Skip to main content
Log in

Computational evaluation of the mechanical properties of synthesized graphene quantum dots under consideration of defects

  • Original Article
  • Published:
Carbon Letters Aims and scope Submit manuscript

Abstract

The behaviour of semiconducting graphene quantum dots (GQDs), as good candidates for various biological carrier applications and optical sensing, are necessary to be studied under various conditions. In this study, GQD models were generated according to the geometrical and chemical specifications of synthesized GQDs to achieve the most realistic models. The GQDs’ bandgap and distribution of their electric surface charges were obtained using computational chemistry method. Finite element analysis was conducted on pristine and defective GQDs to study Young and shear modulus. Buckling load and resonant frequency modes of GQDs were calculated analytically and demonstrated under various boundary conditions. The dimension of GQDs has an average of 3.5 ± 0.4 nm, with an interlayer spacing of 0.36–0.40 nm. Computational chemistry studies revealed the characteristic zero-band-gap nature of graphene. Finite element studies showed that the by introducing the inevitable dislocation, mono atom vacancy and Stone–Wales defects to GQD models, their mechanical properties reduces to approach data from experimental investigations, whereas an increase in the number of layers does not influence the obtained results significantly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

AD:

Atomistic dislocation

AV:

Atom vacancy

CNT:

Carbon nanotube

DFT:

Density functional theory

FE:

Finite element

GQD:

Graphene quantum dots

HOMO:

Highest occupied molecular orbitals

L-J:

Lennard-Jones

LUMO:

Lowest unoccupied molecular orbitals

MD:

Molecular dynamics

QY:

Quantum yield

SW:

Stone–Wales

References

  1. Ma L, Kohli M, Smith A (2013) Nanoparticles for combination drug therapy. ACS Nano 7:9518–9525

    Article  CAS  Google Scholar 

  2. Dong Y, Shao J, Chen C, Li H, Wang R, Chi Y, Lin X, Chen G (2012) Blue luminescent graphene quantum dots and graphene oxide prepared by tuning the carbonization degree of citric acid. Carbon N Y 50:4738–4743. https://doi.org/10.1016/j.carbon.2012.06.002

    Article  CAS  Google Scholar 

  3. Wang S, Chen ZG, Cole I, Li Q (2015) Structural evolution of graphene quantum dots during thermal decomposition of citric acid and the corresponding photoluminescence. Carbon N Y 82:304–313. https://doi.org/10.1016/j.carbon.2014.10.075

    Article  CAS  Google Scholar 

  4. Bagheri Z, Ehtesabi H, Rahmandoust M, Ahadian MM, Hallaji Z, Eskandari F, Jokar E (2017) New insight into the concept of carbonization degree in synthesis of carbon dots to achieve facile smartphone based sensing platform. Sci Rep. 7:1–11. https://doi.org/10.1038/s41598-017-11572-8

    Article  CAS  Google Scholar 

  5. Rahmandoust M, Öchsner A (2009) Influence of structural imperfections and doping on the mechanical properties of single-walled carbon nanotubes. J Nano Res. 6:185–196. https://doi.org/10.4028/www.scientific.net/JNanoR.6.185

    Article  CAS  Google Scholar 

  6. Rahmandoust M, Öchsner A (2012) On finite element modeling of single- and multi-walled carbon nanotubes. J Nanosci Nanotechnol. https://doi.org/10.1166/jnn.2012.4521

    Article  Google Scholar 

  7. Rahmandoust M, Öchsner A (2015) Young’s modulus variation of carbon nanotubes due to defects associated with atomic reconstruction of random vacancies. J Comput Theor Nanosci 12:2281–2286. https://doi.org/10.1166/jctn.2015.4020

    Article  CAS  Google Scholar 

  8. Ghavamian A, Rahmandoust M, Öchsner A (2012) A numerical evaluation of the influence of defects on the elastic modulus of single and multi-walled carbon nanotubes. Comput Mater Sci 62:110–116. https://doi.org/10.1016/j.commatsci.2012.05.003

    Article  CAS  Google Scholar 

  9. Dehghan Pir MM, Rahmandoust M, Öchsner A (2017) Obtaining global equations for the Young’s modulus of perfect and defective carbon nanotubes. Mater Res Express. 4(125012):1–15. https://doi.org/10.1088/2053-1591/aa9bae

