This paper aims to obtain the simple closed-form results for the combined effects of surface elasticity, initial stress/ strain, and material Poisson ratio on the bending stiffness, natural frequency and buckling force of nanowires and nano-plates. The results demonstrate that all these properties of nanowires or nanoplates can be designed either very sensitive or not sensitive at all to the amplitude of an applied electric potential; show how much of those properties can be controlled to vary; and thus provide a reliable guide to the measurement of the Young’s modulus of nanowires/nanoplates and to the design of nano-devices, such as nano-sensors or the cantilever of an AFM.
KeywordsNanowiresNanoplatesBending StiffnessBuckling ForceNatural Frequency
R. E. Miller and V. B. Shenoy, “Size-dependent elastic properties of nanosized structural elements,” Nanotechnology, Vol. 11, 2000, pp. 139-147. doi:10.1088/0957-4484/11/3/301
S. Guenot, C. Fretigny, S. Demoustier-Champagne and B. Nysten, “Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy,” Phys. Rev. B. 69, 2004, p. 165410. doi:10.1103/PhysRevB.69.165410
J. H. Song, X. D. Wang, E. Riedo and Z. L. Wang, “Elastic Property of Vertically Aligned Nanowires,” Nano Lett. Vol. 5, 2005, pp. 1954-1958. doi:10.1021/nl051334v
G. Y. Jing, H. L. Duan, X. M. Sun, Z. S. Zhang, J. Xu, Y. D. Li, J. X. Wang and D. B. Yu, “Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy ,” Phys. Rev. B. 73, 2006, p. 235409. doi:10.1103/PhysRevB.73.235409
C. Q. Chen, Y. Shi, Y. S. Zhang and J. Zhu, Y. J. Yan, “Size dependent Young’s modulus in ZnO nanowires,” Phys. Rev. Lett. Vol. 96, 2006, p. 075505. doi:10.1103/PhysRevLett.96.075505
J. He and C. M. Lilley, “Surface effect on the elastic behaviour of static bending nanowires,” Nano Lett. Vol. 8, 2008, pp. 1798-1802. doi:10.1021/nl0733233
A. Heidelberg, L. T. Ngo, B. Wu, M. A. Phillips, S. Sharma, T. I. Kamins, J. E. Sader and J. J. Boland, “A generalized description of the elastic properties of nanowires,” Nano Lett. Vol. 6, 2006, pp. 1101-1106. doi:10.1021/nl060028u
B. Wu, A. Heidelberg and J. J. Boland, “Mechanical properties of ultrahigh-strength gold nanowires,” Nature Mater. Vol. 4, 2005, pp. 525-529. doi:10.1038/nmat1403
X. Li, T. Ono, Y. Wang and M. Esashi, “Ultrathin single-crystalline-silicon cantilever resonators: Fabrication technology and significant specimen size effect on Young’s modulus,” Appl. Phys. Lett. Vol. 83, 2003, pp. 3081-3083. doi:10.1063/1.1618369
H. S. Park, “Surface stress effects on the resonant properties of silicon nanowires,” J. Appl. Phys. Vol. 103, 2008, p. 123504. doi:10.1063/1.2939576
G. F. Wang and X. Q. Feng, “Effects of surface elasticity and residual surface stress on the natural frequency of microbeams,” Appl. Phys. Lett. Vol. 90, 2007, p. 231904. doi:10.1063/1.2746950
D. A. Smith, V. C. Holmberg, D. C. Lee and B. A. Korgel, “Young’s modulus and size-dependent mechanical quality factor of nanoelectromechanical Germanium nanowire resonators,” J. Phys. Chem. C 112, 2008, pp. 10725-10729. doi:10.1021/jp8010487
J. He and C. M. Lilley, “Surface stress effect on bending resonance of nanowires with different boundary conditions,” Appl. Phys. Lett. Vol. 93, 2008, p. 263108. doi:10.1063/1.3050108
H. S. Park, “Quantifying the size-dependent effect of the residual surface stress on the resonant frequencies of silicon nanowires if finite deformation kinematics are considered ,” Nanotechnology, Vol. 20, 2009, p. 115701. doi:10.1088/0957
M. E. Gurtin and X. Markenscoff, “Effect of surface stress on the natural frequency of thin crystals,” Appl. Phys. Lett. Vol. 29, 1976, pp. 529-530. doi:10.1063/1.89173
J. Lagowski, H. C. Gatos and E. S. Sproles Jr, “Surface stress and the normal mode of vibration of thin crystals: GaAs,” Appl. Phys. Lett. Vol. 26, 1975, pp. 493-495. doi:10.1063/1.88231
G. Y. Chen, T. Thundat, E. A. Wachter and R. J. Warmack, “Dsorption-Induced Surface Stress and its Effects on Resonance Frequencey of Microcantilevers,” J. Appl. Phys. Vol. 77, 1995, pp. 3618-3622. doi:10.1063/1.359562
