Vibrational Behavior Study of Effect of Crack on Atomic Force Microscope Cantilever Using a Structural Mechanics Model

Subject Areas : Computational Mechanics

E Kouroshian ¹ (Department of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran)
Vali Parvaneh ² (Department of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran)
Mohammad Abbasi ³ (Department of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran)

Received: 2023-03-03 Accepted : 2023-04-30 Published : 2023-06-01

Keywords: Structural mechanics, Graphene, Cantilever, Crack, AFM,

Abstract :

In this research, a multi-scale model was used to analyze the vibrational behavior of the atomic force microscope (AFM) on a graphene sheet sample. Cantilever and silicone tip base were simulated based on the continuum mechanics using finite element modeling and the tip apex were modeled based on the Tersoff potential by the structural mechanics modeling. The contact behavior between the tip and graphene was investigated using measuring friction force during the tip movement on the graphene layer, and its results were compared to the results obtained from molecular dynamics simulation and experimental test. The friction force between the tip and graphene increases by enhancing the tip radius and the contact surface between the tip and the sample. Moreover, the friction force dwindles by heightening the number of graphene layers as a result of sliding graphene layers on each other and diminishing the Poker effect (wrinkling). With the initial distance displacement of the tip from the sample, two curves of the tip vibration amplitude variations and the phase change between tip vibration and excitation vibration were plotted, and the effect of crack and its location in the cantilever was studied. The results showed that the crack in the cantilever can dramatically influence the tip vibration amplitude and the phase change between the tip vibration and the excitation signal.

References:

1. Wang D., Russell T.P., 2018, Advances in atomic force microscopy for probing polymer structure and properties, Macromolecules 51: 3-24.


2. Qin Y., Brockett A., Ma Y., 2010, Micro-manufacturing: Research, technology outcomes and development issues, The International Journal of Advanced Manufacturing Technology 47: 821-837.


3. Ding S. Y., Yi J., Li J. F., 2016, Nanostructure-based plasmon-enhanced Raman spectroscopy for surface analysis of materials, Nature Reviews Materials 1: 1-16.


4. Li Z., Yan Y., Wang J., 2020, Molecular dynamics study on tip-based nanomachining: A review, Nanoscale Research Letters 15: 1-12.


5. Garcia R., 2020, Nanomechanical mapping of soft materials with the atomic force microscope: methods, theory and applications, Chemical Society Reviews 49: 5850-5884.


6. Misra S., Dankowicz H., Paul M. R., 2008, Event-driven feedback tracking and control of tapping-mode atomic force microscopy, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464: 2113-2133.


7. Tusset M., Bueno A. M., Nascimento C. B., 2013, Nonlinear state estimation and control for chaos suppression in MEMS resonator, Shock and Vibration 20: 749-761.


8. Bahrami M. R., 2020, Dynamic analysis of atomic force microscope in tapping mode, Vibroengineering Procedia 32: 13-19.


9. Dankowicz H., 2006, Nonlinear dynamics as an essential tool for non-destructive characterization of soft nanostructures using tapping-mode atomic force microscopy, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364: 3505-3520.


10. Rodrigues K. S., Balthazar J. M., Tusset A. M., 2014, Preventing chaotic motion in tapping-mode atomic force microscope, Journal of Control, Automation and Electrical Systems 25: 732-740.


11. Stark R. W., Schitter G., Stark M., 2004, State-space model of freely vibrating and surface-coupled cantilever dynamics in atomic force microscopy, Physical Review B 69: 085412.


12. Payam A. F., Fathipour M., 2009, Modeling and dynamic analysis of atomic force microscope based on Euler-Bernoulli beam theory, Digest Journal of Nanomaterials and Biostructures 4: 565-578.


13. Hsu J. C., Lee H. L., Chang W. J., 2007, Flexural vibration frequency of atomic force microscope cantilevers using the Timoshenko beam model, Nanotechnology 18: 285503.


14. Damircheli M., Korayem M. H., 2014, Dynamic analysis of AFM by applying Timoshenko beam theory in tapping mode and considering the impact of interaction forces in a liquid environment, Canadian Journal of Physics 92: 472-483.


