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Analysis of dynamic characteristics of cantilevers excited at the fixed end in dynamic atomic force microscopy in liquid environments

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Abstract

Dynamic atomic force microscopy (AFM) is commonly employed for the analysis of material morphology and mechanical properties at the micro and nanoscale in liquid environments. A comprehensive understanding of the dynamic characteristics of AFM cantilevers in liquid environments is crucial for the development of quantitative methods to assess mechanical properties accurately. In this study, we investigate the dynamical behaviors of AFM cantilevers in liquid environments by introducing added mass and added damping to simulate the effects of fluid on the cantilever using the finite difference method (FDM). The time-domain response and spectrum of the cantilever are investigated, as well as the dynamic characteristics of the cantilever in bimodal AFM. The results demonstrate that the thickness of the cantilever has a greater impact on the cantilever’s natural frequency and quality factors in liquids. The fluid density dominates the natural frequency, and the fluid viscosity dominates the quality factor. In the presence of tip-sample interaction, the vibration shape curves in liquids tend to incline upwards, and the displacement response no longer takes the form of a sine/cosine curve, according to time domain and spectrum analysis. The squeeze damping decreases the displacement response of the cantilever and inhibits the amplification of higher harmonics of the displacement and interaction force. The continuous beam model based on FDM is suitable for evaluating the dynamics of bimodal AFM in liquid, and it overcomes the constraints on detection position and modal parameters compared to the mode coupling method.

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References

  1. Voigtländer B (2019) Atomic force microscopy. Springer, Cham

    Book  Google Scholar 

  2. Krieg M, Fläschner G, Alsteens D, Gaub BM, Roos WH, Wuite GJL, Gaub HE, Gerber C, Dufrêne YF, Müller DJ (2019) Atomic force microscopy-based mechanobiology. Nat Rev Phys 1:41–57

    Article  Google Scholar 

  3. Garcia R (2020) Nanomechanical mapping of soft materials with the atomic force microscope: methods, theory and applications. Chem Soc Rev 49:5850–5884

    Article  Google Scholar 

  4. Dufrêne YF, Ando T, Garcia R, Alsteens D, Martinez-Martin D, Engel A, Gerber C, Müller DJ (2017) Imaging modes of atomic force microscopy for application in molecular and cell biology. Nat Nanotechnol 12:295–307

    Article  Google Scholar 

  5. Van Eysden CA, Sader JE (2007) Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: arbitrary mode order. J Appl Phys 101:044908

    Article  Google Scholar 

  6. Van Eysden CA, Sader JE (2006) Resonant frequencies of a rectangular cantilever beam immersed in a fluid. J Appl Phys 100:114916

    Article  Google Scholar 

  7. Ghatkesar MK, Braun T, Barwich V, Ramseyer JP, Gerber C, Hegner M, Lang HP (2008) Resonating modes of vibrating microcantilevers in liquid. Appl Phys Lett 92:043106

    Article  Google Scholar 

  8. Basak S, Raman A, Garimella SV (2006) Hydrodynamic loading of microcantilevers vibrating in viscous fluids. J Appl Phys 99:114906

    Article  Google Scholar 

  9. Shen N, Chakraborty D, Sader JE (2023) Frequency response of cantilevered plates of small aspect ratio immersed in viscous fluids. J Appl Phys 133:034501

    Article  Google Scholar 

  10. Shen N, Chakraborty D, Sader JE (2016) Resonant frequencies of cantilevered sheets under various clamping configurations immersed in fluid. J Appl Phys 120:144504

    Article  Google Scholar 

  11. Gesing A, Platz D, Schmid U (2022) Viscous fluid–structure interaction of micro-resonators in the beam–plate transition. J Appl Phys 131:134502

    Article  Google Scholar 

  12. Green CP, Sader JE (2005) Frequency response of cantilever beams immersed in viscous fluids near a solid surface with applications to the atomic force microscope. J Appl Phys 98:114913

    Article  Google Scholar 

  13. Green CP, Sader JE (2005) Small amplitude oscillations of a thin beam immersed in a viscous fluid near a solid surface. Phys Fluids 17:073102

    Article  MathSciNet  Google Scholar 

  14. Rodriguez CG, Flores P, Pierart FG, Contzen LR, Egusquiza E (2012) Capability of structural-acoustical FSI numerical model to predict natural frequencies of submerged structures with nearby rigid surfaces. Comput Fluids 64:117–126

    Article  Google Scholar 

  15. Hu L, Yan H, Zhang W-M, Zou H-X, Peng Z-K, Meng G (2018) Theoretical and experimental study on dynamic characteristics of V-shaped beams immersed in viscous fluids: from small to finite amplitude. J Fluid Struct 82:215–244

