Acta Mechanica Solida Sinica

, Volume 32, Issue 1, pp 81–92 | Cite as

Revealing the Effects of Pore Size and Geometry on the Mechanical Properties of Graphene Nanopore Using the Atomistic Finite Element Method

  • Prapasiri Pongprayoon
  • Attaphon ChaimanatsakunEmail author


Graphene nanopore has been extensively employed in nanoscale sensing devices due to its outstanding properties. The understanding of its mechanical properties at nanoscale is crucial for sensing improvement. In this work, the mechanical properties of graphene nanopore are thus investigated using the atomistic finite element method. Four graphene models with different pore shapes (circle (CR), horizontal rectangle (RH), vertical rectangle (RV) and square (SQ)) in sub-5nm size, which could be successfully fabricated experimentally, have been studied here. The force normal to a pore rim is applied to mimic the impact force due to a fluid flow. As expected, the strength of nanoholed graphene is pore size dependent. Increasing pore size results in the reduction in its strength. Comparing between different pore shapes with comparable sizes, the order of pore strength is \(\hbox {CR}>\hbox {RH}>\hbox {RV}>\hbox {SQ}\). In addition, two different corner structures (V-like or zigzag and C-like or armchair corners) are observed, where the V-like structure causes higher tensile stress. Besides, we find that the highest tensile stress is produced at the corner in all cases. This finding suggests the corners as an origin of pore fracture. The results of RH and RV highlight the impact of a direction of pore orientation on mechanical properties. Aligning a long side of a pore along the zigzag direction gains more tensile stress, while aligning on an armchair side causes a deflection. Not only the pore geometry and size, but also the pore orientation is crucial for defining the mechanical properties of nanopores.


Nanopores Atomistic finite element Graphene nanopores Nanosensors 



We would like to thank Kasetsart University Research and Development Institute (KURDI) and Faculty of Engineering at Sriracha, Kasetsart University for financial supports.

Supplementary material

10338_2018_61_MOESM1_ESM.docx (3.1 mb)
Supplementary material 1 (docx 3129 KB)


