vestiftИзвестия Национальной академии наук Беларуси. Серия физико-технических наукProceedings of the National Academy of Sciences of Belarus. Physical-technical series1561-83582524-244XThe Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8358-2025-70-1-57-68vestift-879Research ArticleРАДИОЭЛЕКТРОНИКА, ПРИБОРОСТРОЕНИЕRADIOELECTRONICS, INSTRUMENT-MAKINGПолуконтактный режим атомно-силового микроскопа при малой жесткости консоли зондаTapping mode of an atomic force microscope with a probe cantilever of a low spring constanthttps://orcid.org/0009-0008-8806-0230АбетковскаяС. О.AbetkovskaiaS. O.

Абетковская Светлана Олеговна – научный сотрудник

ул. П. Бровки, 15, 220072, Минск

Sviatlana O. Abetkovskaia – Researcher

15, P. Brovka St., 220072, Minsk

abetkovskaia@mail.ruhttps://orcid.org/0000-0002-5301-0195ЧижикС. А.ChizhikS. A.

Чижик Сергей Антонович – академик Национальной академии наук Беларуси, доктор технических  наук,  профессор,  заведующий  отделением  теплообмена  и  механики  микро-  и  наноразмерных  систем 

ул. П. Бровки, 15, 220072, Минск

Sergei A. Chizhik – Academician of the National Academy of Sciences of Belarus, Dr. Sci. (Engineering), Professor, Head of the Department of Heat Transfer and Mechanics of Micro- and Nanoscale Systems

15, P. Brovka St., 220072, Minsk

chizhik_sa@tut.byГуанбинЮGuangbinYu

Гуанбин Ю – доктор технических наук, профессор

92, ул. Cида, Наньган, 150001, Харбин

Guangbin Yu – Dr. Sci. (Engineering), Professor

92, Xida St., Nangang, 150001, Harbin

yugb@hit.edu.cnИнститут тепло- и массообмена имени А. В. Лыкова Национальной академии наук БеларусиA. V. Luikov Heat and Mass Transfer Institute of the National Academy of Sciences of BelarusФакультет мехатроники, Харбинский технологический институтSchool of Mechatronics Engineering, Harbin Institute of Technology2025260320257015768Copyright © Абетковская С.О., Чижик С.А., Гуанбин Ю., 20252025Абетковская С.О., Чижик С.А., Гуанбин Ю.Abetkovskaia S.O., Chizhik S.A., Guangbin Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestift.belnauka.by/jour/article/view/879

Методами  математического  моделирования  исследовано  полуконтактное  взаимодействие  зонда атомно-силового микроскопа (АСМ) малой (0,1 Н/м) жесткости его консоли с образцами материалов с модулем Юнга 0,01; 0,1; 1; 10 ГПа при варьировании постоянной Гамакера образца, характеризующей его поверхностную энергию, а также амплитуды колебаний пьезоэлемента и добротности зонда. Для описания контакта зонда и образца использовалась модель Джонсона–Кенделла–Робертса. Внеконтактное взаимодействие учтено с помощью потенциала Леннард–Джонса. Установлено, что при меньших значениях постоянной Гамакера, больших добротности АСМзонда и амплитуды колебаний пьезогенератора наступают условия перехода от нежелательного для получения АСМизображений смешанного режима взаимодействия зонда и образца к чисто упругому режиму. Однако для материалов с модулем Юнга 1 и 10 ГПа возникают скачкообразные изменения характеристик зонда, связанные не с влиянием поверхностной адгезии образца, а с поздним наступлением стационарного режима колебаний зонда. Во избежание неустойчивых колебаний зонда в полуконтактном режиме работы АСМ предложено использование более жестких зондов с целью получения высококачественных АСМ-изображений поверхностей материалов с модулем Юнга 1 ГПа и выше. 

The work presents mathematical simulation results of tapping interaction of an atomic force microscope (AFM) probe with low (0.1 N/m) spring constant of its cantilever with samples of materials with the Young moduli of 0.01; 0.1; 1; 10 GPa under varying the characterizing samples surface energy Hamaker constant, oscillation amplitude of a piezoelectric element, and also the quality factor of the probe. The Johnson–Kendall–Roberts model was used to describe contact between the probe and a sample. Non-contact interaction was taken into account using the Lennard–Jones potential. It was defined that at lower values of the Hamaker constant, higher quality factor of the AFM probe, and higher oscillation amplitude of the piezoelectric generator, conditions for transition from mixed mode of probe–sample interaction, which is undesirable for obtaining AFM images, to purely elastic mode occur. However, for materials with the Young moduli of 1 and 10 GPa abrupt changes in probe characteristics occur, which are associated not with influence of surface adhesion, but with late onset steady-state mode of probe oscillation. In order to avoid non-steady state oscillation of the probe in tapping AFM mode, it is proposed to use probes with higher spring constant to obtain high-quality AFM images of material surfaces with the Young modulus of 1 GPa and higher. 

