Abstract
The potentials of carbon nanotubes (CNTs) as mechanical resonators for atomic-scale mass sensing are presented. To this aim, a nonlocal continuum-based model is proposed to study the dynamic behavior of bridged single-walled carbon nanotube-based mass nanosensors. The carbon nanotube (CNT) is considered as an elastic Euler–Bernoulli beam with von Kármán type geometric nonlinearity. Eringen’s nonlocal elastic field theory is utilized to model the interatomic long-range interactions within the structure of the CNT. This developed model accounts for the arbitrary position of the deposited atomic-mass. The natural frequencies and associated mode shapes are determined based on an eigenvalue problem analysis. An atom of xenon (Xe) is first considered as a specific case where the results show that the natural frequencies and mode shapes of the CNT are strongly dependent on the location of the deposited Xe and the nonlocal parameter of the CNT. It is also indicated that the first vibrational mode is the most sensitive when the mass is deposited at the middle of a single-walled carbon nanotube. However, when deposited in other locations, it is demonstrated that the second or third vibrational modes may be more sensitive. To investigate the sensitivity of bridged single-walled CNTs as mass sensors, different noble gases are considered, namely Xe, argon (Ar), and helium (He). It is shown that the sensitivity of the single-walled CNT to the Ar and He gases is much lower than the Xe gas due to the significant decrease in their masses. The derived model and performed analysis are so needed for mass sensing applications and particularly when the detected mass is randomly deposited.
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Y. Tao, J.M. Boss, B.A. Moores, C.L. Degen, Single-crystal diamond nanomechanical resonators with quality factors exceeding one million. Nat. Commun. (2014). doi:10.1038/ncomms4638
A.K. Huttel, G.A. Steele, B. Witkamp, M. Poot, L.P. Kouwenhoven, H.S. van der Zant, Carbon nanotubes as ultrahigh quality factor mechanical resonators. Nano Lett. 9, 2547–2552 (2009)
J. Moser, A. Eichler, J. Güttinger, M.I. Dykman, A. Bachtold, Nanotube mechanical resonators with quality factors of up to 5 million. Nat. Nanotechnol. 9, 1007–1011 (2014)
M. Shaat, Effects of grain size and microstructure rigid rotations on the bending behavior of nanocrystalline material beams. Int. J. Mech. Sci. 94–95, 27–35 (2015)
M. Shaat, A. Abdelkefi, Modeling of mechanical resonators used for nanocrystalline materials characterization and disease diagnosis of HIVs. Microsyst. Technol. 22(2), 305–318 (2016)
M. Shaat, A. Abdelkefi, Pull-in instability of multi-phase nanocrystalline silicon beams under distributed electrostatic force. Int. J. Eng. Sci. 90, 58–75 (2015)
M. Shaat, A. Abdelkefi, Modeling the material structure and couple stress effects of nanocrystalline silicon beams for pull-in and bio-mass sensing applications. Int. J. Mech. Sci. 101–102, 280–291 (2015)
L. Sekaric et al., Nanomechanical resonant structures in nanocrystalline diamond. Appl. Phys. Lett. 81, 4455–4457 (2002)
A.U. Hutchinson et al., Dissipation in nanocrystalline-diamond nanomechanical resonators. Appl. Phys. Lett. 84, 972–974 (2004)
B. Lassagne, D. Garcia-Sanchez, A. Aguasca, A. Bachtold, Ultrasensitive mass sensing with a nanotube electromechanical resonator. Nano Lett. 4(9), 1775–1779 (2008)
A. Dalgarno, W.D. Davison, Long-range interactions of alkali metals. Mol. Phys. 13(5), 479–486 (1967)
R.J. Leroy, R.B. Bernstein, Dissociation energy and long-range potential of diatomic molecules from vibrational spacings of higher levels. J. Chem. Phys. 52(8), 3869–3879 (1970)
V.M. Mostepanenko, I.Y. Sokolov, Hypothetical long-range interactions and restrictions on their parameters from force measurements. Phys. Rev. D 47(7), 2882–2891 (1993)
P. Poncharal, Z.L. Wang, D. Ugarte, W.A. de Heer, Electrostatic deflections and electromechanical resonances of carbon nanotubes. Science 283, 1513–1516 (1999)
C. Li, T. Chou, Mass detection using carbon nanotube-based nanomechanical resonators. Appl. Phys. Lett. 84, 5246 (2004)
C. Li, T. Chou, Strain and pressure sensing using single-walled carbon nanotubes. Nanotechnology 15, 1493–1496 (2004)
H. Chiu, P. Hung, H.W.C. Postma, M. Bockrath, Atomic-scale mass sensing using carbon nanotubes resonators. Nano Lett. 8(12), 4342–4346 (2008)
S. Sawano, T. Arie, S. Akita, Carbon nanotube resonator in liquid. Nano Lett. 10, 3395–3398 (2010)
Y. Wang, T.W. Yeow, A review of carbon nanotubes-based gas sensors. J. Sens. Article ID 493904, p. 24 (2009)
K. Balasubramanian, M. Burghard, Biosensors based on carbon nanotubes. Anal. Bioanal. Chem. 385, 452–468 (2006)
C. Li, T.-W. Chou, Single-walled carbon nanotubes as ultrahigh frequency nanomechanical resonators. Phys. Rev. B 68, 073405-3 (2003)