  1. 1.
    Rollings RC, Kuan AT, Golovchenko JA. Ion selectivity of graphene nanopores. Nat Commun. 2016;7. (ARTN 11408).
  2. 2.
    Al-Dirini F, Mohammed MA, Hossain MS, Hossain FM, Nirmalathas A, Skafidas E. Tuneable graphene nanopores for single biomolecule detection. Nanoscale. 2016;8(19):10066–77. Scholar
  3. 3.
    Zhang ZS, Shen JW, Wang HB, Wang Q, Zhang JQ, Liang LJ, Agren H, Tu YQ. Effects of graphene nanopore geometry on DNA sequencing. J Phys Chem Lett. 2014;5(9):1602–7. Scholar
  4. 4.
    Qiu W, Nguyen P, Skafidas E. Graphene nanopores: electronic transport properties and design methodology. Phys Chem Chem Phys. 2014;16(4):1451–9. Scholar
  5. 5.
    Heerema SJ, Dekker C. Graphene nanodevices for DNA sequencing. Nat Nanotechnol. 2016;11(2):127–36. Scholar
  6. 6.
    Wells DB, Belkin M, Comer J, Aksimentiev A. Assessing graphene nanopores for sequencing DNA. Nano Lett. 2012;12(8):4117–23. Scholar
  7. 7.
    Wilson J, Sloman L, He ZR, Aksimentiev A. Graphene nanopores for protein sequencing. Adv Funct Mater. 2016;26(27):4830–8. Scholar
  8. 8.
    Schneider GF, Kowalczyk SW, Calado VE, Pandraud G, Zandbergen HW, Vandersypen LMK, Dekker C. DNA translocation through graphene nanopores. Nano Lett. 2010;10(8):3163–7. Scholar
  9. 9.
    Koenig SP, Wang LD, Pellegrino J, Bunch JS. Selective molecular sieving through porous graphene. Nat Nanotechnol. 2012;7(11):728–32. Scholar
  10. 10.
    Cohen-Tanugi D, Grossman JC. Water Desalination across Nanoporous Graphene. Nano Lett. 2012;12(7):3602–8. Scholar
  11. 11.
    Yoon HW, Cho YH, Park HB. Graphene-based membranes: status and prospects. Philos Trans R Soc A. 2016;374:2060. (ARTN 20150024).Google Scholar
  12. 12.
    Zhu CQ, Li H, Meng S. Transport behavior of water molecules through two-dimensional nanopores. J Chem Phys. 2014;141(18) (Artn18c528)
  13. 13.
    Kowalczyk SW, Tuijtel MW, Donkers SP, Dekker C. Unraveling single-stranded DNA in a solid-state nanopore. Nano Lett. 2010;10(4):1414–20. Scholar
  14. 14.
    Clarke J, Wu HC, Jayasinghe L, Patel A, Reid S, Bayley H. Continuous base identification for single-molecule nanopore DNA sequencing. Nat Nanotechnol. 2009;4(4):265–70. Scholar
  15. 15.
    Dekker C. Solid-state nanopores. Nat Nanotechnol. 2007;2(4):209–15. Scholar
  16. 16.
    Howorka S, Siwy Z. Nanopore analytics: sensing of single molecules. Chem Soc Rev. 2009;38(8):2360–84. Scholar
  17. 17.
    Olasagasti F, Lieberman KR, Benner S, Cherf GM, Dahl JM, Deamer DW, Akeson M. Replication of individual DNA molecules under electronic control using a protein nanopore. Nat Nanotechnol. 2010;5(11):798–806. Scholar
  18. 18.
    Fischbein MD, Drndic M. Electron beam nanosculpting of suspended graphene sheets. Appl Phys Lett. 2008;93(11). (Artn 113107).
  19. 19.
    Celebi K, Buchheim J, Wyss RM, Droudian A, Gasser P, Shorubalko I, Kye JI, Lee C, Park HG. Ultimate permeation across atomically thin porous graphene. Science. 2014;344(6181):289–92. Scholar
  20. 20.
    O’Hern SC, Boutilier MSH, Idrobo JC, Song Y, Kong J, Laoui T, Atieh M, Karnik R. Selective ionic transport through tunable subnanometer pores in single-layer graphene membranes. Nano Lett. 2014;14(3):1234–41. Scholar
  21. 21.
    Surwade SP, Smirnov SN, Vlassiouk IV, Unocic RR, Veith GM, Dai S, Mahurin SM. Water desalination using nanoporous single-layer graphene (vol 10, pg 459, 2015). Nat Nanotechnol. 2015;10:459.
  22. 22.
    Kaur S, Narang SB, Randhawa DKK. Influence of the pore shape and dimension on the enhancement of thermoelectric performance of graphene nanoribbons. J Mater Res. 2017;32(6):1149–59. Scholar
  23. 23.
    Lapshin RV. STM observation of a box-shaped graphene nanostructure appeared after mechanical cleavage of pyrolytic graphite. Appl Surf Sci. 2016;360:451–60. Scholar