    Article  CAS  Google Scholar 

  10. Mavalizadeh S, Rahmandoust M, Öchsner A (2011) Numerical investigation of the overall stiffness of carbon nanotube based composite materials. J Nano Res. https://doi.org/10.4028/www.scientific.net/JNanoR.13.47

    Article  Google Scholar 

  11. Eslami Afrooz I, Öchsner A, Rahmandoust M (2012) Effects of the carbon nanotube distribution on the macroscopic stiffness of composite materials. Comput Mater Sci 51:422–429. https://doi.org/10.1016/j.commatsci.2011.08.003

    Article  CAS  Google Scholar 

  12. Farsadi M, Öchsner A, Rahmandoust M (2013) Numerical investigation of composite materials reinforced with waved carbon nanotubes. J Compos Mater. https://doi.org/10.1177/0021998312448495

    Article  Google Scholar 

  13. Rahmandoust M, Ayatollahi MR (2016) Characterization of carbon nanotube based composites under consideration of defects. Springer, Cham. https://doi.org/10.1007/978-3-319-00251-4

    Book  Google Scholar 

  14. Lee C, Wei X, Kysar JW, Hone J (2008) Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321:385–388. https://doi.org/10.1126/science.1157996

    Article  CAS  Google Scholar 

  15. Chen H, Müller MB, Gilmore KJ, Wallace GG, Li D (2008) Mechanically strong, electrically conductive, and biocompatible graphene paper. Adv Mater 20:3557–3561. https://doi.org/10.1002/adma.200800757

    Article  CAS  Google Scholar 

  16. Tsoukleri G, Parthenios J, Papagelis K, Jalil R, Ferrari AC, Geim AK, Novoselov KS, Galiotis C (2009) Subjecting a graphene monolayer to tension and compression. Small 5:2397–2402. https://doi.org/10.1002/smll.200900802

    Article  CAS  Google Scholar 

  17. Rasuli R, Irajizad A, Ahadian MM (2010) Mechanical properties of graphene cantilever from atomic force microscopy and density functional theory. Nanotechnology. 21:185503. https://doi.org/10.1088/0957-4484/21/18/185503

    Article  CAS  Google Scholar 

  18. Mohammadi M, Farajpour A, Moradi A, Ghayour M (2014) Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment. Compos Part B Eng. 56:629–637. https://doi.org/10.1016/J.COMPOSITESB.2013.08.060

    Article  CAS  Google Scholar 

  19. Mukhopadhyay T, Mahata A, Adhikari S, Asle Zaeem M (2017) Effective mechanical properties of multilayer nano-heterostructures. Sci Rep. 7:15818

    Article  CAS  Google Scholar 

  20. Van Lier G, Van Alsenoy C, Van Doren V, Geerlings P (2000) Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene. Chem Phys Lett 326:181–185. https://doi.org/10.1016/S0009-2614(00)00764-8

    Article  Google Scholar 

  21. Ni Z, Bu H, Zou M, Yi H, Bi K, Chen Y (2010) Anisotropic mechanical properties of graphene sheets from molecular dynamics. Phys B Condens Matter. 405:1301–1306. https://doi.org/10.1016/J.PHYSB.2009.11.071

    Article  CAS  Google Scholar 

  22. Min K, Aluru NR (2011) Mechanical properties of graphene under shear deformation. Appl Phys Lett 98:013113. https://doi.org/10.1063/1.3534787

    Article  CAS  Google Scholar 

  23. Shokrieh MM, Rafiee R (2010) Prediction of Young’s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach. Mater Des 31:790–795. https://doi.org/10.1016/J.MATDES.2009.07.058

    Article  CAS  Google Scholar 

  24. Qin Q, An H, He C, Xie L, Peng Q (2019) Anisotropic and temperature dependent mechanical properties of carbon honeycomb. Nanotechnology. 30:325704. https://doi.org/10.1088/1361-6528/ab14a1

    Article  CAS  Google Scholar 

  25. Reddy CD, Rajendran S, Liew KM (2006) Equilibrium configuration and continuum elastic properties of finite sized graphene. Nanotechnology. 17:864–870. https://doi.org/10.1088/0957-4484/17/3/042

    Article  CAS  Google Scholar 

  26. Sakhaee-Pour A (2009) Elastic properties of single-layered graphene sheet. Solid State Commun 149:91–95. https://doi.org/10.1016/j.ssc.2008.09.050

