Skip to main content
SpringerLink
Log in

Elastic properties of Janus transition metal dichalcogenide nanotubes from first principles

  • Regular Article - Mesoscopic and Nanoscale Systems
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We calculate the elastic properties of Janus transition metal dichalcogenide (TMD) nanotubes using first principles Kohn–Sham density functional theory (DFT). Specifically, we perform electronic structure simulations that exploit the cyclic and helical symmetry in the system to compute the Young’s moduli, Poisson’s ratios, and torsional moduli for 27 select armchair and zigzag Janus TMD nanotubes at their equilibrium diameters. We find the following trend in the moduli values: MSSe > MSTe > MSeTe, while their anisotropy with respect to armchair and zigzag configurations has the following ordering: MSTe > MSeTe > MSSe. This anisotropy and its ordering between the different groups is confirmed by computing the shear modulus from the torsional modulus using an isotropic elastic continuum model, and comparing it against the value predicted from the isotropic relation featuring the Young’s modulus and Poisson’s ratio. We also develop a model for the Young’s and torsional moduli of Janus TMD nanotubes based on linear regression.

Graphical abstract

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

Access this article

Log in via an institution

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

Similar content being viewed by others

Data Availability Statement

The data associated with this work can be found in the Supplementary material.

References

  1. R. Tenne, Advances in the synthesis of inorganic nanotubes and fullerene-like nanoparticles. Angew. Chem. Int. Ed. 42(42), 5124–5132 (2003)

    Article  Google Scholar 

  2. C. N. R Rao, M. Nath. Inorganic nanotubes. In Advances In Chemistry: A Selection of CNR Rao’s Publications (1994–2003), pp 310–333. World Scientific, 2003

  3. M. Serra, R. Arenal, R. Tenne, An overview of the recent advances in inorganic nanotubes. Nanoscale 11(17), 8073–8090 (2019)

    Article  Google Scholar 

  4. S. Iijima, Helical microtubules of graphitic carbon. Nature 354(6348), 56–58 (1991)

    Article  ADS  Google Scholar 

  5. J. Zhou, L. Shen, M.D. Costa, K.A. Persson, S.P. Ong, P. Huck, Y. Lu, X. Ma, Y. Chen, H. Tang et al., 2DMatPedia, an open computational database of two-dimensional materials from top-down and bottom-up approaches. Sci. Data 6(1), 1–10 (2019)

    Article  Google Scholar 

  6. M.N. Gjerding, A. Taghizadeh, A. Rasmussen, S. Ali, F. Bertoldo, T. Deilmann, U.P. Holguin, N.R. Knøsgaard, M. Kruse, S. Manti et al., Recent progress of the computational 2D materials database (C2DB). 2D Mater. 8(4), 044002 (2021)

    Article  Google Scholar 

  7. S. Haastrup, M. Strange, M. Pandey, T. Deilmann, P.S. Schmidt, N.F. Hinsche, M.N. Gjerding, D. Torelli, P.M. Larsen, A.C. Riis-Jensen et al., The Computational 2D Materials Database: high-throughput modeling and discovery of atomically thin crystals. 2D Mater. 5(4), 042002 (2018)

    Article  Google Scholar 

  8. W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140(4A), A1133 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  9. P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136(3B), B864 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Kis, D. Mihailovic, M. Remskar, A. Mrzel, A. Jesih, I. Piwonski, A.J. Kulik, W. Benoît, L. Forró, Shear and Young’s moduli of \(MoS_2\) nanotube ropes. Adv. Mater. 15(9), 733–736 (2003)

    Article  Google Scholar 

  11. I. Kaplan-Ashiri, R. Tenne, Mechanical properties of \(WS_2\) nanotubes. J. Cluster Sci. 18(3), 549–563 (2007)

    Article  Google Scholar 

  12. I. Kaplan-Ashiri, S.R. Cohen, K. Gartsman, V. Ivanovskaya, T. Heine, G. Seifert, I. Wiesel, H.D. Wagner, R. Tenne, On the mechanical behavior of \(WS_2\) nanotubes under axial tension and compression. Proc. Natl. Acad. Sci. 103(3), 523–528 (2006)