  24. 24.
    Deng Y, Huang Q, Zhao Y, Zhou D, Ying C, Wang D. Precise fabrication of a 5 nm graphene nanopore with a helium ion microscope for biomolecule detection. Nanotechnology. 2017;28(4):045302. Scholar
  25. 25.
    Lee J, Yang ZQ, Zhou W, Pennycook SJ, Pantelides ST, Chisholm MF. Stabilization of graphene nanopore. Proc Natl Acad Sci U S A. 2014;111(21):7522–6. Scholar
  26. 26.
    Whitney AV, Myers BD, Van Duyne RP. Sub-100 nm triangular nanopores fabricated with the reactive ion etching variant of nanosphere lithography and angle-resolved nanosphere lithography. Nano Lett. 2004;4(8):1507–11. Scholar
  27. 27.
    Li J, Stein D, McMullan C, Branton D, Aziz MJ, Golovchenko JA. Ion-beam sculpting at nanometre length scales. Nature. 2001;412(6843):166–9. Scholar
  28. 28.
    Liu Y, Chen X. Mechanical properties of nanoporous graphene membrane. J Appl Phys. 2014;115(3):034303.Google Scholar
  29. 29.
    Georgantzinos SK, Katsareas DE, Anifantis NK. Limit load analysis of graphene with pinhole defects: a nonlinear structural mechanics approach. Int J Mech Sci. 2012;55(1):85–94. Scholar
  30. 30.
    Zhang T, Li XY, Kadkhodaei S, Gao HJ. Flaw insensitive fracture in nanocrystalline graphene. Nano Lett. 2012;12(9):4605–10. Scholar
  31. 31.
    Cohen-Tanugi D, Grossman JC. Mechanical strength of nanoporous graphene as a desalination membrane. Nano Lett. 2014;14(11):6171–8. Scholar
  32. 32.
    Boutilier MS, Sun C, O’Hern SC, Au H, Hadjiconstantinou NG, Karnik R. Implications of permeation through intrinsic defects in graphene on the design of defect-tolerant membranes for gas separation. Acs Nano. 2014;8(1):841–9. Scholar
  33. 33.
    Agrawal KV, Benck JD, Yuan Z, Misra RP, Rajan AG, Eatmon Y, Kale S, Chu XMS, Li DO, Gong CC, Warner J, Wang QH, Blankschtein D, Strano MS. Fabrication, pressure testing, and nanopore formation of single layer graphene membranes. J Phys Chem C. 2017;121(26):14312–21. Scholar
  34. 34.
    Lu B, Hoogerheide DP, Zhao Q, Zhang HB, Zhipeng TP, Yu DP, Goloychenko JA. Pressure-controlled motion of single polymers through solid-state nanopores. Nano Lett. 2013;13(7):3048–52. Scholar
  35. 35.
    Wang L, Williams CM, Boutilier MSH, Kidambi PR, Karnik R. Single-layer graphene membranes withstand ultrahigh applied pressure. Nano Lett. 2017;17(5):3081–8. Scholar
  36. 36.
    Song ZG, Xu ZP, Huang XL, Kim JY, Zheng QS. On the fracture of supported graphene under pressure. J Appl Mech-T Asme. 2013;80(4). (Artn 040911).
  37. 37.
    Khandoker N, Islam S, Hiung YS. Finite element simulation of mechanical properties of graphene sheets. In: 29th symposium of Malaysian chemical engineers (Somche) 2016. 2017;206. (Unsp 012057).
  38. 38.
    Lee HL, Hsu JC, Lin SY, Chang WJ. Sensitivity analysis of single-layer graphene resonators using atomic finite element method. J Appl Phys. 2013;114(12). (Artn 123506)
  39. 39.
    Gong XH, Jiang SW, Wang XF, Liu S, Wang S. Finite element analysis of graphene resonator tuned by pressure difference. In: 2014 15th international conference on electronic packaging technology (Icept), 2014;516–519.Google Scholar
  40. 40.
    Tserpes KI, Papanikos P. Finite element modeling of single-walled carbon nanotubes. Compos Part B-Eng. 2005;36(5):468–77. Scholar
  41. 41.
    Lee HL, Wang SW, Yang YC, Chang WJ. Effect of porosity on the mechanical properties of a nanoporous graphene membrane using the atomic-scale finite element method. Acta Mech. 2017;228(7):2623–9. Scholar
  42. 42.
    She H, Wang BA. A geometrically nonlinear finite element model of nanomaterials with consideration of surface effects. Finite Elem Anal Des. 2009;45(6–7):463–7. Scholar
  43. 43.
