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Strength and buckling behavior of defective phosphorene nanotubes under axial compression

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Abstract

Atomic defects can be generated relatively easily in phosphorene due to their low formation energies. How these defects affect the buckling behavior of phosphorene nanotubes (PNTs) remains unexplored. Using molecular dynamics simulations, we investigate the effect of vacancies on the buckling properties of PNTs. We show that compared to a pristine PNT, the defective one exhibits a much lower buckling strength and strain. Remarkably, 1% concentration of vacancies in a PNT is able to cause a 30% reduction in buckling strength. Interestingly, for long PNTs, the buckling occurs via column or global buckling. As a result, the buckling strength decreases significantly with the increase (decrease) in the tube length (diameter) for both the pristine and defective PNTs, consistent with the Euler buckling theory. For short PNTs with small slenderness ratio (L/D), however, buckling occurs via shell or local buckling. As a result, the buckling strength increases with decreasing the tube diameter, consistent with shell buckling theory. Finally, with the increase in temperature, the buckling strength and strain can be reduced significantly for both the pristine and defective PNTs. These findings may provide important guidelines for the design and applications of PNTs-based nanodevices.

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References

  1. Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA (2004) Electric field effect in atomically thin carbon films. Science 306:666–669

    Article  Google Scholar 

  2. Novoselov KS, Fal’ko VI, Colombo L, Gellert PR, Schwab MG, Kim K (2012) A roadmap for graphene. Nature 490:192–200

    Article  Google Scholar 

  3. Georgakilas V, Tiwari JN, Kemp KC, Perman JA, Bourlinos AB, Kim KS, Zboril R (2016) Noncovalent functionalization of graphene and graphene oxide for energy materials, biosensing, catalytic, and biomedical applications. Chem Rev 116:5464–5519

    Article  Google Scholar 

  4. Heerema SJ, Dekker C (2016) Graphene nanodevices for DNA sequencing. Nat Nanotechnol 11:127–136

    Article  Google Scholar 

  5. Pei QX, Zhang YW, Shenoy VB (2010) A molecular dynamics study of the mechanical properties of hydrogen functionalized graphene. Carbon 48:898–904

    Article  Google Scholar 

  6. Jiao SP, Duan CH, Xu ZP (2017) Structures and thermodynamics of water encapsulated by graphene. Sci Rep 7:2646

    Article  Google Scholar 

  7. Xu ZP, Buehler MJ (2010) Geometry controls conformation of graphene sheets: membranes, ribbons, and scrolls. ACS Nano 4:3869–3876

    Article  Google Scholar 

  8. Li L, Yu Y, Ye GJ, Ge Q, Ou X, Wu H, Feng D, Chen XH, Zhang YB (2014) Black phosphorus field-effect transistors. Nat Nanotechnol 9:372–377

    Article  Google Scholar 

  9. Fei R, Yang L (2014) Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus. Nano Lett 14:2884–2889

    Article  Google Scholar 

  10. Liu H, Neal AT, Zhu Z, Luo Z, Xu X, Tomanek D, Ye PD (2014) Phosphorene: an unexplored 2D semiconductor with a high hole mobility. ACS Nano 8:4033–4041

    Article  Google Scholar 

  11. Buscema M, Groenendijk DJ, Blanter SI, Steele GA, van der Zant HSJ, Castellanos-Gomez A (2014) Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors. Nano Lett 14:3347–3352

    Article  Google Scholar 

  12. Qiao J, Kong X, Hu ZX, Yang F, Ji W (2014) High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus. Nat Commun 5:4475

    Google Scholar 

  13. Xia F, Wang H, Jia Y (2014) Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. Nat Commun 5:4458

    Google Scholar 

  14. Castellanos-Gomez A (2015) Black phosphorus: narrow gap, wide applications. J Phys Chem Lett 6:4280–4291

    Article  Google Scholar 

  15. Ren XL, Lian PC, Xie DL, Yang Y, Mei Y, Huang XR, Wang ZR, Yin XT (2017) Properties, preparation and application of black phosphorus/phosphorene for energy storage: a review. J Mater Sci 52:10364–10386. https://doi.org/10.1007/s10853-017-1194-3

    Article  Google Scholar 

  16. Zhang YY, Pei QX, Jiang JW, Wei N, Zhang YW (2016) Thermal conductivities of single- and multi-layer phosphorene: a molecular dynamics study. Nanoscale 8:483–491

    Article  Google Scholar 

  17. Qin G, Yan QB, Qin Z, Yue SY, Hu M, Su G (2015) Anisotropic intrinsic lattice thermal conductivity of phosphorene from first principles. Phys Chem Chem Phys 17:4854–4858