    Article  ADS  Google Scholar 

  13. D.-M. Tang, X. Wei, M.-S. Wang, N. Kawamoto, Y. Bando, C. Zhi, M. Mitome, A. Zak, R. Tenne, D. Golberg, Revealing the anomalous tensile properties of \(WS_2\) nanotubes by in situ transmission electron microscopy. Nano Lett. 13(3), 1034–1040 (2013)

    Article  ADS  Google Scholar 

  14. A. Bhardwaj, A. Sharma, P. Suryanarayana, Torsional moduli of transition metal dichalcogenide nanotubes from first principles. Nanotechnology 32(28), 28LT02 (2021)

    Article  Google Scholar 

  15. N. Zibouche, M. Ghorbani-Asl, T. Heine, A. Kuc, Electromechanical properties of small transition-metal dichalcogenide nanotubes. Inorganics 2(2), 155–167 (2014)

    Article  Google Scholar 

  16. S. Oshima, M. Toyoda, S. Saito, Geometrical and electronic properties of unstrained and strained transition metal dichalcogenide nanotubes. Phys. Rev. Mater. 4(2), 026004 (2020)

    Article  Google Scholar 

  17. W. Li, G. Zhang, M. Guo, Y.-W. Zhang, Strain-tunable electronic and transport properties of \(MoS_2\) nanotubes. Nano Res. 7(4), 518–527 (2014)

    Article  Google Scholar 

  18. M. Ghorbani-Asl, N. Zibouche, M. Wahiduzzaman, A.F. Oliveira, A. Kuc, T. Heine, Electromechanics in \(MoS_2\) and \(WS_2\): nanotubes vs. monolayers. Sci. Rep. 3, 29613 (2013)

    Google Scholar 

  19. P. Lu, X. Wu, W. Guo, X.C. Zeng, Strain-dependent electronic and magnetic properties of \(MoS_2\) monolayer, bilayer, nanoribbons and nanotubes. Phys. Chem. Chem. Phys. 14(37), 13035–13040 (2012)

    Article  Google Scholar 

  20. R. Ansari, S. Malakpour, M. Faghihnasiri, S. Sahmani, An ab initio investigation into the elastic, structural and electronic properties of \(MoS_2\) nanotubes. Superlattices Microstruct. 82, 188–200 (2015)

    Article  ADS  Google Scholar 

  21. R. Levi, J. Garel, D. Teich, G. Seifert, R. Tenne, E. Joselevich, Nanotube electromechanics beyond carbon: the case of \(WS_2\). ACS Nano 9(12), 12224–12232 (2015)

    Article  Google Scholar 

  22. A. Bhardwaj, A. Sharma, P. Suryanarayana, Torsional strain engineering of transition metal dichalcogenide nanotubes: an ab initio study. Nanotechnology 32(47), 47LT01 (2021)

    Article  Google Scholar 

  23. S. Kumar, P. Suryanarayana, Bending moduli for forty-four select atomic monolayers from first principles. Nanotechnology 31(43), 43LT01 (2020)

    Article  Google Scholar 

  24. A.-Y. Lu, H. Zhu, J. Xiao, C.-P. Chuu, Y. Han, M.-H. Chiu, C.-C. Cheng, C.-W. Yang, K.-H. Wei, Y. Yang et al., Janus monolayers of transition metal dichalcogenides. Nat. Nanotechnol. 12(8), 744–749 (2017)

    Article  Google Scholar 

  25. J. Zhang, S. Jia, I. Kholmanov, L. Dong, D. Er, W. Chen, H. Guo, Z. Jin, V.B. Shenoy, L. Shi et al., Janus monolayer transition-metal dichalcogenides. ACS Nano 11(8), 8192–8198 (2017)