V. V. Dobrokhotov, M. M. Yazdanpanah, S. Pabba, A. Safir and R. W. Cohn, “Visual force sensing with flexible nanowires buckling springs,” Nanotechnology, Vol. 19, 2008, p. 035502. doi:10.1088/0957-4484/19/03/035502
C. Hsin, W. Wai, Y. Gu, Y. Gao, C.T. Huang, Y. Liu, L. J. Chen and Z. L. Wang, “Elastic properties and buckling of silicon nanowires,” Adv. Mater. Vol. 20, 2008, pp. 3919-3923. doi:10.1002/adma.200800485
M. Riaz, O. Nur, M. Willander and P. Klason, “Buckling of ZnO nanowires under uniaxial compression,” Appl. Phys. Lett. Vol. 92, 2008, p. 103118. doi:10.1063/1.2894184
G. F. Wang and X. Q. Feng, “Surface effects on buckling of nanowires under uniaxial compression,” Appl. Phys. Lett. Vol. 94, 2009, p. 141913. doi:10.1063/1.3117505
F. Xu, Q. Qin, A. Mishra, Y. Gu and Y. Zhu, “Mechanical properties of ZnO nanowires under different loading modes,” Nano Res. Vol. 3, 2010, pp. 271-280. doi:10.1007/s12274-010-1030-4
K. L. Ekinci, M. H. Huang and M. L. Roukes, “Ultrasensitive nanoelectromechanical mass detection,” Appl. Phys. Lett. Vol. 84, 2004, pp. 4469-4471. doi:10.1063/1.1755417
H.X. Zhu, “The effects of surface and initial stresses on the bending stiffness of nanowires,” Nanotechnology, Vol. 19, 2008, p. 405703. doi:10.1088/0957-4484/19/40/405703
H. X. Zhu, J. Wang and B. L. Karihaloo, “Effects of surface and initial stresses on the bending stiffness of trilayer plates and nanofilms,” Journal of Mechanics of Materials and Structures, Vol. 4, 2009, pp. 589-604. doi:10.2140/jomms.2009.4.589
J. Biener, A. Wittstock, L. A. Zepeda-Ruiz, M. M. Biener, V. Zielasek, D. Kramer, R. N. Viswanath, J. Wessmuller, M. Baumer and A. V. Hamza, “Surface-chemistry-driven actuation in nanoporous gold,” Nature Materials, Vol. 8, 2009, pp. 47-51. doi:10.1038/nmat2335
R. Raiteri and H. J. Butt, “Measuring electrochemically induced surface stress with an atomic force microscope,” J. Phys. Chem. Vol. 99, 1995, pp. 15728-15732. doi:10.1021/j100043a008
R. C. Cammarata and K. Sieradzki, “Surface and Interface Stresses,” Annual Review of Mater. Sci. Vol. 24, 1994, pp. 215-234. doi:10.1146/annurev.ms.24.080194.001243
J. Weissmuller, R. N. Viswanath, D. Kramer, P. Zimmer, R. Wurschum and H. Gleiter, “Charge-induced reversible strain in a metal，” Science, Vol. 300, 2003, pp. 312-315. doi:10.1126/science.1081024
D. Kramer, R. N. Viswanath and J. Weissmuller, “Surface-stress induced macroscopic bending of nanoporous gold cantilevers,” Nano Lett. Vol. 4, 2004, pp. 793-796. doi:10.1021/nl049927d
W. Haiss, R. J. Nichols, J. K. Sass and K. P. Charle, “Linear correlation between surface stress and surface charge in anion adsorption on Au(111),” J. Electroana-lytical Chemistry, Vol. 452, 1998, pp. 199-202. doi:10.1016/S0022-0728(98)00137-5
J. Diao, K. Gall, M. L. Duan and J. A. Zimmerman, “Atomistic simulations of the yielding of gold nanowires,” Acta Mater. Vol. 54, 2006, pp. 643-653. doi:10.1016/j.actamat.2005.10.008
Z. C. Lin and J. C. Huang, “A study on a rigid body boundary layer interface force model for stress calculation and stress–strain behaviour of nanoscale uniaxial tension,” Nanotechnology, Vol. 15, 2004, pp.1509-1518. doi:10.1088/0957-4484/15/11/024
H.X. Zhu, “Size-dependent elastic properties of micro- and nano-honeycombs,” J. Mech. Phys. Solids, Vol. 58, 2010, pp. 696-709. doi:10.1016/j.jmps.2010.02.009
H.X. Zhu, L.B. Yan, R. Zhang and X.M. Qiu, “Size-dependent and tunable elastic properties of hierarchical honeycombs with regular square and equilateral triangular cells,” to appear in Acta Materialia, 2012. http://dx.doi.org/10.1016/j.actamat.2012.05.009
V. Tabard-Cossa, M. Godin, L. Y. Beaulieu and P. Grutter, “A differential microcantilever-based system for measuring surface stress changes inducted by electro-chemical rection,” Sensors and Actuators, B107, 2005, pp. 233-241. doi:10.1016/j.snb.2004.10.007
Z. L. Wang, Z. R. Dai, R. P. Gao and J. L. Gole, “Measuring the Young's modulus of solid nanowires by in situ TEM,” J. Electron Microscopy, Vol. 51, 2002, S79-85. doi:10.1093/jmicro/51.Supplement.S79