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Surface elasticity-based modeling and simulation for dynamic and sensing performances of nanomechanical resonators

  • Kilho Eom (Biomechanics Lab, College of Sport Science, Sungkyunkwan University (SKKU))
  • Received : 2022.08.23
  • Accepted : 2022.12.12
  • Published : 2023.03.25

Abstract

The dynamic and sensing performances of nanomechanical resonators with their different boundary conditions are studied based on surface elasticity-based modeling and simulation. Specifically, the effect of surface stress is included in Euler-Bernoulli beam model for different boundary conditions. It is shown that the surface effect on the intrinsic elastic property of nanowire is independent of boundary conditions, while these boundary conditions affect the frequency behavior of nanowire resonator. The detection sensitivity of nanowire resonator is remarkably found to depend on the boundary conditions such that double-clamping boundary condition results in the higher mass sensitivity of the resonator in comparison with simple-support or cantilever boundary condition. Furthermore, we show that the frequency shift of nanowire resonator due to mass adsorption is determined by its length, whereas the frequency shift is almost independent of its thickness. This study enables a design principle providing an insight into how the dynamic and sensing performances of nanomechanical resonator is determined and tuned.

Keywords

References

  1. Adali, S. (2009), "Variational principles for transversely vibrating multiwalled carbon nanotubes based on nonlocal Euler-Bernoulli beam model", Nano Lett., 9(5), 1737-1741. https://doi.org/10.1021/nl8027087.
  2. Agrawal, R., Peng, B., Gdoutos, E.E. and Espinosa, H.P. (2008), "Elasticity size effects in ZnO nanowires - a combinding experimental-computational approach", Nano Lett., 8(11), 3668-3674. https://doi.org/10.1021/nl801724b.
  3. Atalaya, J., Isacsson, A. and Kinaret, J.M. (2008), "Continuum elastic modeling of graphene resonators", Nano Lett., 8(12), 4196-4200. https://doi.org/10.1021/nl801733d.
  4. Azamat, J. (2021), "Application of graphene, graphene oxide, and boron nitride nanosheets in the water treatment", Membr. Water Treat., 12(5), 227-243. https://doi.org/10.12989/mwt.2021.12.5.227.
  5. Azandariani, M.G., Gholami, M. and Nikzad A. (2022), "Eringen's nonlocal theory for non-linear bending analysis of BGF Timoshenko nanobeams", Adv. Nano Res., 12(1), 37-47. https://doi.org/10.12989/anr.2022.12.1.037.
  6. Balchi, M.N. (2022), "Longitudinal vibration of a nanorod embedded in viscoelastic medium considering nonlocal strain gradient theory", Adv. Nano Res., 13(2), 147-164. https://doi.org/10.12989/anr.2022.13.2.147.
  7. Braun, T., Barwich, V., Ghatkesar, M.K., Bredekamp, A.H., Gerber, C., Hegner, M. and Lang H.P. (2005), "Micromechanical mass sensors for biomolecular detection in a physiological environment", Phys. Rev. E., 72(3), 031907. https://doi.org/10.1103/PhysRevE.72.031907.
  8. Cammarata, R.C. (1994), "Surface and interface stress effects in thin films", Prog. Surf. Sci., 46(1), 1-38. https://doi.org/10.1016/0079-6816(94)90005-1.
  9. Chan, J., Alegre, T.P.M., Safavi-Naeini, A.H., Hill, J.T., Krause, A., Groblacher, S., Aspelmeyer, M. and Painter, O. (2011), "Laser cooling of a nanomechanical oscillator into its quantum ground state", Nature, 478(7367), 89-92. https://doi.org/10.1038/nature10461.
  10. Choi, J.W., Lee, H., Lee, G., Kim, Y.R., Ahn, M.J., Park, H.J., Eom, K., Kwon, T. (2017), "Blood droplet-based cancer diagnosis via proteolytic activity measurement in cancer progression", Theranostics, 7(11), 2878-2887. https://doi.org/10.7150/thno.19358.
  11. Dai, M. D., Kim, C.-W. and Eom, K. (2011), "Finite size effect on nanomechanical mass detection: The role of surface elasticity", Nanotechnology, 22, 265502. https://doi.org/10.1088/0957-4484/22/26/265502
  12. Dai, M.D., Kim, C.W. and Eom, K. (2012), "Nonlinear vibration behavior of graphene resonators and their applications in sensitive mass detection", Nanoscale Res. Lett., 7, 499. https://doi.org/10.1186/1556-276X-7-499.
  13. Dai, M.D. Eom, K. and Kim, C.W. (2009), "Nanomechanical mass detection using nonlinear oscillations", Appl. Phys. Lett., 95(20), 203104. https://doi.org/10.1063/1.3265731.