    Article  CAS  Google Scholar 

  27. Scarpa F, Adhikari S, Srikantha Phani A (2009) Effective elastic mechanical properties of single layer graphene sheets. Nanotechnology. 20:065709. https://doi.org/10.1088/0957-4484/20/6/065709

    Article  CAS  Google Scholar 

  28. Georgantzinos SK, Giannopoulos GI, Katsareas DE, Kakavas PA, Anifantis NK (2011) Size-dependent non-linear mechanical properties of graphene nanoribbons. Comput Mater Sci 50:2057–2062. https://doi.org/10.1016/J.COMMATSCI.2011.02.008

    Article  CAS  Google Scholar 

  29. Wang SP, Guo JG, Jiang Y (2013) The size- and chirality-dependent elastic properties of graphene nanofilms. J Comput Theor Nanosci 10:250–256. https://doi.org/10.1166/jctn.2013.2687

    Article  CAS  Google Scholar 

  30. Rahmandoust M, Öchsner A (2016) Defects: defects in carbon nanotubes. In: Kharisov BI, Kharissova OV, Ortiz-Mendez U (eds) CRC Concise Encycl. Nanotechnol, Boca Raton, pp 158–165

    Google Scholar 

  31. Salvetat J-P, Briggs G, Bonard J-M, Bacsa R, Kulik A, Stöckli T, Burnham N, Forró L (1999) Elastic and shear moduli of single-walled carbon nanotube ropes. Phys Rev Lett 82:944–947. https://doi.org/10.1103/PhysRevLett.82.944

    Article  CAS  Google Scholar 

  32. Jespersen TS, Nygard J (2007) Probing induced defects in individual carbon nanotubes using electrostatic force microscopy. Appl Phys A 88:309–313. https://doi.org/10.1007/s00339-007-3927-7

    Article  CAS  Google Scholar 

  33. Ghavamian A, Rahmandoust M, Öchsner A (2013) On the determination of the shear modulus of carbon nanotubes. Compos Part B Eng. 44:52–59. https://doi.org/10.1016/j.compositesb.2012.07.040

    Article  CAS  Google Scholar 

  34. Jing N, Xue Q, Ling C, Shan M, Zhang T, Zhou X, Jiao Z (2012) Effect of defects on Young’s modulus of graphene sheets: a molecular dynamics simulation. RSC Adv. 2:9124. https://doi.org/10.1039/c2ra21228e

    Article  CAS  Google Scholar 

  35. Wang SP, Guo JG, Zhou LJ (2013) Influence of Stone-Wales defects on elastic properties of graphene nanofilms. Phys E Low-Dimens Syst Nanostructures. 48:29–35. https://doi.org/10.1016/j.physe.2012.11.002

    Article  CAS  Google Scholar 

  36. Xu N, Guo J-G, Cui Z (2016) The influence of tilt grain boundaries on the mechanical properties of bicrystalline graphene nanoribbons. Phys E Low-dimens Syst Nanostr. 84:168–174. https://doi.org/10.1016/J.PHYSE.2016.06.002

    Article  CAS  Google Scholar 

  37. Chu L, Shi J, Braun R (2019) The equivalent Young’s modulus prediction for vacancy defected graphene under shear stress. Phys E Low-Dimens Syst Nanostr. 110:115–122. https://doi.org/10.1016/j.physe.2019.01.023

    Article  CAS  Google Scholar 

  38. Li M, Deng T, Zheng B, Zhang Y, Liao Y, Zhou H (2019) Effect of defects on the mechanical and thermal properties of graphene. Nanomaterials. 9(347):1–15. https://doi.org/10.3390/nano9030347

    Article  CAS  Google Scholar 

  39. Xie L, Sun T, He C, An H, Qin Q, Peng Q (2019) Effect of angle, temperature and vacancy defects on mechanical properties of PSI-graphene. Crystals. 9(238):1–10. https://doi.org/10.3390/cryst9050238

    Article  CAS  Google Scholar 

  40. Rahmandoust M, Öchsner A (2011) Buckling behaviour and natural frequency of zigzag and armchair single-walled carbon nanotubes. J Nano Res. 16:153–160. https://doi.org/10.4028/www.scientific.net/JNanoR.16.153

    Article  CAS  Google Scholar 

  41. Sakhaee-Pour A (2009) Elastic buckling of single-layered graphene sheet. Comput Mater Sci 45:266–270. https://doi.org/10.1016/J.COMMATSCI.2008.09.024

