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Effects of appearance characteristics on the mechanical properties of defective SWCNTs: using finite element methods and molecular dynamics simulation

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Abstract

In this article, finite element methods and molecular dynamics method were employed to simulate covalent bonds between carbon atoms in nanotubes with a linear beam element. Single-walled carbon nanotubes with different structures, and a wide diameter and longitudinal range were analyzed. The effect of geometric parameters of CNTs including diameter, length, and chirality on the Young's and shear modulus of the nanotubes was independently investigated. Also, the decrease in Young's modulus of CNTs was determined due to the presence of a vacancy defect and an increase in the number and location of the defect. The results showed in all three types of defective nanotubes (armchair, zigzag, and chiral) with a small-diameter, Young's, and shear moduli increased with incrementing the nanotube diameter. Also, in all three types of structures with a diameter greater than 20 \(\AA \), the effect of the diameter of the nanotube is significantly reduced, and the Young's and shear modulus approached those of a graphene sheet. For nanotubes with a diameter greater than 20 \(\AA \) and a length greater than 240 \(\AA \), the effect of nanotube dimensions on Young's and shear moduli was negligible and the only factor affecting the mechanical properties of these nanotubes was the chirality or structure of the nanotube, and among the studied nanotubes, the vacancy defect had the greatest impact on Young's modulus of chiral nanotubes, with a chiral angle of 15.49\(^\circ \). Also the results demonstrated that the diameter of the nanotube has a greater effect on the elastic properties than the length of the nanotube. Comparing the results obtained for armchair, zigzag, and chiral nanotubes, the vacancy defect had the greatest impact on Young's modulus of chiral nanotubes. The present theoretical study highlights the important role played by vacancy defected CNTs in determining their mechanical behaviors as reinforcements in multifunctional nanocomposites.

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Abbreviations

a c-c :

Carbon–carbon bond lengths equal (0.142 nm)

E s :

Elastic potential energy

E b :

Bending energy

E t :

Torsional potential energy

E l :

Off-plane potential energy

E vdw :

Van der Waals bonds forces

E es :

Electrostatic bonds forces

E hb :

Hydrogen bonds forces

k r :

Force constants of bond tension

k θ :

Force constants of bond bending

k φ :

Force constants of bond torsion

Δr :

Show the changes in bond length

Δθ :

Show the changes in-plane angle of the bond

Δφ :

Show the changes in out-of-plane torsion of the bond

\(L0_{NT}\) :

Initial length of the nanotube

\(\Delta L_{NT}\) :

Changes in the length of the nanotube

\(A_{NT}\) :

Cross-sectional area of the nanotube

D :

Diameter of CNTs

t :

Walled thickness of CNTs

v CNT :

Poisson's ratio of CNT

G CNT :

Shear modulus of CNT

\(\rho\) :

Density modulus of CNT

References

  1. H. Sbiaai, A. Hader, S. Boufass et al., The effect of the substitution on the failure process in heterogeneous materials: fiber bundle model study. Eur. Phys. J. Plus. 134, 148 (2019). https://doi.org/10.1140/epjp/i2019-12475-7

    Article  Google Scholar 

  2. A.G. Arani, A. Farazin, M. Mohammadimehr, The effect of nanoparticles on enhancement of the specific mechanical properties of the composite structures: a review research. Adv. Nano Res. 10, 327 (2021)

    Google Scholar 

  3. M. Naheed, M. Faryad, Excitation of surface plasmon–polariton waves at the interface of a metal and an isotropic chiral material in the prism-coupled configurations. Eur. Phys. J. Plus 135, 724 (2020). https://doi.org/10.1140/epjp/s13360-020-00757-2

    Article  Google Scholar 

  4. Iijima S (1998) Graphite filaments having tubular structure and method of forming the same

  5. J.-C. Sublet, I.P. Bondarenko, G. Bonny et al., Neutron-induced damage simulations: beyond defect production cross-section, displacement per atom and iron-based metrics. Eur. Phys. J. Plus 134, 350 (2019). https://doi.org/10.1140/epjp/i2019-12758-y

    Article  Google Scholar 

  6. J. Hristov, Linear viscoelastic responses and constitutive equations in terms of fractional operators with non-singular kernels. Eur. Phys. J. Plus 134, 283 (2019). https://doi.org/10.1140/epjp/i2019-12697-7