    Article  Google Scholar 

  26. D.B. Trivedi, G. Turgut, Y. Qin, M.Y. Sayyad, D. Hajra, M. Howell, L. Liu, S. Yang, N.H. Patoary, H. Li et al., Room-temperature synthesis of 2D Janus crystals and their heterostructures. Adv. Mater. 32(50), 2006320 (2020)

    Article  Google Scholar 

  27. Y.-C. Lin, C. Liu, Y. Yu, E. Zarkadoula, M. Yoon, A.A. Puretzky, L. Liang, Y. Kong, X. Gu, A. Strasser et al., Low energy implantation into transition-metal dichalcogenide monolayers to form Janus structures. ACS Nano 14(4), 3896–3906 (2020)

    Article  Google Scholar 

  28. Q.-L. Xiong, J. Zhou, J. Zhang, T. Kitamura, Z.-H. Li, Spontaneous curling of freestanding Janus monolayer transition-metal dichalcogenides. Phys. Chem. Chem. Phys. 20(32), 20988–20995 (2018)

    Article  Google Scholar 

  29. Y.Z. Wang, R. Huang, B.L. Gao, G. Hu, F. Liang, Y.L. Ma, Mechanical and strain-tunable electronic properties of Janus MoSSe nanotubes. Chalcogenide Lett. 15(11), 535–543 (2018)

    Google Scholar 

  30. Z.-K. Tang, B. Wen, M. Chen, L.-M. Liu, Janus MoSSe nanotubes: tunable band gap and excellent optical properties for surface photocatalysis. Adv. Theory Simul. 1(10), 1800082 (2018)

    Article  Google Scholar 

  31. A.E.G. Mikkelsen, F.T. Bölle, K.S. Thygesen, T. Vegge, I.E. Castelli, Band structure of MoSTe Janus nanotubes. Phys. Rev. Mater. 5(1), 014002 (2021)

    Article  Google Scholar 

  32. Y.F. Luo, Y. Pang, M. Tang, Q. Song, M. Wang, Electronic properties of Janus MoSSe nanotubes. Comput. Mater. Sci. 156, 315–320 (2019)

    Article  Google Scholar 

  33. W. Zhao, Y. Li, W. Duan, F. Ding, Ultra-stable small diameter hybrid transition metal dichalcogenide nanotubes X-M-Y (X, Y= S, Se, Te; M= Mo, W, Nb, Ta): a computational study. Nanoscale 7(32), 13586–13590 (2015)

    Article  ADS  Google Scholar 

  34. L. Ju, P. Liu, Y. Yang, L. Shi, G. Yang, L. Sun, Tuning the photocatalytic water-splitting performance with the adjustment of diameter in an armchair WSSe nanotube. J. Energy Chem. 61, 228–235 (2021)

    Article  Google Scholar 

  35. L. Ju, J. Qin, G. Shi, L. Yang, J. Zhang, L. Sun, Rolling the WSSe bilayer into double-walled nanotube for the enhanced photocatalytic water-splitting performance. Nanomaterials 11(3), 705 (2021)

    Article  Google Scholar 

  36. S. Zhang, H. Jin, C. Long, T. Wang, R. Peng, B. Huang, Y. Dai, MoSSe nanotube: a promising photocatalyst with an extremely long carrier lifetime. J. Mater. Chem. A 7(13), 7885–7890 (2019)

    Article  Google Scholar 

  37. S. Xie, H. Jin, Y. Wei, S. Wei, Theoretical investigation on stability and electronic properties of Janus MoSSe nanotubes for optoelectronic applications. Optik 227, 166105 (2021)

    Article  ADS  Google Scholar 

  38. M. Yagmurcukardes, Y. Qin, S. Ozen, M. Sayyad, F.M. Peeters, S. Tongay, H. Sahin, Quantum properties and applications of 2D Janus crystals and their superlattices. Appl. Phys. Rev. 7(1), 011311 (2020)