    Article  Google Scholar 

  18. Liu B, Bai LC, Korznikova EA, Dmitriev SV, Law AWK, Zhou K (2017) Thermal conductivity and tensile response of phosphorene nanosheets with vacancy defects. J Phys Chem C 121:13876–13887

    Article  Google Scholar 

  19. Pei QX, Zhang X, Ding Z, Zhang YY, Zhang YW (2017) Thermal stability and thermal conductivity of phosphorene in phosphorene/graphene van der Waals heterostructures. Phys Chem Chem Phys 19:17180–17186

    Article  Google Scholar 

  20. Jiang JW, Park HS (2014) Mechanical properties of single-layer black phosphorus. J Phys D Appl Phys 47:385304

    Article  Google Scholar 

  21. Sha ZD, Pei QX, Ding ZW, Jiang JW, Zhang YW (2015) Mechanical properties and fracture behavior of single-layer phosphorene at finite temperatures. J Phys D Appl Phys 48:395303

    Article  Google Scholar 

  22. Yang Z, Zhao J, Wei N (2015) Temperature-dependent mechanical properties of monolayer black phosphorus by molecular dynamics simulations. Appl Phys Lett 107:023107

    Article  Google Scholar 

  23. Liu N, Hong JW, Pidaparti R, Wang XQ (2016) Fracture patterns and the energy release rate of phosphorene. Nanoscale 8:5728–5736

    Article  Google Scholar 

  24. Wei Q, Peng X (2014) Superior mechanical flexibility of phosphorene and few-layer black phosphorus. Appl Phys Lett 104:251915

    Article  Google Scholar 

  25. Li L, Feng C, Yang J (2017) Tensile and compressive behaviors of prestrained single-layer black phosphorus: a molecular dynamics study. Nanoscale 9:3609–3619

    Article  Google Scholar 

  26. Jiang JW, Park HS (2014) Negative Poisson’s ratio in single-layer black phosphorus. Nat Commun 5:4727

    Google Scholar 

  27. Du YC, Maassen J, Wu WR, Luo Z, Xu XF, Ye PD (2016) Auxetic black phosphorus: a 2D material with negative Poisson’s ratio. Nano Lett 16:6701–6708

    Article  Google Scholar 

  28. Treacy MMJ, Ebbesen TW, Gibson JM (1996) Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature 381:678–680

    Article  Google Scholar 

  29. Liew KM, Wong CH, He XQ, Tan MJ, Meguid SA (2004) Nanomechanics of single and multiwalled carbon nanotubes. Phys Rev B 69:115429

    Article  Google Scholar 

  30. Seifert G, Hernandez E (2000) Theoretical prediction of phosphorus nanotubes. Chem Phys Lett 318:355–360

    Article  Google Scholar 

  31. Cabria I, Mintmire JW (2004) Stability and electronic structure of phosphorus nanotubes. Europhys Lett 65:82–88

    Article  Google Scholar 

  32. Guo H, Lu N, Dai J, Wu X, Zeng XC (2014) Phosphorene nanoribbons, phosphorus nanotubes, and van der Waals multilayers. J Phys Chem C 118:14051–14059

    Article  Google Scholar 

  33. Liao X, Hao F, Xiao H, Chen X (2016) Effects of intrinsic strain on the structural stability and mechanical properties of phosphorene nanotubes. Nanotechnology 27:215701

    Article  Google Scholar 

  34. Cai K, Wan J, Wei N, Cai H, Qin QH (2016) Thermal stability of a free nanotube from single-layer black phosphorus. Nanotechnology 27:35703

    Article  Google Scholar 

  35. Cai K, Wan J, Wei N, Qin QH (2016) Strength and stability analysis of a single-walled black phosphorus tube under axial compression. Nanotechnology 27:275701

    Article  Google Scholar 

  36. Yu S, Zhu H, Eshun K, Arab A, Badwan A, Li Q (2015) A computational study of the electronic properties of one-dimensional armchair phosphorene nanotubes. J Appl Phys 118:164306

    Article  Google Scholar 

  37. Banhart F, Kotakoski J, Krasheninnikov AV (2011) Structural defects in graphene. ACS Nano 5:26–41

    Article  Google Scholar 

  38. Gao JF, Zhang JF, Liu HS, Zhang QF, Zhao JJ (2013) Structures, mobilities, electronic and magnetic properties of point defects in silicene. Nanoscale 5:9785–9792

    Article  Google Scholar 

  39. Hu W, Yang J (2015) Defects in phosphorene. J Phys Chem C 119:20474–20480

    Article  Google Scholar 

  40. Ding ZW, Pei QX, Jiang JW, Zhang YW (2015) Manipulating the thermal conductivity of monolayer MoS2 via lattice defect and strain engineering. J Phys Chem C 119:16358–16365