  14. Eom, K., Kwon, T.Y., Yoon, D.S., Lee, H.L. and Kim, T.S. (2007), "Dynamical response of nanomechanical resonators to biomolecular interactions", Phys. Rev. B, 76(11), 113408. https://doi.org/10.1103/PhysRevB.76.113408.
  15. Eom, K., Park, H.S., Yoon, D.S. and Kwon, T. (2011), "Nanomechanical resonators and their applications in biological/chemical detection: Nanomechanics principles", Phys. Rep., 503(4-5), 115-163. https://doi.org/10.1016/j.physrep.2011.03.002.
  16. Eom, K. (2020), "Computational simulations of nanomechanical resonators for understanding their frequency dynamics and sensing performances", Multiscale Sci. Eng., 2(4), 214-226. https://doi.org/10.1007/s42493-020-00051-4.
  17. Eringen, A.C. (1983), "On differential equation of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803.
  18. Falk, K., Sedlmeier, F., Joly, L., Netz, R.R. and Bocquet, L. (2010), "Molecular origin of fast water transport in carbon nanotube membranes: superlubricity versus curvature dependent friction", Nano Lett., 10(10), 4067-4073. https://doi.org/10.1021/nl1021046.
  19. Feng, X., He, R., Yang, P. and Roukes, M.L. (2007), "Very high frequency silicon nanowire electromechanical resonators", Nano Lett., 7(7), 1953-1959. https://doi.org/10.1021/nl0706695.
  20. Freund, L.B. and Suresh, S. (2003), Thin Film Materials, Cambridge University Press, Cambridge, U.K.
  21. Gil-Santos, E., Ramos, D., Martinez, J., Fernandez-Regulez, M., Garcia, R., San Paulo, A., Calleja, M. and Tamayo, J. (2010), "Nanomechanical mass sensing and stiffness spectrometry based on two-dimensional vibrations of resonant nanowires", Nat. Nano., 6, 641-645. https://doi.org/10.1038/nnano.2010.151.
  22. Gupta, A.K., Nair, P.R., Akin, D., Ladisch, M.R., Broyles, S., Alam, M.A. and Bashir, R. (2006), "Anomalous resonance in a nanomechanical biosensor", Proc. Natl. Acad. Sci. U.S.A., 103(36), 13362-13367. https://doi.org/10.1073/pnas.0602022103.
  23. Gurtin, M.E., Markenscoff, X. and Thurston, R.N. (1976), "Effect of surface stress on the natural frequency of thin crystals", Appl. Phys. Lett., 29(9), 529-530. https://doi.org/10.1063/1.89173.
  24. Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surfaces", Arch. Ration. Mech. Anal., 57, 291-323. https://doi.org/10.1007/BF00261375.
  25. Hanay, M.S., Kelber, S., Naik, A.K., Chi, D., Hentz, S., Bullard, E.C., Colinet, E., Duraffourg, L. and Roukes, M.L. (2012), "Single-protein nanomechanical mass spectrometry in real time", Nat. Nano., 7, 602-608. https://doi.org/10.1038/nnano.2012.119.
  26. He, J. and Lilley, C.M. (2008), "Surface effect on the elastic behavior of static bending nanowires", Nano Lett., 8(7), 1798-1802. https://doi.org/10.1021/nl0733233.
  27. He, J. and Lilley, C.M. (2008), "Surface stress effect on bending resonance of nanowires with different boundary conditions", Appl. Phys. Lett., 93(26), 263108. https://doi.org/10.1063/1.3050108.
  28. Hibert, W. (2012), "Mass sensing: Devices reach single-proton limit", Nat. Nano., 7, 278-280. https://doi.org/10.1038/nnano.2012.66.
  29. Huang, X.M.H., Feng, X.L., Zorman, C.A., Mehregany, M. and Roukes, M.L. (2005), "VHF, UHF, and microwave frequency nanomechanical resonators", N. J. Phys., 7, 247. https://doi.org/10.1088/1367-2630/7/1/247.
  30. Ibach, H. (1997), "The role of surface stress in reconstruction, epitaxial growth, and stabilization of mesoscopic structures", Surf. Sci. Rep., 29(5-6), 193-263. https://doi.org/10.1016/S0167-5729(97)00010-1.
  31. Ilic, B., Yang, Y. and Craighead, H.G. (2004), "Virus detection using nanoelectromechanical devices", Appl. Phys. Lett., 85(13), 2604-2606. https://doi.org/10.1063/1.1794378.
  32. Ilic, B., Yang, Y., Aubin, K., Reichenbach, R., Krylov, S. and Craighead, H.G. (2005), "Enumeration of DNA molecules bound to a nanomechanical oscillator", Nano Lett., 5(5), 925-929. https://doi.org/10.1021/nl050456k.