    Article  ADS  Google Scholar 

  39. D. Yudilevich, R. Levi, I. Nevo, R. Tenne, A. Ya’akobovitz, E. Joselevich, Self-sensing torsional resonators based on inorganic nanotubes. ICME, pp 1–4 (2018)

  40. Y. Divon, R. Levi, J. Garel, D. Golberg, R. Tenne, A. Ya’akobovitz, E. Joselevich, Torsional resonators based on inorganic nanotubes. Nano Lett. 17(1), 28–35 (2017)

    Article  ADS  Google Scholar 

  41. M. Shtein, R. Nadiv, N. Lachman, H.D. Wagner, O. Regev, Fracture behavior of nanotube-polymer composites: insights on surface roughness and failure mechanism. Compos. Sci. Technol. 87, 157–163 (2013)

    Article  Google Scholar 

  42. G. Otorgust, H. Dodiuk, S. Kenig, R. Tenne, Important insights into polyurethane nanocomposite-adhesives; a comparative study between INT-\(WS_2\) and CNT. Eur. Polymer J. 89, 281–300 (2017)

    Article  Google Scholar 

  43. D.M. Simić, D.B. Stojanović, M. Dimić, K. Mišković, M. Marjanović, Z. Burzić, P.S. Uskoković, A. Zak, R. Tenne, Impact resistant hybrid composites reinforced with inorganic nanoparticles and nanotubes of \(WS_2\). Compos. B Eng. 176, 107222 (2019)

    Article  Google Scholar 

  44. R. Nadiv, M. Shtein, M. Refaeli, A. Peled, O. Regev, The critical role of nanotube shape in cement composites. Cement Concr. Compos. 71, 166–174 (2016)

    Article  Google Scholar 

  45. S.-J. Huang, C.-H. Ho, Y. Feldman, R. Tenne, Advanced AZ31 Mg alloy composites reinforced by \(WS_2\) nanotubes. J. Alloy. Compd. 654, 15–22 (2016)

    Article  Google Scholar 

  46. M. Naffakh, A.M. Diez-Pascual, C. Marco, Polymer blend nanocomposites based on poly (l-lactic acid), polypropylene and \(WS_2\) inorganic nanotubes. RSC Adv. 6(46), 40033–40044 (2016)

    Article  ADS  Google Scholar 

  47. F.T. Bölle, A.E.G. Mikkelsen, K.S. Thygesen, T. Vegge, I.E. Castelli, Structural and chemical mechanisms governing stability of inorganic Janus nanotubes. NPJ Comput. Mater. 7(1), 1–8 (2021)

    Article  ADS  Google Scholar 

  48. M. Nath, C.N.R. Rao, Nanotubes of group 4 metal disulfides. Angew. Chem. Int. Ed. 41(18), 3451–3454 (2002)

    Article  Google Scholar 

  49. A.V. Bandura, R.A. Evarestov, \(TiS_2\) and \(ZrS_2\) single-and double-wall nanotubes: First-principles study. J. Comput. Chem. 35(5), 395–405 (2014)

    Article  Google Scholar 

  50. A. Sharma, P. Suryanarayana, Real-space density functional theory adapted to cyclic and helical symmetry: application to torsional deformation of carbon nanotubes. Phys. Rev. B 103(3), 035101 (2021)

    Article  ADS  Google Scholar 

  51. Q. Xu, A. Sharma, B. Comer, H. Huang, E. Chow, A.J. Medford, J.E. Pask, P. Suryanarayana, SPARC: simulation package for ab-initio real-space calculations. SoftwareX 15, 100709 (2021)

