Investigation of Vibrational Behavior of Perfect and Defective Carbon Nanotubes Using Non–Linear Mass–Spring Model
الموضوعات :
A.A Shariati
1
(Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University)
A.R Golkarian
2
(Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University)
M Jabbarzadeh
3
(Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University)
الکلمات المفتاحية: Natural frequency, Carbon Nanotube, Vacancy defect, Stone–wales defect, Non–linear spring,
ملخص المقالة :
In the present study, the effects of arrangement and distribution of multifarious types of defects on fundamental frequency of carbon nanotubes are investigated with respect to different chirality and boundary conditions. Interatomic interactions between each pair of carbon atoms are modeled using two types of non–linear spring–like elements. To obtain more information about the influences of defects; the effects of location, number and distribution (gathered or scattered defects) of two most common types of defects (vacancy and Stone–Wales defects) are examined on vibrational behavior of carbon nanotubes. Obtained results are in good agreement with the results reported in other literature. The results show that, gathered vacancy defects cause to a reduction in natural frequency of nanotubes, especially in the case of fix–fix boundary condition. It is also observed that the effect of defects depends on chirality intensively. In addition, the influence of the first vacancy defect is significantly more than the first Stone–Wales defect.
[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354: 56-58.
[2] Demczyk B.G., Wang Y.M., Cumings J., Hetman M., Han W., Zettl A., 2002, Direct mechanical measurement of the tensile strength and elastic modulus of multiwalled carbon nanotubes, Materials Science and Engineering A 334: 173-178.
[3] Goze C., Vaccarini L., Henrard L., Bernier P., Hernandez E., Rubio A., 1999, Elastic and mechanical properties of carbon nanotubes, Synthetic Metals 103: 2500-2501.
[4] Krishnan A., Dujardin E., Ebbesen T.W., Yianilos P.N., Treacy M.M.J., 1998, Young’s modulus of single–walled nanotubes, Physical Review B 58(20): 14013-14019.
[5] Popov V.N., 2004, Carbon nanotubes: properties and applications, Materials Science and Engineering R 43: 61-102.
[6] Ruoff R.S., Lorents D.C., 1995, Mechanical and thermal properties of carbon nanotubes, Carbon 33: 925-930.
[7] Lasjaunias J. C., 2003, Thermal properties of carbon nanotubes, C R Physique 4: 1047-1054.
[8] Issi J.P., Langer L., Heremans J., Olk C.H., 1995, Electronic properties of carbon nanotubes: experimental results, Carbon 33: 941-948.
[9] Mintmire J.W., White C.T., 1995, Electronic and structural properties of carbon nanotubes, Carbon 33: 893-902.
[10] Thostenson E.T., Ren Z., Chou T.W., 2001, Advanced in the science and technology of carbon nanotubes and their composites: a review, Composite Science and Technology 61: 1899-1912.
[11] Ruoff R.S., Qian D., Liu W.K., 2003, Mechanical properties of carbon nanotubes: theoretical predictions and experimental measurements, C R Physique 4: 993-1008.
[12] Paradise M., Goswami T., 2007, Carbon nanotubes production and industrial applications, Materials and Design 28: 1477-1489.
[13] Hoenlein W., Kreupl F., Duesberg G.S., Graham A.P., Liebau M., Seidel R., 2003, Carbon nanotubes for microelectronics: status and future prospects, Materials Science and Engineering C 23: 663-669.
[14] Tran P.A., Zhang L., Webster T.J., 2009, Carbon nanofibers and carbon nanotubes in regenerative medicine, Advanced Drug Delivery Reviews 61: 1097-1114.
[15] Li C., Thostenson E.T., Chou T.W., 2008, Sensors and actuators based on carbon nanotubes and their composites: A review, Composites Science and Technology 68: 1227-1249.
[16] Gibson R.F., Ayorinde E.O., Wen Y.F., 2007, Vibrations of carbon nanotubes and their composites: A review, Composites Science and Technology 67: 1-28.
[17] Andrews R., Jacques D., Qian D., Dickey E.C., 2001, Purification and structural annealing of multiwalled carbon nanotubes at graphitization temperatures, Carbon 39: 1681-1687.