    Article  Google Scholar 

  7. C.-L. Zhang, H.-S. Shen, Buckling and postbuckling analysis of single-walled carbon nanotubes in thermal environments via molecular dynamics simulation. Carbon N. Y. 44, 2608–2616 (2006). https://doi.org/10.1016/j.carbon.2006.04.037

    Article  Google Scholar 

  8. A. Ghasemi, M. Dardel, M.H. Ghasemi, M.M. Barzegari, Analytical analysis of buckling and post-buckling of fluid conveying multi-walled carbon nanotubes. Appl. Math. Model 37, 4972–4992 (2013). https://doi.org/10.1016/j.apm.2012.09.061

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Ghasemi, M. Dardel, M.H. Ghasemi, Control of the non-linear static deflection experienced by a fluid-carrying double-walled carbon nanotube using an external distributed load. Proc. Inst. Mech. Eng. Part N. J. Nanoeng. Nanosyst. 226, 181–190 (2012). https://doi.org/10.1177/1740349912451387

    Article  Google Scholar 

  10. J. Yang, H.-S. Shen, Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels. J. Sound Vib. 261, 871–893 (2003). https://doi.org/10.1016/S0022-460X(02)01015-5

    Article  ADS  Google Scholar 

  11. A. Ghasemi, M. Dardel, M.H. Ghasemi, Collective effect of fluid’s coriolis force and nanoscale’s parameter on instability pattern and vibration characteristic of fluid-conveying carbon nanotubes. J. Press. Vessel Technol. (2015). https://doi.org/10.1115/1.4029522

    Article  Google Scholar 

  12. Z. Shah, K.P. Ikramullah et al., Impact of nanoparticles shape and radiation on the behavior of nanofluid under the Lorentz forces. Case Stud. Therm. Eng. 26, 101161 (2021). https://doi.org/10.1016/j.csite.2021.101161

    Article  Google Scholar 

  13. M. Shoaib, M.A.Z. Raja, M.T. Sabir et al., A stochastic numerical analysis based on hybrid NAR-RBFs networks nonlinear SITR model for novel COVID-19 dynamics. Comput. Methods Programs Biomed. 202, 105973 (2021). https://doi.org/10.1016/j.cmpb.2021.105973

    Article  Google Scholar 

  14. M. Bilal, H. Arshad, M. Ramzan et al., Unsteady hybrid-nanofluid flow comprising ferrousoxide and CNTs through porous horizontal channel with dilating/squeezing walls. Sci. Rep. 11, 12637 (2021). https://doi.org/10.1038/s41598-021-91188-1

    Article  ADS  Google Scholar 

  15. Z. Shah, M.R. Hajizadeh, Ikramullah et al., Entropy optimization and heat transfer modeling for Lorentz forces effect on solidification of NEPCM. Int. Commun. Heat Mass Transf. 117, 104715 (2020). https://doi.org/10.1016/j.icheatmasstransfer.2020.104715

    Article  Google Scholar 

  16. M.M.J. Treacy, T.W. Ebbesen, J.M. Gibson, Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature 381, 678–680 (1996)

    Article  ADS  Google Scholar 

  17. A. Krishnan, E. Dujardin, T.W. Ebbesen et al., Young’s modulus of single-walled nanotubes. Phys. Rev. B 58, 14013 (1998)

    Article  ADS  Google Scholar 

  18. G.L. Burkholder, Y.W. Kwon, R.D. Pollak, Effect of carbon nanotube reinforcement on fracture strength of composite adhesive joints. J. Mater. Sci. 46, 3370–3377 (2011)

    Article  ADS  Google Scholar 

  19. P. Jojibabu, Y.X. Zhang, A.N. Rider, J. Wang, Mechanical performance of adhesive joints using high-performance nanocomposite adhesive material with carbon nanotube and triblock copolymer hybrids. Compos Part B Eng 186, 107813 (2020)

    Article  Google Scholar 

  20. A. Farazin, M. Mohammadimehr, Effect of different parameters on the tensile properties of printed Polylactic acid samples by FDM: experimental design tested with MDs simulation. Int. J. Adv. Manuf. Technol. (2021). https://doi.org/10.1007/s00170-021-07330-w

    Article  Google Scholar 

  21. A. Farazin, M. Mohammadimehr, Computer modeling to forecast accurate of efficiency parameters of different size of graphene platelet, carbon, and boron nitride nanotubes: a molecular dynamics simulation. Comput. Concr. 27, 111 (2021)