  52. S. Ghosh, P. Suryanarayana, SPARC: accurate and efficient finite-difference formulation and parallel implementation of density functional theory: isolated clusters. Comput. Phys. Commun. 212, 189–204 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. S. Ghosh, P. Suryanarayana, SPARC: Aaccurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: extended systems. Comput. Phys. Commun. 216, 109–125 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  54. S. Ghosh, A.S. Banerjee, P. Suryanarayana, Symmetry-adapted real-space density functional theory for cylindrical geometries: application to large group-IV nanotubes. Phys. Rev. B 100(12), 125143 (2019)

    Article  ADS  Google Scholar 

  55. A.S. Banerjee, P. Suryanarayana, Cyclic density functional theory: a route to the first principles simulation of bending in nanostructures. J. Mech. Phys. Solids 96, 605–631 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  56. A.S. Banerjee, L. Lin, P. Suryanarayana, C. Yang, J.E. Pask, Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations. J. Chem. Theory Comput. 14(6), 2930–2946 (2018)

    Article  Google Scholar 

  57. D. Codony, I. Arias, P. Suryanarayana, Transversal flexoelectric coefficient for nanostructures at finite deformations from first principles. Phys. Rev. Mater. 5(3), L030801 (2021)

    Article  ADS  Google Scholar 

  58. S. Kumar, D. Codony, I. Arias, P. Suryanarayana, Flexoelectricity in atomic monolayers from first principles. Nanoscale 13(3), 1600–1607 (2021)

    Article  Google Scholar 

  59. K. Momma, F. Izumi, VESTA: a three-dimensional visualization system for electronic and structural analysis. J. Appl. Crystallogr. 41(3), 653–658 (2008)

    Article  Google Scholar 

  60. M. F. Shojaei, J. E. Pask, A.J. Medford, P. Suryanarayana, Structural energy differences optimized pseudopotentials. in preparation

  61. D.R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials. Phys. Rev. B 88(8), 085117 (2013)

    Article  ADS  Google Scholar 

  62. W. Shi, Z. Wang, Mechanical and electronic properties of Janus monolayer transition metal dichalcogenides. J. Phys.: Condens. Matter 30(21), 215301 (2018)

    ADS  Google Scholar 

  63. J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77(18), 3865 (1996)

    Article  ADS  Google Scholar 

  64. Y.Z. Wang, R. Huang, X.Q. Wang, Q.F. Zhang, B.L. Gao, L. Zhou, G. Hua, Strain-tunable electronic properties of \(CrS_2\) nanotubes. Chalcogenide Lett. 13(7), 301–307 (2016)

    Google Scholar 

  65. J. Xiao, M. Long, X. Li, H. Xu, H. Huang, Y. Gao, Theoretical prediction of electronic structure and carrier mobility in single-walled \(MoS_2\) nanotubes. Sci. Rep. 4(1), 1–7 (2014)

    Google Scholar 

  66. C. Ataca, H. Sahin, S. Ciraci, Stable, single-layer MX2 transition-metal oxides and dichalcogenides in a honeycomb-like structure. J. Phys. Chem. C 116(16), 8983–8999 (2012)

    Article  Google Scholar 

  67. C.-H. Chang, X. Fan, S.-H. Lin, J.-L. Kuo, Orbital analysis of electronic structure and phonon dispersion in \(MoS_2\), \(MoSe_2\), \(WS_2\), and \(WSe_2\) monolayers under strain. Phys. Rev. B 88(19), 195420 (2013)

    Article  ADS  Google Scholar 

  68. B. Amin, T.P. Kaloni, U. Schwingenschlögl, Strain engineering of \(WS_2\), \(WSe_2\), and \(WTe_2\). RSC Adv. 4(65), 34561–34565 (2014)

    Article  ADS  Google Scholar 

  69. H. Guo, N. Lu, L. Wang, X. Wu, X.C. Zeng, Tuning electronic and magnetic properties of early transition-metal dichalcogenides via tensile strain. J. Phys. Chem. C 118(13), 7242–7249 (2014)