    Li C, Chou T-W. A structural mechanics approach for the analysis of carbon nanotubes. Int J Solids Struct. 2003;40(10):2487–99. Scholar
  44. 44.
    Rappé AK, Casewit CJ, Colwell K, Goddard Iii W, Skiff W. UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J Am Chem Soc. 1992;114(25):10024–35.Google Scholar
  45. 45.
    Gelin BR. Molecular modeling of polymer structures and properties. Munich: Hanser Publishers; 1994.Google Scholar
  46. 46.
    Tserpes KI, Papanikos P. Finite element modeling of single-walled carbon nanotubes. Compos Part B Eng. 2005;36(5):468–77. Scholar
  47. 47.
    Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. J Am Chem Soc. 1995;117(19):5179–97. Scholar
  48. 48.
    Ghaderi SH, Hajiesmaili E. Molecular structural mechanics applied to coiled carbon nanotubes. Comput Mater Sci. 2012;55:344–9.Google Scholar
  49. 49.
    Lee H-L, Chang W-J. Vibrational analysis of a single-layered nanoporous graphene membrane. Nano. 2016;11(04):1650043.Google Scholar
  50. 50.
    Lee H-L, Hsu J-C, Lin S-Y, Chang W-J. Sensitivity analysis of single-layer graphene resonators using atomic finite element method. J Appl Phys. 2013;114(12):123506. Scholar
  51. 51.
    Rangel JH, Brostow W, Castano VM. Mechanical modeling of a single-walled carbon nanotube using the finite element approach. Polimery. 2013;58(4):276–81.Google Scholar
  52. 52.
    Hamed Mashhadzadeh A, Fereidoon A, Ghorbanzadeh Ahangari M. Combining density functional theory-finite element multi-scale method to predict mechanical properties of polypropylene/graphene nanocomposites: Experimental study. Mater Chem Phys. 2017;201(Supplement C):214–23. Scholar
  53. 53.
    Lee H-L, Wang S-W, Yang Y-C, Chang W-J. Effect of porosity on the mechanical properties of a nanoporous graphene membrane using the atomic-scale finite element method. Acta Mech. 2017;228(7):2623–9. Scholar
  54. 54.
    Karimi M, Montazeri A, Ghajar R. On the elasto-plastic behavior of CNT-polymer nanocomposites. Compos Struct. 2017;160(Supplement C):782–91. Scholar
  55. 55.
    Ansari R, Rouhi S. Atomistic finite element model for axial buckling of single-walled carbon nanotubes. Phys E Low-dimens Syst Nanostruct. 2010;43(1):58–69. Scholar
  56. 56.
    Rouhi S, Ansari R. Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets. Phys E Low-dimens Syst Nanostruct. 2012;44(4):764–72. Scholar
  57. 57.
    Reddy C, Rajendran S, Liew K. Equilibrium configuration and continuum elastic properties of finite sized graphene. Nanotechnology. 2006;17(3):864.Google Scholar
  58. 58.
    Hu L, Wyant S, Muniz AR, Ramasubramaniam A, Maroudas D. Mechanical behavior and fracture of graphene nanomeshes. J Appl Phys. 2015;117(2). (Artn 024302).
  59. 59.
    Fang TH, Lee ZW, Chang WJ. Molecular dynamics study of the shear strength and fracture behavior of nanoporous graphene membranes. Curr Appl Phys. 2017;17(10):1323–8. Scholar
  60. 60.
    Cohen-Tanugi D, Grossman JC. Mechanical strength of nanoporous graphene as a desalination membrane. Nano Lett. 2014;14(11):6171–8.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2018

Authors and Affiliations

  • Prapasiri Pongprayoon
    • 1
    • 2
    • 3
  • Attaphon Chaimanatsakun
    • 4
    Email author
  1. 1.Department of Chemistry, Faculty of ScienceKasetsart UniversityChatuchak, BangkokThailand
  2. 2.Center for Advanced Studies in Nanotechnology for Chemical, Food and Agricultural Industries, KU Institute for Advanced StudiesKasetsart UniversityBangkokThailand
  3. 3.Computational Biomodelling Laboratory for Agricultural Science and Technology (CBLAST)Kasetsart UniversityBangkokThailand
  4. 4.Department of Mechanical Engineering, Faculty of Engineering at SrirachaKasetsart UniversityChonburiThailand

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