  33. Jing, G.Y., Duan, H.L., Sun, X.M., Zhang, Z.S., Xu, J., Li, Y.D., Wang, J.X. and Yu, D.P. (2006), "Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy", Phys. Rev. B., 73(23), 235409. https://doi.org/10.1103/PhysRevB.73.235409.
  34. Kim, S.Y. and Park, H.S. (2008), "Utilizing mechanical strain to mitigate the intrinsic loss mechanisms in oscillating metal nanowires", Phys. Rev. Lett., 101, 215502. https://doi.org/10.1103/PhysRevLett.101.215502.
  35. Kim, S.Y. and Park, H.S. (2009), "The importance of edge effects on the intrinsic loss mechanisms of graphene nanoresonators", Nano Lett., 9(3), 969-974. https://doi.org/10.1021/nl802853e.
  36. Kim, C.W., Dai, M.D. and Eom, K. (2016), "Finite size effect on the dynamic and sensing performances of graphene resonators: The role of edge stress", Beilstein J. Nanotechnol., 7(1), 685-696. https://doi.org/10.3762/bjnano.7.61.
  37. Kwon, T., Park, J., Yang, J., Yoon, D.S., Na, S., Kim, C.W., Suh, J.S., Huh, Y.M., Haam, S. and Eom, K. (2009), "Nanomechanical in situ monitoring of proteolysis of peptide by cathepsin B", PLoS ONE, 4(7), e6248. https://doi.org/10.1371/journal.pone.0006248.
  38. Kwon, T.Y., Eom, K., Park, J.H., Yoon, D.S., Kim, T.S. and Lee, H.L. (2007), "In situ real-time monitoring of biomolecular interactions based on resonating microcantilevers immersed in a viscous fluid", Appl. Phys. Lett., 90(22), 223903. https://doi.org/10.1063/1.2741053.
  39. LaHaye, M.D., Buu, O., Camarota, B. and Schwab, K.C. (2004), "Approaching the quantum limit of a nanomechanical resonator", Science, 304(5667), 74-77. https://doi.org/10.1126/science.1094419
  40. Lee, B. and Rudd, R.E. (2007), "First-principles calculation of mechanical properties of Si<001> nanowires and comparison to nanomechanical theory", Phys, Rev. B., 75(19), 195328. https://doi.org/10.1103/PhysRevB.75.195328.
  41. Lee, C.Y., Choi, W., Han, J.H. and Strano, M.S. (2010), "Coherence resonance in a single-walled carbon nanotube ion channel", Science, 329(5997), 1320-1324. https://doi.org/10.1126/science.1193383.
  42. Lee, J., Jang, J., Akin, D., Savran, C.A. and Bashir, R. (2008), "Real-time detection of airborne viruses on a mass-sensitive device", Appl. Phys. Lett., 93(1), 013901. https://doi.org/10.1063/1.2956679.
  43. Lu, P., Lee, H.P., Lu, C. and O'Shea, S.J. (2005), "Surface stress effects on the resonance properties of cantilever sensors", Phys. Rev. B., 72(8), 085405. https://doi.org/10.1103/PhysRevB.72.085405.
  44. McDowell, M.T., Leach, A.M. and Gall, K. (2008a), "Bending and tensile deformation of metallic nanowires", Model. Simul. Mater. Sci. Eng., 16(4), 045003. https://doi.org/10.1088/0965-0393/16/4/045003.
  45. McDowell, M.T., Leach, A.M. and Gall, K. (2008b), "On the elastic modulus of metallic nanowires", Nano Lett., 8, 3613-3618. https://doi.org/10.1021/nl801526c
  46. Meirovitch, L. (1967), Analytical Methods in Vibration, Macmillan, New York, U.S.A.
  47. Miller, R.E. and Shenoy, V.B. (2000), "Size-dependent elastic properties of nanosized structural elements", Nanotechnology, 11(3), 139-147. https://doi.org/10.1088/0957-4484/11/3/301.
  48. Park, H.S. (2008), "Surface stress effects on the resonant properties of silicon nanowires", J. Appl. Phys., 103(12), 123504. https://doi.org/10.1063/1.2939576
  49. Park, H.S., Cai, W., Espinosa, H.D. and Huang, H. (2009), "Mechanics of crystalline nanowires", MRS Bull., 34(3), 178-183. https://doi.org/10.1557/mrs2009.49.
  50. Park, H.S. and Klein, P.A. (2007), "Surface Cauchy-Born analysis of surface stress effects on metallic nanowires", Phys. Rev. B., 75(8), 085408. https://doi.org/10.1103/PhysRevB.75.085408.
  51. Park, H.S. and Klein, P.A. (2008), "Surface stress effects on the resonant properties of metal nanowires: The importance of finite deformation kinematics and the impact of the residual surface stress", J. Mech. Phys. Solids, 56(11), 3144-3166. https://doi.org/10.1016/j.jmps.2008.08.003.