    Google Scholar 

  22. M. Kuwar, S. Kamal, Molecular dynamics simulation study of novel properties of defect full single walled carbon nanotubes. Int. J. Appl. or Innov. Eng. Manag. 2, 77–81 (2013)

    Google Scholar 

  23. A. Kumar, K. Sharma, P.K. Singh, V.K. Dwivedi, Mechanical characterization of vacancy defective single-walled carbon nanotube/epoxy composites. Mater. Today Proc. 4, 4013–4021 (2017). https://doi.org/10.1016/j.matpr.2017.02.303

    Article  Google Scholar 

  24. M. Sammalkorpi, A. Krasheninnikov, A. Kuronen et al., Mechanical properties of carbon nanotubes with vacancies and related defects. Phys. Rev. B 70, 245416 (2004). https://doi.org/10.1103/PhysRevB.70.245416

    Article  ADS  Google Scholar 

  25. A. Farazin, M. Mohammadimehr, Nano research for investigating the effect of SWCNTs dimensions on the properties of the simulated nanocomposites: a molecular dynamics simulation. Adv. Nano Res. 9, 83–90 (2020)

    Google Scholar 

  26. J. Blumberger, M.-P. Gaigeot, M. Sulpizi, R. Vuilleumier, Frontiers in molecular simulation of solvated ions, molecules and interfaces. Phys. Chem. Chem. Phys. 22, 10393–10396 (2020). https://doi.org/10.1039/D0CP90091E

    Article  Google Scholar 

  27. O. Barrera, D. Bombac, Y. Chen et al., Correction to: Understanding and mitigating hydrogen embrittlement of steels: a review of experimental, modelling and design progress from atomistic to continuum. J. Mater. Sci. 53, 10593–10594 (2018). https://doi.org/10.1007/s10853-018-2291-7

    Article  ADS  Google Scholar 

  28. J.F. Castillo-Lara, E.A. Flores-Johnson, A. Valadez-Gonzalez et al., Mechanical properties of natural fiber reinforced foamed concrete. Materials (Basel) 13, 3060 (2020). https://doi.org/10.3390/ma13143060

    Article  ADS  Google Scholar 

  29. M. Mohammadimehr, B. Rousta Navi, A. Ghorbanpour Arani, Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method. Compos. Struct. 131, 654–671 (2015). https://doi.org/10.1016/j.compstruct.2015.05.077

    Article  Google Scholar 

  30. M. Mazaheri, J. Payandehpeyman, M. Khamehchi, A developed theoretical model for effective electrical conductivity and percolation behavior of polymer-graphene nanocomposites with various exfoliated filleted nanoplatelets. Carbon N. Y. (2020). https://doi.org/10.1016/j.carbon.2020.07.059

    Article  Google Scholar 

  31. A.F. Ávila, G.S.R. Lacerda, Molecular mechanics applied to single-walled carbon nanotubes. Mater. Res. 11, 325–333 (2008). https://doi.org/10.1590/S1516-14392008000300016

    Article  Google Scholar 

  32. T. Belin, F. Epron, Characterization methods of carbon nanotubes: a review. Mater. Sci. Eng. B Solid-State Mater. Adv. Technol. 119, 105–118 (2005). https://doi.org/10.1016/j.mseb.2005.02.046

    Article  Google Scholar 

  33. Y. Gogotsi, Nanomaterials Handbook (CRC Press, Boca Raton, 2006)

    Book  Google Scholar 

  34. S.Y. Mensah, F.K.A. Allotey, N.G. Mensah, G. Nkrumah, Differential thermopower of a CNT chiral carbon nanotube. J. Phys. Condens. Matter. 13, 5653–5662 (2001). https://doi.org/10.1088/0953-8984/13/24/310

    Article  ADS  Google Scholar 

  35. Z. Shah, E. Bonyah, S. Islam, T. Gul, Impact of thermal radiation on electrical MHD rotating flow of Carbon nanotubes over a stretching sheet. AIP Adv. 9, 015115 (2019). https://doi.org/10.1063/1.5048078

    Article  ADS  Google Scholar 

  36. N. Feroz, Z. Shah, S. Islam et al., Entropy generation of carbon nanotubes flow in a rotating channel with hall and ion-slip effect using effective thermal conductivity model. Entropy 21, 52 (2019). https://doi.org/10.3390/e21010052

    Article  ADS  Google Scholar 

  37. A. Saeed, Z. Shah, A. Dawar et al., Entropy generation in MHD flow of carbon nanotubes in a rotating channel with four different types of molecular liquids. Int. J. Heat Technol. 37, 509–519 (2019). https://doi.org/10.18280/ijht.370218