15. Claeyssen J. R., Tsukazan T., Tonetto L., 2013, Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory, Nanoscale Systems: Mathematical Modeling, Theory and Applications 2: 124-144.


16. Espinoza-Beltrán F. J., Geng K., Muñoz Saldaña J., 2009, Simulation of vibrational resonances of stiff AFM cantilevers by finite element methods, New Journal of Physics 11: 083034.


17. Mendels D.A., Lowe M., Cuenat A., 2006, Dynamic properties of AFM cantilevers and the calibration of their spring constants, Journal of Micromechanics and Microengineering 16: 1720-1733.


18. Wang B., Wu X., Gan T. H., 2014, Finite element modelling of atomic force microscope cantilever beams with uncertainty in material and dimensional parameters, Engineering Transaction 62: 403-421.


19. Rodrigues K. S., Trindade M. A., 2018, Finite element modeling and analysis of an atomic force microscope cantilever beam coupled to a piezoceramic base actuator, Journal of the Brazilian Society of Mechanical Sciences and Engineering 40: 427.


20. Hu X., Egberts P., Dong Y., 2015, Molecular dynamics simulation of amplitude modulation atomic force microscopy, Nanotechnology 26: 235705.


21. Hu X., Chan N., Martini A., 2017, Tip convolution on HOPG surfaces measured in AM-AFM and interpreted using a combined experimental and simulation approach, Nanotechnology 28: 025702.


22. Kim H., Venturini G., Strachan A., 2012, Molecular dynamics study of dynamical contact between a nanoscale tip and substrate for atomic force microscopy experiments, Journal of Applied Physics 112: 094325.


23. Onofrio N., Venturini G. N., Strachan A., 2013, Molecular dynamic simulation of tip-polymer interaction in tapping-mode atomic force microscopy, Journal of Applied Physics 114: 094309.


24. Ye Z., Tang Ch., Dong Y., 2012, Role of wrinkle height in friction variation with number of graphene layers, Journal of Applied Physics 112: 116102.


25. Dou Z., Qian J., Li Y., 2020, Molecular dynamics simulation of bimodal atomic force microscopy, Ultramicroscopy 212:


26. Lee H. L., Chang W.J., 2012, Sensitivity analysis of a cracked atomic force microscope cantilever, Japanese Journal of Applied Physics 51: 035202.


27. Lee H. L., Chang W. J., 2012, Dynamic response of a cracked atomic force microscope cantilever used for nanomachining, Nanoscale Research Letters 7: 131.


28. Chang W.J., Lee H.L., Yang Y.C., 2015, Free vibration analysis of a cracked atomic force microscope cantilever, Proceedings of the World Congress on New Technologies, Barcelona, Spain.


29. Dastjerdi Sh., Abbasi M., 2019, A vibration analysis of a cracked micro-cantilever in an atomic force microscope by using transfer matrix method, Ultramicroscopy 196: 33-39.


30. StuartJ., Tutein A.B., Harrison J. A., 2000, A reactive potential for hydrocarbons with intermolecular interactions, The Journal of Chemical Physics 112: 6472-6486,


31. OngY., Pop E., 2010, Molecular dynamics simulation of thermal boundary conductance between carbon nanotubes and SiO2, Physical Review B 81: 155408.


32. Neek-Amal , Peeters F., 2010, Nanoindentation of a circular sheet of bilayer graphene, Physical Review B 81: 235421.


33. Yoon H.M., Jung Y., Jun S.C., Kondaraju S., Lee J.S., 2015, Molecular dynamics simulations of nanoscale and subnanoscale friction behavior between graphene and a silicon tip: Analysis of tip apex motion, Nanoscale 7: 6295-6303.


34. Garcıa R., Perez R., 2002, Dynamic atomic force microscopy methods, Surface Science Reports 47: 197-301.


35. Vahdat V., Grierson D.S., Turner K.T., Carpick R.W., 2011, Nano-scale forces, stresses, and tip geometry evolution of amplitude modulation atomic force microscopy probes, ASME 2011 International Design Engineering TechnicalConferences and Computers and Information in Engineering Conference (American Society of Mechanical Engineers).