters 84: 5246.
[3] Sakhaee-Pour A., Ahmadian M.T., Vafai A., 2008, Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors, Solid State Communications 145: 168-172.
[4] Dai H., Hafner J. H., Rinzler A. G., Colbert D. T., 1996, Nanotubes as nanoprobes in scanning probe microscopy, Nature 384: 147-150.
[5] Pradhan S.C., Murmu T., 2010, Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory, Physica E 42: 1293-1301.
[6] Tapia A., Peon-Escalante R., Villanueva C., Aviles F., 2012, Influence of vacancies on the elastic properties of a graphene sheet, Computational Materials Science 55: 255-262.
[7] Lu Q., Huang R., 2009, Nonlinear mechanics of single-atomic-layer graphene sheets, International Journal of Applied Mechanics 1(3): 443-467.
[8] Rapaport D.C., 2004, The Art and Science of Molecular Dynamics Simulation, Cambridge University Press, Cambridge.
[9] Frenkel D., Smit B., 2002, Understanding Molecular Simulation: From Algorithms to Applications, Academic Press, San Diego.
[10] Hu H., Onyebueke L., Abatan A., 2010, Characterizing and modeling mechanical properties of nanocomposites-review and evaluation, Journal of Minerals and Materials Characterization and Engineering 9(4): 275-319.
[11] Li C., Chou T.W.A., 2003, A structural mechanics approach for the analysis of carbon nanotubes, International Journal of Solids and Structures 40: 2487-2499.
[12] Sakharova N.A., Pereira A.F.G., Antunes J.M., Fernandes J.V., 2016, Numerical simulation study of the elastic properties of single-walled carbon nanotubes containing vacancy defects, Composites Part B 89: 155-168.
[13] Canadijal M., Brcicl M., Brnicl J., 2013, Bending behavior of single layered graphene nanosheets with vacancy defects, Engineering Review 33(1): 9-14.
[14] Hemmasizadeh A., Mahzoon M., Hadi E., Khandan R., 2008, A method for developing the equivalent continuum model of a single layer graphene sheet, Thin Solid Films 516: 7636-7640.
[15] Shokrieh M.M., Rafiee R., 2010, Prediction of Young’s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach, Materials and Design 31: 790-795.
[16] Cheng Y.Z., Shi G.Y., 2014, Equivalent mechanical properties of graphene predicted by an improved molecular structural mechanics model, Key Engineering Materials 609-610: 351-356.
[17] Boukhvalov D.W., Katsnelson M.I., 2008, Chemical functionalization of graphene with defects, Nano Letters 8: 4373-4379.
[18] Zhang X., Jiao K., Sharma P., Yakobson B., 2006, An atomistic and non-classical continuum field theoretic perspective of elastic interactions between defects (force dipoles) of various symmetries and application to graphene, Journal of the Mechanics and Physics of Solids 54: 2304-2329.
[19] Lu P., Zhang P.Z., Guo W., 2009 ,Electronic and magnetic properties of zigzag edge graphenenanoribbons with Stone–Wales defects, Physics Letters A 373: 3354-3358.
[20] Fan B., Yang X., Zhang R., 2010, Anisotropic mechanical properties and Stone-Wales defects in graphene monolayer: A theoretical study, Physics Letters A 374: 2781-2784.
[21] Tsai J.L, Tzeng S.H., Tzou Y.J., 2010, Characterizing the fracture parameters of a graphene sheet using atomistic simulation and continuum mechanics, International Journal of Solids and Structures 47: 503-509.
[22] Xiaoa J.R., Staniszewskia J., Gillespie Jr J.W., 2010, Tensile behaviors of graphene sheets and carbon nanotubes with multiple Stone–Wales defects, Materials Science and Engineering: A 527: 715-723.
[23] Gelin B.R., 1994, Molecular Modeling of Polymer Structures and Properties, Hanser/Gardner Publishers, Cincinnati.
[24] Kalamkarov A.L., Georgiades A.V., Rokkam S.K., Veedu V.P., Ghasemi-Nejhad M.N. , 2006, Analytical and numerical techniques to predict carbon nanotubes properties, International Journal of Solids and Structures 43: 6832-6854.
[25] Allinger N.L., Yuh Y.H., Lii J.H., 1989, Molecular mechanics, the MM3 force field for hydrocarbons, Journal of the American Chemical Society 111: 8551-8566.
[26] Cornell W.D., Cieplak P., Bayly C.I., 1995, A second generation force-field for the simulation of proteins, nucleic-acids, and organic molecules, Journal of the American Chemical Society 117: 5179-5197.
[27] Sakhaee-pour A., 2009, Elastic properties of single-layered graphene sheet, Solid State Communications 149: 91-95.
[28] Lier G.V., Alsenoy C.V., Doren V.V., Geerlings P., 2000, Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene, Chemical Physics Letters 326: 181-185.
[29] Kudin K.N., Scuseria G.E., Yakobson B.I., 2000, C2F, BN, and C nanoshell elasticity from ab initio computations, Physical Review B 64: 1-10.
[30] Xiao J.R., Gama B.A., Gillespie Jr J.W., 2005, An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes, International Journal of Solids and Structures 42: 3075-3092.
[31] Reddy C.D., Rajendran S., Liew K.M., 2005, Equivalent continuum modeling of graphene sheets, International Journal of Nanoscience 4: 631-636.
[32] Wu Y., Zhang X., Leung A.Y.T., Zhong W., 2006, An energy-equivalent model on studying the mechanical properties of single-walled carbon nanotubes, Thin-walled structures 44: 667-676.
[33] Natsuki T., Tantrakarn K., Endo M., 2004, Prediction of elastic properties for single walled carbon nanotubes, Carbon 42: 39-45.
[34] Chen W.F., Lui E.M., 1987, Structural Stability, Theory and Application, Elsevier Science Publishing Co. Inc., New York.