X.L. Feng, R. He, P. Yang, M.L. Roukes, Very high frequency silicon nanowire electromechanical resonators. Nano Lett. 7(7), 1953–1959 (2007)
T. Murmu, M.A. McCarthy, S. Adhikari, Nonlocal elasticity based magnetic field affected vibration response of double single-walled carbon nanotube systems. J. Appl. Phys. 111, 113511 (2012)
J. Li, K. Zhu, Weighing a single atom using a coupled plasmon-carbon nanotube system. Sci. Technol. Adv. Mater. 13, 025006 (2012). (6pp)
R. Chowdhury, S. Adhikari, J. Mitchell, Vibrating carbon nanotube based bio-sensors. Phys. E 42, 104–109 (2009)
S. Adhikari, R. Chowdhury, The calibration of carbon nanotube based bionanosensors. J. Appl. Phys. 107, 124322 (2010)
I. Mehdipour, A. Barari, G. Domairry, Application of a cantilevered SWCNT with mass at the tip as a nanomechanical sensor. Comput. Mater. Sci. 50, 1830–1833 (2011)
I. Mehdipour, A. Barari, Why the center-point of bridged carbon nanotube length is the most mass sensitive location for mass attachment? Comput. Mater. Sci. 55, 136–141 (2012)
Y. Joshi, A. Hrasha, C. Shatma, Vibration signature analysis of single walled carbon nanotube based nanomechanical sensors. Phys. E 42, 2115–2123 (2010)
T. Natsuki, N. Matsuyama, J. Shi, Q. Ni, Vibration analysis of nanomechanical mass sensor using carbon nanotubes under axial tensile loads. Appl. Phys. A 116, 1001–1007 (2014)
H. Lee, J. Hsu, W. Chang, Frequency shift of carbon-nanotube-based mass sensor using nonlocal elasticity theory. Nanoscale Res. Lett. 5, 1774–1778 (2010)
T. Murmu, S. Adhikari, Nonlocal frequency analysis of nanoscale biosensors. Sens. Actuators A 137, 41–48 (2012)
M. Aydogdu, S. Filiz, Modeling carbon nanotube-based mass sensors using axial vibration and nonlocal elasticity. Phys. E 43, 1229–1234 (2011)
Z. Shen, G. Tang, L. Zhang, X. Li, Vibration of double-walled carbon nanotube based nanomechanical sensor with initial axial stress. Comput. Mater. Sci. 58, 51–58 (2012)
Z. Shen, X. Li, L. Sheng, G. Tang, Nonlocal Timoshenko beam theory for vibration of carbon nanotube-based biosensor. Phys. E 44, 1169–1175 (2012)
K. Kiani, H. Ghaffari, B. Mehri, Application of elastically supported single-walled carbon nanotubes for sensing arbitrarily attached nano-objects. Curr. Appl. Phys. 13, 107–120 (2013)
X. Li, G. Tang, Z. Shen, K. Lee, Resonance frequency and mass identification of zeptogram-scale nanosensor based on the nonlocal beam theory. Ultrasonics 55, 75–84 (2015)
A.C. Eringen, Nonlocal Continuum Field Theories (Springer, New York, 2002)
A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703 (1983)
C. Polizzotto, Nonlocal elasticity and related variational principles. Int. J. Solids Struct. 38(42), 7359–7380 (2001)
X. Zeng, Y. Chen, J.D. Lee, Determining material constants in nonlocal micromorphic theory through phonon dispersion relations. Int. J. Eng. Sci. 44, 1334–1345 (2006)
J. Peddieson, G.R. Buchanan, R.P. McNitt, Application of nonlocal continuum models to nanotechnology. Int. J. Eng. Sci. 41, 305–312 (2003)
L.J. Sudak, Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics. J. Appl. Phys. 94, 7281–7287 (2003)
L.F. Wang, H.Y. Hu, Flexural wave propagation in single-walled carbon nanotubes. Phys. Rev. B 71, 195412 (2005)
Y.Q. Zhang, G.R. Liu, X.Y. Xie, Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity. Phys. Rev. B 71, 195404 (2005)
P. Lu, H.P. Lee, C. Lu, P.Q. Zhang, Dynamic properties of flexural beams using a nonlocal elasticity model. J. Appl. Phys. 99, 073510 (2006)
M. Xu, Free transverse vibrations of nano-to-micron scale beams. Proc. Roy. Soc. A 462, 2977–2995 (2006)
J.N. Reddy, Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45, 288–307 (2007)
M. Shaat, Iterative nonlocal elasticity for Kirchhoff plates. Int. J. Mech. Sci. 90, 162–170 (2015)
P. Lu, P.Q. Zhang, H.P. Lee, C.M. Wang, J.N. Reddy, Non-local elastic plate theories. Proc. R. Soc. A 463, 3225–3240 (2007)
Y. Aboelkassem, A.H. Nayfeh, M. Ghommem, Bio-mass sensor using an electrostatically actuated microcantilever in a vacuum microchannel. Microsyst. Technol. 16, 1749–1755 (2010)
S.A. Emam, A Theoretical and Experimental Study of Nonlinear Dynamics of Buckled Beams. PhD dissertation, (Virginia Polytechnic Institute and State University, Blacksburg, VA, 2002)
H.L. Dai, L. Wang, A. Abdelkefi, Q. Ni, On nonlinear behavior and buckling of fluid-transporting nanotubes. Int. J. Eng. Sci. 87, 13–22 (2015)
T. Murmu, S. Adhikari, Nonlocal vibration of carbon nanotubes with attached buckyballs at tip. Mech. Res. Commun. 38, 62–67 (2011)
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Ali-Akbari, H.R., Shaat, M. & Abdelkefi, A. Bridged single-walled carbon nanotube-based atomic-scale mass sensors. Appl. Phys. A 122, 762 (2016). https://doi.org/10.1007/s00339-016-0274-6
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DOI: https://doi.org/10.1007/s00339-016-0274-6