    Article  Google Scholar 

  38. Z. Shah, M. Sheikholeslami, K.P. Ikramullah, Influence of nanoparticles inclusion into water on convective magneto hydrodynamic flow with heat transfer and entropy generation through permeable domain. Case Stud. Therm. Eng. 21, 100732 (2020). https://doi.org/10.1016/j.csite.2020.100732

    Article  Google Scholar 

  39. L.G. Do, C.Z. Wang, E. Yoon et al., Diffusion, coalescence, and reconstruction of vacancy defects in graphene layers. Phys. Rev. Lett. 95, 1–4 (2005). https://doi.org/10.1103/PhysRevLett.95.205501

    Article  Google Scholar 

  40. Z. Huang, S. Yi, H. Chen, X. He, Parameter analysis of damaged region for laminates with matrix defects. J. Sandw. Struct. Mater. 23, 580–620 (2021). https://doi.org/10.1177/1099636219842290

    Article  Google Scholar 

  41. L. Cao, Changing port governance model: port spatial structure and trade efficiency. J. Coast. Res. 95, 963 (2020). https://doi.org/10.2112/SI95-187.1

    Article  Google Scholar 

  42. B. Mou, F. Zhao, Q. Qiao et al., Flexural behavior of beam to column joints with or without an overlying concrete slab. Eng. Struct. 199, 109616 (2019). https://doi.org/10.1016/j.engstruct.2019.109616

    Article  Google Scholar 

  43. Z. Yang, P. Xu, W. Wei et al., Influence of the crosswind on the pantograph arcing dynamics. IEEE Trans. Plasma Sci. 48, 2822–2830 (2020). https://doi.org/10.1109/TPS.2020.3010553

    Article  ADS  Google Scholar 

  44. C. Zuo, J. Sun, J. Li et al., High-resolution transport-of-intensity quantitative phase microscopy with annular illumination. Sci. Rep. 7, 7654 (2017). https://doi.org/10.1038/s41598-017-06837-1

    Article  ADS  Google Scholar 

  45. C.Q. Ru, Effective bending stiffness of carbon nanotubes. Phys. Rev. B 62, 9973–9976 (2000). https://doi.org/10.1103/PhysRevB.62.9973

    Article  ADS  Google Scholar 

  46. K.T. Lau, C. Gu, D. Hui, A critical review on nanotube and nanotube/nanoclay related polymer composite materials. Compos. Part. B Eng. 37, 425–436 (2006). https://doi.org/10.1016/j.compositesb.2006.02.020

    Article  Google Scholar 

  47. M. Meo, M. Rossi, Prediction of Young’s modulus of single wall carbon nanotubes by molecular-mechanics based finite element modelling. Compos. Sci. Technol. 66, 1597–1605 (2006). https://doi.org/10.1016/j.compscitech.2005.11.015

    Article  Google Scholar 

  48. J. Zhang, Q. Chen, J. Sun et al., On a universal solution to the transport-of-intensity equation. Opt. Lett. 45, 3649 (2020). https://doi.org/10.1364/OL.391823

    Article  ADS  Google Scholar 

  49. Y. Hu, Q. Chen, S. Feng, C. Zuo, Microscopic fringe projection profilometry: a review. Opt. Lasers Eng. 135, 106192 (2020). https://doi.org/10.1016/j.optlaseng.2020.106192

    Article  Google Scholar 

  50. Q. Dong, L. Cui, Reliability analysis of a system with two-stage degradation using Wiener processes with piecewise linear drift. IMA J. Manag. Math. 32, 3–29 (2021). https://doi.org/10.1093/imaman/dpaa009

    Article  MathSciNet  Google Scholar 

  51. C. Zhang, H. Wang, Swing vibration control of suspended structures using the active rotary inertia driver system: theoretical modeling and experimental verification. Struct. Control Heal. Monit. (2020). https://doi.org/10.1002/stc.2543

    Article  Google Scholar 

  52. L. Zhu, L. Kong, C. Zhang, Numerical study on hysteretic behaviour of horizontal-connection and energy-dissipation structures developed for prefabricated shear walls. Appl. Sci. 10, 1240 (2020). https://doi.org/10.3390/app10041240

    Article  Google Scholar 

  53. J.M. Wernik, S.A. Meguid, Multiscale modeling of the nonlinear response of nano-reinforced polymers. Acta Mech. 217, 1–16 (2011). https://doi.org/10.1007/s00707-010-0377-7