  52. Pin, L., Lee, H.P., Lu, C. and Zhang, P.Q. (2006), "Dynamic properties of flexural beams using a nonlocal elasticity model", J. Appl. Phys., 99(7), 073510. https://doi.org/10.1063/1.2189213.
  53. Poot, M. and van der Zant, H.S.J. (2012), "Mechanical systems in the quantum regime", Phys. Rep., 511, 273-335. https://doi.org/10.1016/j.physrep.2011.12.004
  54. Postma, H.W.C., Kozinsky, I., Husain, A. and Roukes, M.L. (2005), "Dynamic range of nanotube- and nanowire-based electromechanical systems", Appl. Phys. Lett., 86, 223105.
  55. Rayleigh, L. (1890), "On the theory of surface forces", Phil. Mag., 30, 285-298. https://doi.org/10.1080/14786449008620028
  56. Sharma, P., Ganti, S. and Bhate, N. (2003), "Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities", Appl. Phys. Lett., 82(4), 535-537. https://doi.org/10.1063/1.1539929.
  57. Shuttleworth, R. (1950), "The surface tension of solids", Proc. Phys. Soc. Lond. Sect. A., 63(5), 444-457. https://doi.org/10.1088/0370-1298/63/5/302.
  58. Tamayo, J., Ramos, D., Mertens, J. and Calleja, M. (2006), "Effect of the adsorbate stiffness on the resonance response of microcantilever sensors", Appl. Phys. Lett., 89(22), 224104. https://doi.org/10.1063/1.2388925.
  59. Timoshenko, S. (1940), Theory of Plates and Shells, McGrow Hill, New York, U.S.A.
  60. Timoshenko, S. and Goodier, J.N. (1970), Theory of Elasticity, McGraw Hill, New York, U.S.A.
  61. Verbridge, S.S., Shapiro, D.F., Craighead, H.G. and Parpia, J.M. (2007), "Macroscopic tuning of nanomechanics: Substrate bending for reversible control of frequency and quality factor of nanostring resonators", Nano Lett., 7(6), 1728-1735. https://doi.org/10.1021/nl070716t.
  62. Waggoner, P.S. and Craighead, H.G. (2007), "Micro- and nanomechanical sensors for environmental, chemical, and biological detection", Lab Chip, 7(10), 1238-1255. https://doi.org/10.1039/B707401H.
  63. Wang, G.F. and Feng, X.Q. (2009), "Surface effects on buckling of nanowires under uniaxial compression", Appl. Phys. Lett., 94(14), 141913. https://doi.org/10.1063/1.3117505.
  64. Wu, G., Datar, R.H., Hansen, K.M., Thundat, T., Cote, R.J. and Majumdar, A. (2001), "Bioassay of prostate-specific antigen (PSA) using microcantilevers", Nat. Biotech., 19(9), 856-860. https://doi.org/10.1038/nbt0901-856.
  65. Wu, B., Heidelberg, A. and Boland, J.J. (2005), "Mechanical properties of ultrahigh-strength gold nanowires", Nat. Mater., 4(7), 525-529. https://doi.org/10.1038/nmat1403.
  66. Yang, Y.T., Callegari, C., Feng, X.L., Ekinci, K.L. and Roukes, M.L. (2006), "Zeptogram-scale nanomechanical mass sensing", Nano Lett., 6(4), 583-586. https://doi.org/10.1021/nl052134m.
  67. Yi, W. (2022), "Intelligent computer modelling and simulation for the large amplitude of nano systems", Adv. Nano Res., 13(1), 63-75.
  68. Yoon, G., Park, H.J., Na, S. and Eom, K. (2009), "Mesoscopic model for mechanical characterization of biological protein materials", J. Comput. Chem., 30(6), 873-880. https://doi.org/10.1002/jcc.21107.
  69. Yun, G. and Park, H.S. (2009), "Surface stress effects on the bending properties of fcc metal nanowires", Phys. Rev. B., 79(19), 195421. https://doi.org/10.1103/PhysRevB.79.195421.
  70. Zhao, Y., Ma, C.C., Chen, G. and Jiang, Q. (2003), "Energy dissipation mechanisms in carbon nanotube oscillators", Phys. Rev. Lett., 91(17), 175504. https://doi.org/10.1103/PhysRevLett.91.175504.
  71. Zheng, M., Eom, K. and Ke, C. (2009), "Calculation of the resonant response of carbon nanotubes to binding of DNA", J. Phys. D Appl. Phys., 42(14), 145408. https://doi.org/10.1088/0022-3727/42/14/145408.
  72. Zhu, Y., Xu, F., Qin, Q., Fung, W.Y. and Lu, W. (2009), "Mechanical properties of vapor-liquid-solid synthesized silicon nanowires", Nano Lett., 9(11), 3934-3939. https://doi.org/10.1021/nl902132w.