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Vibration of a carbyne nanomechanical mass sensor with surface effect

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Abstract

This paper presents a comprehensive model to investigate the influence of surface elasticity and residual surface tension on the natural frequency of flexural vibrations of nanomechanical mass sensor using a carbyne resonator. Carbyne is modeled as an equivalent continuum circular cross-section Timoshenko nanobeam including rotary inertia and shear deformation effects. Surface stress and surface elasticity are presented via the Young–Laplace equation. The analytical solution is presented and verified with molecular dynamics solution. The results show that the carbyne resonator can measure a very small mass with weight below 10−3 zg. The effects of surface elasticity, residual surface tension, carbyne length, and mass position on the fundamental frequencies are illustrated. This study is helpful for characterizing the mechanical behavior of high-precision measurement devices such as chemical and biological sensor.

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References

  1. S. Abbasion, A. Rafsanjani, R. Avazmohammadi, A. Farshidianfar, Free vibration of microscaled Timoshenko beams. Appl. Phys. Lett. 95(14), 143122 (2009)

    Article  ADS  Google Scholar 

  2. V.I. Artyukhov, M. Liu, B.I. Yakobson, Mechanically induced metal–insulator transition in carbyne. Nano Lett. 14(8), 4224–4229 (2014)

    Article  ADS  Google Scholar 

  3. M.A. Eltaher, F.F. Mahmoud, A.E. Assie, E.I. Meletis, Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams. Appl. Math. Comput. 224, 760–774 (2013)

    Article  MathSciNet  Google Scholar 

  4. M.A. Eltaher, M.A. Agwa, F.F. Mahmoud, Nanobeam sensor for measuring a zeptogram mass. Int. J. Mech. Mater. Des. 1–11 (2015). doi:10.1007/s10999-015-9302-5

  5. B. Farshi, A. Assadi, A. Alinia-ziazi, Frequency analysis of nanotubes with consideration of surface effects. Appl. Phys. Lett. 96(9), 093105 (2010)

    Article  ADS  Google Scholar 

  6. G.I. Giannopoulos, Fullerenes as mass sensors: a numerical investigation. Phys. E Low Dimens. Syst. Nanostruct. 56, 36–42 (2014)

    Article  ADS  Google Scholar 

  7. M.E. Gurtin, A.I. Murdoch, A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57(4), 291–323 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  8. S.M. Hasheminejad, B. Gheshlaghi, Dissipative surface stress effects on free vibrations of nanowires. Appl. Phys. Lett. 97(25), 253103 (2010)

    Article  ADS  Google Scholar 

  9. J. He, C.M. Lilley, Surface effect on the elastic behavior of static bending nanowires. Nano Lett. 8(7), 1798–1802 (2008)

    Article  ADS  Google Scholar 

  10. J. He, C.M. Lilley, Surface stress effect on bending resonance of nanowires with different boundary conditions. Appl. Phys. Lett. 93(26), 263108 (2008)

    Article  ADS  Google Scholar 

  11. H. Ibach, The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structures. Surf. Sci. Rep. 29(5), 195–263 (1997)

    Article  ADS  Google Scholar 

  12. L.Y. Jiang, Z. Yan, Timoshenko beam model for static bending of nanowires with surface effects. Physica E: Low-dimens. Syst. Nanostruct. 42(9), 2274–2279 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  13. G.Y. Jing, H. Duan, X.M. Sun, Z.S. Zhang, J. Xu, Y.D. Li, D.P. Yu, Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy. Phys. Rev. B 73(23), 235409 (2006)

    Article  ADS  Google Scholar 

  14. P. Kasirajan, R. Amirtham, J.N. Reddy, Surface and non-local effects for non-linear analysis of Timoshenko beams. Int. J. Non Linear Mech. 76, 100–111 (2015)

    Article  ADS  Google Scholar 

  15. M.E. Khater, M.A. Eltaher, E. Abdel-Rahman, M. Yavuz, Surface and thermal load effects on the buckling of curved nanowires. Eng. Sci. Technol. Int. J. 17(4), 279–283 (2014)

    Article  Google Scholar 

  16. X.W. Lei, T. Natsuki, J.X. Shi, Q.Q. Ni, An atomic-resolution nanomechanical mass sensor based on circular monolayer graphene sheet: theoretical analysis of vibrational properties. J. Appl. Phys. 113(15), 154313 (2013)

