Dynamic Analysis of AFM in Air and Liquid Environments Considering Linear and Non-linear Interaction Forces by Timoshenko Beam Model

Subject Areas : Mechanical Engineering

P. Maleki Moghadam Abyaneh ¹ , M.H. Korayem ² , B. Manafi ³ , M. Damircheli ⁴

1 - Department of Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
4 - Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

Received: 2014-04-26 Accepted : 2014-10-12 Published : 2015-06-01

Keywords: Frequency Response, AFM, Liquid Environment, Timoshenko theory, Interaction force,

Abstract :

The atomic force microscopy of the cantilever beam frequency response behaviour in the liquid environment is different in comparison with air environment. In this paper, the dynamic analysis of AFM in the air and liquid environments is carried out in consideration of linear and non-linear interaction forces and also the effect of geometrical parameters such as length, width, height; and inclined angle on the vibrating motion of the rectangular cantilever is investigated. A rectangular cantilever based on the Timoshenko theory is simulated in ADAMS software and more accurate results are obtained by considering the probe tip and the angular location of cantilever at simulation. At the end of the cantilever, a silicone probe is considered where the applied forces on it are approximated using two tangential and vertical springs. The vibrational simulation of cantilever at two states is carried out with regard to linear and non-linear interaction forces. The amplitude and resonance frequency of the simulated cantilever based on Timoshenko theory are different from obtained results of Euler-Bernoulli theory due to the effect of shear deformation and rotary moment in Timoshenko theory. Therefore, the Timoshenko theory has better accuracy in comparison with Euler theory. Many chemical and biological processes occur instantly; therefore the use of cantilevers with small length for improving the imaging speed at the tapping mode and in the liquid environment is essential. Eventually short cantilever that is modeled based on the Timoshenko theory may produce more accurate results. This paper is aimed to demonstrate that the amplitude and resonance frequency of vibration in the liquid environment is different from amplitude and frequency of vibration in the air environment due to the damping coeficient and added mass of liquid.

References:

[1]      Binnig, G., Quate, CF., and Gerber, C., “Atomic Force Microscope”, Physical Review Letters 56.9, 1986, pp. 930.

[2]      Timoshenko, SP., Goodier, JN., “Theory of Elasticity”, New York: McGraw Hill, 1951.

[3]      Meirovitch, L., Elements of vibration analysis. McGraw Hill, 1975.

[4]      Rao, JA., “Advanced Theory of Vibration”, New York: Wiley, 1992.

[5]      Turner, JA., Wiehn, JS., “Sensitivity of flexural and torsional vibration modes of atomic force microscope cantilevers to surface stiffness variations”, Nanotechnology 12.3, 2001, pp. 322.

[6]      Rabe, U., Janser, K., and Arnold, W., “Vibrations of free and surface-coupled atomic force microscope cantilevers: theory and experiment”, Review of Scientific Instruments 67.9, 1996, pp. 3281-3293.

[7]      Chang, WJ., Chu, SS., “Analytical solution of flexural vibration responses on taped atomic force microscope cantilevers”, Physics Letters A309.1, 2003, pp. 133-137.

[8]      Song, Y., Bhushan, B., “Simulation of dynamic modes of atomic force microscopy using a 3D finite element model”, Ultramicroscopy 106.8, 2006, pp. 847-873.

[9]      Arafat, HN., Nayfeh, AH., and Abdel-Rahman, EM., “Modal interactions in contact-mode atomic force microscopes”, Nonlinear Dynamics, Vol. 54, No. 1-2, 2008, pp. 151-166.

[10]   Wang, HC., “Generalized hyper geometric function solutions on the transverse vibration of a class of nonuniform beams” Journal of Applied Mechanics, Vol. 34, 1967, pp. 702.

[11]   Auciello, NM., “Transverse vibrations of a linearly tapered cantilever beam with tip mass of rotary inertia and eccentricity”,. Journal of Sound and Vibration 194.1, 1996, pp. 25-34.

[12]   Rank, C., Pastushenko, V., Kienberger, F., Stroh, CM., and Hinterdorfer, P., “Hydrodynamic damping of a magnetically oscillated cantilever close to a surface”, Ultramicroscopy 100.3, 2004, pp. 301-308.

[13]   Vancur, C., Dufour, I., Heinrich, S.M., Josse, F., and Hierlemann, A., “Analysis of resonating microcantilevers operating in a viscous liquid environment”, Sensors and Actuators 141, 2008, pp. 43–51.

[14]   Korayem, MH., Ebrahimi, N., “Nonlinear dynamics of tapping-mode atomic force microscopy in liquid”, Journal of Applied Physics 84301, 2011, pp. 109-117.

[15]   Kim, Y., Kang, SK., Choi, I., Lee, J., and Yi, J., “Dependence of image distortion in a liquid-cell atomic force microscope on fluidic properties”, Applied Physics Letters173121, Vol. 88, No. 17, 2006.

[16]   Kim, Y., Yi, J., “Enhancement of topographic images obtained in liquid media by atomic force microscopy”, Journal of Physical Chemistry B, Vol. 110, No. 41, 2006, pp. 20526–32.

[17]   Biswas, S., Hirtz, M., Lenhert, S., and Fuchs, H., “Measurement of DPN-Ink Viscosity using an AFM Cantilever”, In: Nanotechnology Conference and Expo, NSTI-Nanotech, Vol. 2, 2010, pp. 231-4.

[18]   Damircheli, M., Korayem, MH., “Dynamic analysis of the AFM by applying the Timoshenko beam theory in the tapping mode and considering the impact of the interaction forces in a liquid environment”, Canadian Journal of Physics, 2013.

[19]   Korayem, MH., Damircheli, M., “The effect of fluid properties and geometrical parameters of cantilever on the frequency response of atomic force microscopy”, Precision Engineering, 2013.