[18] Mawhinney D.B., Naumenko V., Kuznetsova A., Yates Jr. J.T., Liu J., Smalley R.E., 2000, Surface defect site density on single walled carbon nanotubes by titration, Chemical Physics Letters 324: 213-216.
[19] Nardelli M.B., Fattebert J.L., Orlikowski D., Roland C., Zhao Q., Bernholc J., 2000, Mechanical properties, defects and electronic behavior of carbon nanotubes, Carbon 38: 1703-1711.
[20] Terrones M., Botello–Mendez A.R., Campos-Delgado J., Lopez-Urias F., Vega-Cantu Y.I., Rodriguez-Macias F.J., 2010, Graphene and graphite nanoribbons: Morphology, properties, synthesis, defects and applications, Nano Today 5: 351-372.
[21] Duan W.H., Wang C.M., Zhang Y.Y., 2007, Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics, Journal of Applied Physics 101: 024305.
[22] Hashemnia K., Farid M., Vatankhah R., 2009, Vibrational analysis of carbon nanotubes and graphene sheets using molecular structural mechanics approach, Computational Materials Science 47: 79-85.
[23] Sakhaee–Pour A., Ahmadian M.T., Vafai A., 2009, Vibrational analysis of single–walled carbon nanotubes using beam element, Thin–Walled Structures 47: 646-652.
[24] Georgantzinos S.K., Anifantis N.K., 2009, Vibration analysis of multi–walled carbon nanotubes using a mass–spring based finite element model, Computational Materials Science 47: 168-177.
[25] Chowdhury R., Adhikari S., Wang C.Y., Scarpa F., 2010, A molecular mechanics approach for the vibration of single–walled carbon nanotubes, Computational Materials Science 48: 730-735.
[26] Arghavan S., Singh A.V., 2011, On the vibrations of single–walled carbon nanotubes, Journal of Sound and Vibration 330: 3102-3122.
[27] Yan Y., Shi G., Zhao P., 2011, Frequency study of single–walled carbon nanotubes based on a space–frame model with flexible connections, Journal of Computers 6: 1125-1130.
[28] Joshi A.Y., Sharma S.C., Harsha S.P., 2011, The effect of pinhole defect on vibrational characteristics of single walled carbon nanotube, Physica E 43: 1040-1045.
[29] Parvaneh V., Shariati M., Torabi H., 2011, Frequency analysis of perfect and defective SWCNTs, Computational Materials Science 50: 2051-2056.
[30] Ebrahim Zadeh Z., Yadollahpour M., Ziaei-Rad S., Karimzadeh F., 2012, The effect of vacancy defects and temperature on fundamental frequency of single walled carbon nanotubes, Computational Materials Science 63: 12-19.
[31] Ansari R., Ajori S., Arash B., 2012, Vibrations of single- and double-walled carbon nanotubes with layerwise boundary conditions: A molecular dynamics study, Current Applied Physics 12: 707-711.
[32] Ghavamian A., Ochsner A., 2013, Numerical modeling of eigen modes and eigenfrequencies of single- and multi-walled carbon nanotubes under the influence of atomic defects, Computational Materials Science 72: 42-48.
[33] Golkarian A.R., Jabbarzadeh M., 2013, The density effect of van der Waals forces on the elastic modules in graphite layers, Computational Materials Science 74: 138-142.
[34] Golkarian A.R., Jabbarzadeh M., 2012, The attitude of variation of elastic modules in single wall carbon nanotubes: nonlinear mass-spring model, Journal of Solid Mechanics 4(1): 106-113.
[35] WenXing B., ChangChun Z., WanZhao C., 2004, Simulation of Young’s modulus of single–walled carbon nanotubes by molecular dynamics, Physica B 352: 156-163.
[36] Rappe A.K., Casewit C.J., Colwell K.S., Goddard W.A., Skiff W.M., 1992, A full periodic table force field for molecular mechanics and molecular dynamics simulations, Journal of American Chemical Society 114: 10024-10035.
[37] 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.
[38] Machida K., 1999, Principles of Molecular Structural Mechanics,Wiley and Kodansha.
[39] Odegard G.M., Gates T.S., Nicholson L.M., Wise K.E., 2002, Equivalent–continuum modeling of nano–structured materials, Composite Science and Technology 62: 1869-1880.