    Article  Google Scholar 

  70. J. Chen, S.-L. Li, Z.-L. Tao, Y.-T. Shen, C.-X. Cui, Titanium disulfide nanotubes as hydrogen-storage materials. J. Am. Chem. Soc. 125(18), 5284–5285 (2003)

    Article  Google Scholar 

  71. M. Nath, S. Kar, A.K. Raychaudhuri, C.N.R. Rao, Superconducting \(NbSe_2\) nanostructures. Chem. Phys. Lett. 368(5–6), 690–695 (2003)

  72. M. Nath, C.N.R. Rao, \(MoSe_2\) and \(WSe_2\) nanotubes and related structures. Chem. Commun. 1(21), 2236–2237 (2001)

    Article  Google Scholar 

  73. A.R. Klots, A.K.M. Newaz, B. Wang, D. Prasai, H. Krzyzanowska, J. Lin, D. Caudel, N.J. Ghimire, J. Yan, B.L. Ivanov et al., Probing excitonic states in suspended two-dimensional semiconductors by photocurrent spectroscopy. Sci. Rep. 4(1), 1–7 (2014)

  74. M.M. Ugeda, A.J. Bradley, S.-F. Shi, H. Felipe, Y. Zhang, D.Y. Qiu, W. Ruan, S.-K. Mo, Z. Hussain, Z.-X. Shen et al., Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nat. Mater. 13(12), 1091–1095 (2014)

    Article  ADS  Google Scholar 

  75. H.M. Hill, A.F. Rigosi, K.T. Rim, G.W. Flynn, T.F. Heinz, Band alignment in \(MoS_2/WS_2\) transition metal dichalcogenide heterostructures probed by scanning tunneling microscopy and spectroscopy. Nano Lett. 16(8), 4831–4837 (2016)

  76. K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.V. Morozov, A.K. Geim, Two-dimensional atomic crystals. Proc. Natl. Acad. Sci. 102(30), 10451–10453 (2005)

    Article  ADS  Google Scholar 

  77. J.N. Coleman, M. Lotya, A. O’Neill, S.D. Bergin, P.J. King, U. Khan, K. Young, A. Gaucher, S. De, R.J. Smith et al., Two-dimensional nanosheets produced by liquid exfoliation of layered materials. Science 331(6017), 568–571 (2011)

    Article  ADS  Google Scholar 

  78. K.S. Nagapriya, O. Goldbart, I. Kaplan-Ashiri, G. Seifert, R. Tenne, E. Joselevich, Torsional stick-slip behavior in \(WS_2\) nanotubes. Phys. Rev. Lett. 101(19), 195501 (2008)

    Article  ADS  Google Scholar 

  79. Y. Huang, J. Wu, K.-C. Hwang, Thickness of graphene and single-wall carbon nanotubes. Phys. Rev. B 74(24), 245413 (2006)

    Article  ADS  Google Scholar 

  80. M.M. Jebbessen Treacy, T.W. Ebbesen, J.M. Gibson, Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature 381(6584), 678–680 (1996)

    Article  ADS  Google Scholar 

  81. T.C.T. Ting, T. Chen, Poisson’s ratio for anisotropic elastic materials can have no bounds. Quart. J. Mech. Appl. Math. 58(1), 73–82 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support of the US National Science Foundation (CAREER-1553212 and MRI-1828187).

Author information

Authors and Affiliations

  1. College of Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Arpit Bhardwaj & Phanish Suryanarayana

Authors
  1. Arpit Bhardwaj
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Phanish Suryanarayana
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The authors contributed equally to this work.

Corresponding author

Correspondence to Phanish Suryanarayana.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 7570 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bhardwaj, A., Suryanarayana, P. Elastic properties of Janus transition metal dichalcogenide nanotubes from first principles. Eur. Phys. J. B 95, 13 (2022). https://doi.org/10.1140/epjb/s10051-021-00272-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-021-00272-y

Search

Navigation