    Article  Google Scholar 

  16. Wei Z, Liu J, Zheng XT, Sun Y, Wei RH (2021) Influence of squeeze film damping on quality factor in tapping mode atomic force microscope. J Sound Vib 491:115720

    Article  Google Scholar 

  17. Melcher J, Carrasco C, Xu X, Carrascosa JL, Gomez-Herrero J, de Pablo PJ, Raman A (2009) Origins of phase contrast in the atomic force microscope in liquids. Proc Natl Acad Sci USA 106:13655–13660

    Article  Google Scholar 

  18. Xu X, Melcher J, Basak S, Reifenberger R, Raman A (2009) Compositional contrast of biological materials in liquids using the momentary excitation of higher eigenmodes in dynamic atomic force microscopy. Phys Rev Lett 102:060801

    Article  Google Scholar 

  19. Basak S, Raman A (2007) Dynamics of tapping mode atomic force microscopy in liquids: theory and experiments. Appl Phys Lett 91:064107

    Article  Google Scholar 

  20. Melcher J, Xu X, Raman A (2008) Multiple impact regimes in liquid environment dynamic atomic force microscopy. Appl Phys Lett 93:093111

    Article  Google Scholar 

  21. Kiracofe D, Raman A (2010) Microcantilever dynamics in liquid environment dynamic atomic force microscopy when using higher-order cantilever eigenmodes. J Appl Phys 108:034320

    Article  Google Scholar 

  22. Chen YH, Niu D, Huang WH (2011) Influence of microstructure-confined fluids on the atomic force microscope probe dynamics. Micro Nano Lett 6:914–917

    Article  Google Scholar 

  23. Ebeling D, Solares SD (2013) Amplitude modulation dynamic force microscopy imaging in liquids with atomic resolution: comparison of phase contrasts in single and dual mode operation. Nanotechnology 24:135702

    Article  Google Scholar 

  24. Amo CA, Perrino AP, Payam AF, Garcia R (2017) Mapping elastic properties of heterogeneous materials in liquid with angstrom-scale resolution. ACS Nano 11:8650–8659

    Article  Google Scholar 

  25. Lozano JR, Garcia R (2009) Theory of phase spectroscopy in bimodal atomic force microscopy. Phys Rev B 79:014110

    Article  Google Scholar 

  26. Xu X, Raman A (2007) Comparative dynamics of magnetically, acoustically, and Brownian motion driven microcantilevers in liquids. J Appl Phys 102:034303

    Article  Google Scholar 

  27. Herruzo ET, Garcia R (2007) Frequency response of an atomic force microscope in liquids and air: magnetic versus acoustic excitation. Appl Phys Lett 91:143113

    Article  Google Scholar 

  28. Payam AF (2013) Sensitivity of flexural vibration mode of the rectangular atomic force microscope micro cantilevers in liquid to the surface stiffness variations. Ultramicroscopy 135:84–88

    Article  Google Scholar 

  29. Maali A, Hurth C, Boisgard R, Jai C, Cohen-Bouhacina T, Aimé J-P (2005) Hydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluids. J Appl Phys 97:074907

    Article  Google Scholar 

  30. Sader JE (1998) Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J Appl Phys 84:64–76

    Article  Google Scholar 

  31. Hosaka H, Itao K, Kuroda S (1995) Damping characteristics of beam-shaped micro-oscillators. Sens Actuators A 49:87–95

    Article  Google Scholar 

  32. Huang ZY, Wen PF, Zhou XL (2021) Comparison of different excitation schemes in bimodal atomic force microscopy in air and liquid environments. Acta Mech Solida Sin 34:163–173

    Article  Google Scholar 

  33. Turner JA, Hirsekorn S, Rabe U, Arnold W (1997) High-frequency response of atomic-force microscope cantilevers. J Appl Phys 82:966–979

    Article  Google Scholar 

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Acknowledgements

The authors gratefully thank the financial support from Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics under Grant No. TAM202205.

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Authors and Affiliations

  1. College of Energy and Mining Engineering, Shandong University of Science and Technology, Qingdao, 266590, China

    Xilong Zhou, Changyun Yang & Bangzhi Zhang

  2. Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics, Wuhan University of Technology, Wuhan, 430070, China

    Xilong Zhou

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  1. Xilong Zhou
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  2. Changyun Yang
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Correspondence to Xilong Zhou.

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Zhou, X., Yang, C. & Zhang, B. Analysis of dynamic characteristics of cantilevers excited at the fixed end in dynamic atomic force microscopy in liquid environments. Meccanica 59, 75–88 (2024). https://doi.org/10.1007/s11012-023-01742-6

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  • DOI: https://doi.org/10.1007/s11012-023-01742-6

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