    Article  CAS  Google Scholar 

  42. Anjomshoa A, Shahidi AR, Hassani B, Jomehzadeh E (2014) Finite element buckling analysis of multi-layered graphene sheets on elastic substrate based on nonlocal elasticity theory. Appl Math Model. https://doi.org/10.1016/j.apm.2014.03.036

    Article  Google Scholar 

  43. Fadaee M (2016) Buckling analysis of a defective annular graphene sheet in elastic medium. Appl Math Model 40:1863–1872. https://doi.org/10.1016/J.APM.2015.09.029

    Article  Google Scholar 

  44. Chu L, Shi J, Ben S (2018) Buckling analysis of vacancy-defected graphene sheets by the stochastic finite element method. Materials. 11(1545):1–15. https://doi.org/10.3390/ma11091545

    Article  CAS  Google Scholar 

  45. Genoese A, Genoese A, Rizzi NL, Salerno G (2019) Buckling analysis of single-layer graphene sheets using molecular mechanics. Front Mater. 6:1–13. https://doi.org/10.3389/fmats.2019.00026

    Article  Google Scholar 

  46. Poot M, van der Zant HSJ (2008) Nanomechanical properties of few-layer graphene membranes. Appl Phys Lett 92:063111. https://doi.org/10.1063/1.2857472

    Article  CAS  Google Scholar 

  47. Garcia-Sanchez D, van der Zande AM, Paulo AS, Lassagne B, McEuen PL, Bachtold A (2008) Imaging mechanical vibrations in suspended graphene sheets. Nano Lett 8:1399–1403. https://doi.org/10.1021/nl080201h

    Article  CAS  Google Scholar 

  48. Akgöz B, Civalek Ö (2012) Free vibration analysis for single-layered graphene sheets in an elastic matrix via modified couple stress theory. Mater Des 42:164–171. https://doi.org/10.1016/j.matdes.2012.06.002

    Article  CAS  Google Scholar 

  49. Lin RM (2012) Nanoscale vibration characteristics of multi-layered graphene sheets. Mech Syst Signal Process. 29:251–261. https://doi.org/10.1016/j.ymssp.2011.11.005

    Article  Google Scholar 

  50. Lu L, Ru CQ, Guo XM (2017) Vibration of a multilayer graphene sheet under layerwise tension forces. Int J Mech Sci 121:157–163. https://doi.org/10.1016/j.ijmecsci.2017.01.007

    Article  Google Scholar 

  51. Chu L, Shi J, de Cursi ES (2018) Vibration analysis of vacancy defected graphene sheets by monte carlo based finite element method. Nanomaterials. 8(489):1–21. https://doi.org/10.3390/nano8070489

    Article  CAS  Google Scholar 

  52. Namnabat MS, Barzegar A, Javanbakht M (2019) Finite element buckling analysis of double-layered graphene nanoribbons. Mater Res Express. 6(055023):1–20. https://doi.org/10.1088/2053-1591/ab032d

    Article  CAS  Google Scholar 

  53. Mohammadi A, Rahmandoust M, Mirzajani F, AzadkhahShalmani A, Raoufi M (2020) Optimization of the interaction of graphene quantum dots with lipase for biological applications. J Biomed Mater Res Part B Appl Biomater. https://doi.org/10.1002/jbm.b.34579

    Article  Google Scholar 

  54. Horcas I, Fernández R, Gómez-Rodríguez JM, Colchero J, Gómez-Herrero J, Baro AM (2007) WSXM: a software for scanning probe microscopy and a tool for nanotechnology. Rev Sci Instrum 78:013705. https://doi.org/10.1063/1.2432410

    Article  CAS  Google Scholar 

  55. Wang L, Zhang Q (2012) Elastic behavior of bilayer graphene under in-plane loadings. Curr Appl Phys 12:1173–1177. https://doi.org/10.1016/J.CAP.2012.02.043

    Article  Google Scholar 

Download references

Acknowledgements

The present work was accomplished with the research grant of the vice–presidency for research and technology, Shahid Beheshti University, G.C., 600/1446.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Moones Rahmandoust.

Ethics declarations

Conflict of interest

The author has no competing interest to declare.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rahmandoust, M. Computational evaluation of the mechanical properties of synthesized graphene quantum dots under consideration of defects. Carbon Lett. 31, 427–440 (2021). https://doi.org/10.1007/s42823-020-00171-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42823-020-00171-9

Keywords

Navigation