    Article  MATH  Google Scholar 

  54. K.I. Tserpes, P. Papanikos, Finite element modeling of single-walled carbon nanotubes. Compos. Part B Eng. 36, 468–477 (2005). https://doi.org/10.1016/j.compositesb.2004.10.003

    Article  Google Scholar 

  55. C. Li, T.-W. Chou, A structural mechanics approach for the analysis of carbon nanotubes. Int. J. Solids Struct. 40, 2487–2499 (2003). https://doi.org/10.1016/S0020-7683(03)00056-8

    Article  MATH  Google Scholar 

  56. Y. Xiang, H.-S. Shen, Shear buckling of rippled graphene by molecular dynamics simulation. Mater. Today Commun. 3, 149–155 (2015). https://doi.org/10.1016/j.mtcomm.2015.01.001

    Article  Google Scholar 

  57. I. Benedetti, H. Nguyen, R.A. Soler-Crespo et al., Formulation and validation of a reduced order model of 2D materials exhibiting a two-phase microstructure as applied to graphene oxide. J. Mech. Phys. Solids 112, 66–88 (2018). https://doi.org/10.1016/j.jmps.2017.11.012

    Article  ADS  MathSciNet  Google Scholar 

  58. J.P. Lu, Elastic properties of carbon nanotubes and nanoropes. Phys. Rev. Lett. 79, 1297–1300 (1997). https://doi.org/10.1103/PhysRevLett.79.1297

    Article  ADS  Google Scholar 

  59. E. Hernández, C. Goze, P. Bernier, A. Rubio, Elastic properties of single-wall nanotubes. Appl. Phys. A Mater. Sci. Process 68, 287–292 (1999). https://doi.org/10.1007/s003390050890

    Article  ADS  Google Scholar 

  60. B.K. Sharma, Graphene—an exotic condensed matter and its impact on technology. Emerg. Mater. Res. 9, 1–49 (2020). https://doi.org/10.1680/jemmr.16.00147

    Article  ADS  Google Scholar 

  61. L. Chen, Q. Zhao, Z. Gong, H. Zhang, The effects of different defects on the elastic constants of single-walled carbon nanotubes. in 2010 IEEE 5th International Conference on Nano/Micro Engineered and Molecular Systems. IEEE, pp 777–780 (2010)

  62. X. Lu, Z. Hu, Mechanical property evaluation of single-walled carbon nanotubes by finite element modeling. Compos. Part B Eng. 43, 1902–1913 (2012). https://doi.org/10.1016/j.compositesb.2012.02.002

    Article  Google Scholar 

  63. J.R. Xiao, J. Staniszewski, J.W. Gillespie, Tensile behaviors of graphene sheets and carbon nanotubes with multiple Stone-Wales defects. Mater. Sci. Eng. A 527, 715–723 (2010). https://doi.org/10.1016/j.msea.2009.10.052

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank the referees for their valuable comments. This research is financially supported by the Ministry of Science and Technology of China (Grant No. 2019YFE0112400), National Science Foundation of China (Grant No. 51678322), the Taishan Scholar Priority Discipline Talent Group program funded by the Shan Dong Province, and the first-class discipline project funded by the Education Department of Shandong Province.

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Authors and Affiliations

  1. Structural Vibration Control Group, Qingdao University of Technology, Qingdao, 266033, China

    Arameh Eyvazian & Chunwei Zhang

  2. Department of Mechanical Engineering, Politecnico Di Milano, 20156, Milan, Italy

    Arameh Eyvazian

  3. Department of Mechanical and Industrial Engineering, Qatar University, P.O. Box 2713, Doha, Qatar

    Farayi Musharavati

  4. Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box, 87317-53153, Kashan, Iran

    Ashkan Farazin & Mehdi Mohammadimehr

  5. Research Institute of Experimental Mechanical Engineering, Center for Vibration Testing and Monitoring of the State of Structures, South Ural State University (SUSU), Lenin Prospect 76, Chelyabinsk, 454080, Russian Federation

    Afrasyab Khan

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Eyvazian, A., Zhang, C., Musharavati, F. et al. Effects of appearance characteristics on the mechanical properties of defective SWCNTs: using finite element methods and molecular dynamics simulation. Eur. Phys. J. Plus 136, 946 (2021). https://doi.org/10.1140/epjp/s13360-021-01840-y

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