    Article  Google Scholar 

  41. Ng TY, Yeo JJ, Liu ZS (2012) A molecular dynamics study of the thermal conductivity of graphene nanoribbons containing dispersed Stone–Thrower–Wales defects. Carbon 50:4887–4893

    Article  Google Scholar 

  42. Sha ZD, Pei QX, Zhang YY, Zhang YW (2016) Atomic vacancies significantly degrade the mechanical properties of phosphorene. Nanotechnology 27:315704

    Article  Google Scholar 

  43. Wang S, Qin Z, Jung GS, Martin-Martinez FJ, Zhang K, Buehler MJ, Warner JH (2016) Atomically sharp crack tips in monolayer MoS2 and their enhanced toughness by vacancy defects. ACS Nano 10:9831–9839

    Article  Google Scholar 

  44. Ansari R, Motevalli B, Montazeri A, Ajori S (2011) Fracture analysis of monolayer graphene sheets with double vacancy defects via MD simulation. Solid State Commun 151:1141–1146

    Article  Google Scholar 

  45. Zhan H, Zhang Y, Bell JM, Gu Y (2015) Suppressed thermal conductivity of bilayer graphene with vacancy-initiated linkages. J Phys Chem C 119:1748–1752

    Article  Google Scholar 

  46. Babar R, Kabir M (2016) Transition metal and vacancy defect complexes in phosphorene: a spintronic perspective. J Phys Chem C 120:14991–15000

    Article  Google Scholar 

  47. Chen WH, Chen IC, Cheng HC, Yu CF (2017) Influence of structural defect on thermal-mechanical properties of phosphorene sheets. J Mater Sci 52:3225–3232. https://doi.org/10.1007/s10853-016-0611-3

    Article  Google Scholar 

  48. Liu P, Pei QX, Huang W, Zhang YW (2017) Mechanical properties and fracture behaviour of defective phosphorene nanotubes under uniaxial tension. J Phys D Appl Phys 50:485303

    Article  Google Scholar 

  49. Plimpton S (1995) Fast parallel algorithms for short-range molecular-dynamics. J Comput Phys 117:1–19

    Article  Google Scholar 

  50. Jiang JW (2015) Parametrization of Stillinger–Weber potential based on valence force field model: application to single-layer MoS2 and black phosphorus. Nanotechnology 26:315706

    Article  Google Scholar 

  51. Diao JK, Gall K, Dunn ML (2004) Atomistic simulation of the structure and elastic properties of gold nanowires. J Mech Phys Solids 52:1935–1962

    Article  Google Scholar 

  52. Komsa HP, Kotakoski J, Kurasch S, Lehtinen O, Kaiser U, Krasheninnikov AV (2012) Two-dimensional transition metal dichalcogenides under electron Irradiation: Defect production and doping. Phys Rev Lett 109:035503

    Article  Google Scholar 

  53. Zhang YY, Xiang Y, Wang CM (2009) Buckling of defective carbon nanotubes. J Appl Phys 106:113503

    Article  Google Scholar 

  54. Shokuhfar A, Ebrahimi-Nejad S (2013) Effects of structural defects on the compressive buckling of boron nitride nanotubes. Phys E 48:53–60

    Article  Google Scholar 

  55. Timoshenko SP, Gere JM (2012) Theory of elastic stability. Courier Corporation, North Chelmsford

    Google Scholar 

Download references

Acknowledgements

This work was partially supported by a grant from the Science and Engineering Research Council, A*STAR, Singapore (152-70-00017). The authors gratefully acknowledge the computational support provided by A*STAR Computational Resource Centre of Singapore.

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Authors and Affiliations

  1. Institute of High Performance Computing, A*STAR, Singapore, 138632, Singapore

    Ping Liu, Qing-Xiang Pei & Yong-Wei Zhang

  2. School of Aeronautics, Northwestern Polytechnical University, Xi’an, 710072, China

    Wei Huang

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  1. Ping Liu
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  2. Qing-Xiang Pei
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  3. Wei Huang
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  4. Yong-Wei Zhang
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Correspondence to Qing-Xiang Pei or Yong-Wei Zhang.

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Liu, P., Pei, QX., Huang, W. et al. Strength and buckling behavior of defective phosphorene nanotubes under axial compression. J Mater Sci 53, 8355–8363 (2018). https://doi.org/10.1007/s10853-018-2152-4

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  • DOI: https://doi.org/10.1007/s10853-018-2152-4

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