    Article  ADS  Google Scholar 

  17. X.F. Li, X.L. Peng, Theoretical analysis of surface stress for a microcantilever with varying widths. J. Phys. D Appl. Phys. 41(6), 065301 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  18. X.F. Li, H. Zhang, K.Y. Lee, Dependence of Young’s modulus of nanowires on surface effect. Int. J. Mech. Sci. 81, 120–125 (2014)

    Article  Google Scholar 

  19. X.F. Li, G.J. Tang, Z.B. Shen, K.Y. Lee, Resonance frequency and mass identification of zeptogram-scale nanosensor based on the nonlocal beam theory. Ultrasonics 55, 75–84 (2015)

    Article  Google Scholar 

  20. M. Liu, V.I. Artyukhov, H. Lee, F. Xu, B.I. Yakobson, Carbyne from first principles: chain of C atoms, a nanorod or a nanorope. ACS Nano 7(11), 10075–10082 (2013)

    Article  Google Scholar 

  21. W. Luo, W. Windl, First principles study of the structure and stability of carbynes. Carbon 47(2), 367–383 (2009)

    Article  Google Scholar 

  22. F.F. Mahmoud, M.A. Eltaher, A.E. Alshorbagy, E.I. Meletis, Static analysis of nanobeams including surface effects by nonlocal finite element. J. Mech. Sci. Technol. 26(11), 3555–3563 (2012)

    Article  Google Scholar 

  23. E.M. Miandoab, A. Yousefi-Koma, H.N. Pishkenari, M. Fathi, Nano-resonator frequency response based on strain gradient theory. J. Phys. D Appl. Phys. 47(36), 365303 (2014)

    Article  Google Scholar 

  24. H. Mobki, M.H. Sadeghi, G. Rezazadeh, M. Fathalilou, Nonlinear behavior of a nano-scale beam considering length scale-parameter. Appl. Math. Model. 38(5), 1881–1895 (2014)

    Article  MathSciNet  Google Scholar 

  25. T. Natsuki, N. Matsuyama, J.X. Shi, Q.Q. Ni, Vibration analysis of nanomechanical mass sensor using carbon nanotubes under axial tensile loads. Appl. Phys. A 116(3), 1001–1007 (2014)

    Article  ADS  Google Scholar 

  26. P. Pine, Y.E. Yaish, J. Adler, Vibrational analysis of thermal oscillations of single-walled carbon nanotubes under axial strain. Phys. Rev. B 89(11), 115405 (2014)

    Article  ADS  Google Scholar 

  27. Z.B. Shen, L.P. Sheng, X.F. Li, G.J. Tang, Nonlocal Timoshenko beam theory for vibration of carbon nanotube-based biosensor. Phys. E Low Dimens. Syst. Nanostruct. 44(7), 1169–1175 (2012)

    Article  ADS  Google Scholar 

  28. J.X. Shi, Y. Liu, M. Shimoda, Vibration analysis of a carbyne-based resonator in nano-mechanical mass sensors. J. Phys. D Appl. Phys. 48(11), 115303 (2015)

    Article  ADS  Google Scholar 

  29. A.M. Sladkov, Y.P. Kudryavtsev, Polyynes. Russ. Chem. Rev. 32(5), 229–243 (1963)

    Article  ADS  Google Scholar 

  30. S. Souayeh, N. Kacem, Computational models for large amplitude nonlinear vibrations of electrostatically actuated carbon nanotube-based mass sensors. Sens. Actuators A 208, 10–20 (2014)

    Article  Google Scholar 

  31. G.F. Wang, X.Q. Feng, Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Appl. Phys. Lett. 90(23), 231904 (2007)

    Article  ADS  Google Scholar 

  32. G.F. Wang, X.Q. Feng, Timoshenko beam model for buckling and vibration of nanowires with surface effects. J. Phys. D Appl. Phys. 42(15), 155411 (2009)

    Article  ADS  Google Scholar 

  33. Z. Yan, L.Y. Jiang, The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects. Nanotechnology 22(24), 245703 (2011)

    Article  ADS  Google Scholar 

  34. Q. Yuan, F. Ding, Formation of carbyne and graphyne on transition metal surfaces. Nanoscale 6(21), 12727–12731 (2014)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt

    M. A. Agwa & M. A. Eltaher

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  1. M. A. Agwa
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  2. M. A. Eltaher
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Correspondence to M. A. Eltaher.

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Agwa, M.A., Eltaher, M.A. Vibration of a carbyne nanomechanical mass sensor with surface effect. Appl. Phys. A 122, 335 (2016). https://doi.org/10.1007/s00339-016-9934-9

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  • DOI: https://doi.org/10.1007/s00339-016-9934-9

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