атомно-силовая микроскопия (АСМ)полуконтактный режимжесткость консоли микрозондамодуль Юнгапостоянная Гамакераatomic force microscopyAFMtapping modeprobeprobe spring constantYoung modulusHamaker constantработа выполнена в рамках задания 3.03.3 Государственной программы научных исследований «Конвергенция–2025» на 2021–2025 годы и проекта Белорусского республиканского фонда фундаментальных исследований № T17KIG-009.the work is performed within the framework of the project 3.03.3 of the State Program of Scientific Research “Convergence-2025” for 2021–2025 and the grant of Belarusian Republican Foundation for Fundamental Research no. T17KIG-009.ReferencesSongen H., Bechstein R., Kuhnle A. Quantitative atomic force microscopy. Journal of Physics: Condensed Matter, 2017, vol. 29, no. 27, pp. 274001-1–17. https://doi.org/10.1088/1361-648X/aa6f8bSongen H., Bechstein R., Kuhnle A. Quantitative atomic force microscopy. Journal of Physics: Condensed Matter, 2017, vol. 29, no. 27, pp. 274001-1–17. https://doi.org/10.1088/1361-648X/aa6f8bGarcia R., San Paulo A. Attractive and repulsive tip-sample interaction regimes in tapping-mode atomic force microscopy. Physical Review B, 1999, vol. 60, no. 7, pp. 4961–4967. https://doi.org/10.1103/PhysRevB.60.4961Garcia R., San Paulo A. Attractive and repulsive tip-sample interaction regimes in tapping-mode atomic force microscopy. Physical Review B, 1999, vol. 60, no. 7, pp. 4961–4967. https://doi.org/10.1103/PhysRevB.60.4961Stark M., Stark R. W., Heckl W. M., Guckenberger R. Inverting dynamic force microscopy: From signals to time-resolved interaction forces. The Proceedings of the National Academy of Sciences (PNAS), 2002, vol. 99, no. 13, pp. 8473–8478. https://doi.org/10.1073/pnas.122040599Stark M., Stark R. W., Heckl W. M., Guckenberger R. Inverting dynamic force microscopy: From signals to time-resolved interaction forces. The Proceedings of the National Academy of Sciences (PNAS), 2002, vol. 99, no. 13, pp. 8473–8478. https://doi.org/10.1073/pnas.122040599Lee S. I., Howell S. W., Raman A., Reifenberger R. Nonlinear dynamics of microcantilevers in tapping mode atomic force microscopy: A comparison between theory and experiment. Physical Review B, 2002, vol. 66, pp. 115409-1–10. https://doi.org/10.1103/PhysRevB.66.115409Lee S. I., Howell S. W., Raman A., Reifenberger R. Nonlinear dynamics of microcantilevers in tapping mode atomic force microscopy: A comparison between theory and experiment. Physical Review B, 2002, vol. 66, pp. 115409-1–10. https://doi.org/10.1103/PhysRevB.66.115409Lee S. I., Howell S. W., Raman A., Reifenberger R. Nonlinear dynamic perspectives on dynamic force microscopy. Ultramicroscopy, 2003, vol. 97, no. 1/4, 25 p. https://doi.org/10.1016/s0304-3991(03)00043-3Lee S. I., Howell S. W., Raman A., Reifenberger R. Nonlinear dynamic perspectives on dynamic force microscopy. Ultramicroscopy, 2003, vol. 97, no. 1/4, 25 p. https://doi.org/10.1016/s0304-3991(03)00043-3Hu Sh., Raman A. Analytical formulas and scaling laws for peak interaction forces in dynamic atomic force microscopy. Applied Physics Letters, 2007, vol. 91, pp. 123106-1–3. https://doi.org/10.1063/1.2783226Hu Sh., Raman A. Analytical formulas and scaling laws for peak interaction forces in dynamic atomic force microscopy. Applied Physics Letters, 2007, vol. 91, pp. 123106-1–3. https://doi.org/10.1063/1.2783226Kiracofe D., Melcher J., Raman A. Gaining insight into the physics of dynamic atomic force microscopy in complex environments using the VEDA simulator. Review of Scientific Instruments, 2012, vol. 83, no. 1, pp. 013702-1–17. https://doi.org/10.1063/1.3669638Kiracofe D., Melcher J., Raman A. Gaining insight into the physics of dynamic atomic force microscopy in complex environments using the VEDA simulator. Review of Scientific Instruments, 2012, vol. 83, no. 1, pp. 013702-1–17. https://doi.org/10.1063/1.3669638Guzman H. V., Garcia P. D., Garcia R. Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments. Beilstein Journal of Nanotechnology, 2015, vol. 6, pp. 369–379. https://doi.org/10.3762/bjnano.6.36Guzman H. V., Garcia P. D., Garcia R. Dynamic force microscopy simulator (dForce): A tool for planning and understanding tapping and bimodal AFM experiments. Beilstein Journal of Nanotechnology, 2015, vol. 6, pp. 369–379. https://doi.org/10.3762/bjnano.6.36Wagner T. Steady-state and transient behavior in dynamic atomic force microscopy. Journal of Applied Physics, 2019, vol. 125, no. 4, pp. 044301-1–13. https://doi.org/10.1063/1.5078954Wagner T. Steady-state and transient behavior in dynamic atomic force microscopy. Journal of Applied Physics, 2019, vol. 125, no. 4, pp. 044301-1–13. https://doi.org/10.1063/1.5078954Bahrami M. R. Dynamic analysis of atomic force microscope in tapping mode. Vibroengineering Procedia, 2020, vol. 32, 7 p. https://doi.org/10.21595/vp.2020.21488Bahrami M. R. Dynamic analysis of atomic force microscope in tapping mode. Vibroengineering Procedia, 2020, vol. 32, 7 p. https://doi.org/10.21595/vp.2020.21488Chandrashekar A., Belardinelli P., Lenci S., Staufer U., Alijani F. Mode coupling in dynamic atomic force microscopy. Physical Rewiew Applied, 2021, vol. 15, no. 2, pp. 024013-1–11. https://doi.org/10.1103/PhysRevApplied.15.024013Chandrashekar A., Belardinelli P., Lenci S., Staufer U., Alijani F. Mode coupling in dynamic atomic force microscopy. Physical Rewiew Applied, 2021, vol. 15, no. 2, pp. 024013-1–11. https://doi.org/10.1103/PhysRevApplied.15.024013Melcher J., Hu Sh., Raman A. Invited Article: VEDA: A web-based virtual environment for dynamic atomic force microscopy. Rewiew of Scientific Instruments, 2008, vol. 79, no. 6, pp. 061301-1–11. https://doi.org/10.1063/1.2938864Melcher J., Hu Sh., Raman A. Invited Article: VEDA: A web-based virtual environment for dynamic atomic force microscopy. Rewiew of Scientific Instruments, 2008, vol. 79, no. 6, pp. 061301-1–11. https://doi.org/10.1063/1.2938864Thorén P.-A., Borgani R., Forchheimer D., Dobryden I., Claesson P. M., Kassa H. G., Leclère Ph. [et al.]. Modeling and measuring viscoelasticity with dynamic atomic force microscopy. Physical Rewiew Applied, 2018, vol. 10, no. 2, pp. 024017-1–13. https://doi.org/10.1103/PhysRevApplied.10.024017Thorén P.-A., Borgani R., Forchheimer D., Dobryden I., Claesson P. M., Kassa H. G., Leclère Ph. [et al.]. Modeling and measuring viscoelasticity with dynamic atomic force microscopy. Physical Rewiew Applied, 2018, vol. 10, no. 2, pp. 024017-1–13. https://doi.org/10.1103/PhysRevApplied.10.024017Keyvani A., Tamer M. S., Wingerden J.-W. van, Goosen J. F. L., Keulen F. van. A comprehensive model for transient behavior of tapping mode atomic force microscope. Nonlinear Dynamics, 2019, vol. 97, pp. 1601–1617. https://doi.org/10.1007/s11071-019-05079-2Keyvani A., Tamer M. S., Wingerden J.-W. van, Goosen J. F. L., Keulen F. van. A comprehensive model for transient behavior of tapping mode atomic force microscope. Nonlinear Dynamics, 2019, vol. 97, pp. 1601–1617. https://doi.org/10.1007/s11071-019-05079-2Farokh Payam A., Morelli A., Lemoine P. Multiparametric analytical quantification of materials at nanoscale in tapping force microscopy. Applied Surface Science, 2021, vol. 536, pp. 147698-1–15. https://doi.org/10.1016/j.apsusc.2020.147698Farokh Payam A., Morelli A., Lemoine P. Multiparametric analytical quantification of materials at nanoscale in tapping force microscopy. Applied Surface Science, 2021, vol. 536, pp. 147698-1–15. https://doi.org/10.1016/j.apsusc.2020.147698Johnson K. L. Contact Mechanics. Cambridge University Press, 1987. 452 p.Johnson K. L. Contact Mechanics. Cambridge University Press, 1987. 452 p.Abetkovskaia S. О., Chizhik S. А. Dynamic force spectroscopy of «soft» materials. Teplo- i massoperenos – 2007: sbornik nauchnykh trudov [Heat and Mass Transfer – 2007: Scientific Papers]. Minsk, A. V. Luikov Institute of Heat and Mass Transfer of the National Academy of Sciences of Belarus, 2007, pp. 323–330 (in Russian).Abetkovskaia S. О., Chizhik S. А. Dynamic force spectroscopy of «soft» materials. Teplo- i massoperenos – 2007: sbornik nauchnykh trudov [Heat and Mass Transfer – 2007: Scientific Papers]. Minsk, A. V. Luikov Institute of Heat and Mass Transfer of the National Academy of Sciences of Belarus, 2007, pp. 323–330 (in Russian).Garcia R., Gómez C. J., Martinez N. F., Patil S., Dietz C., Magerle R. Identification of nanoscale dissipation processes by dynamic atomic force microscopy. Physical Rewiew Letters, 2006, vol. 97, no. 1, pp. 016103-1–4. https://doi.org/10.1103/PhysRevLett.97.016103Garcia R., Gómez C. J., Martinez N. F., Patil S., Dietz C., Magerle R. Identification of nanoscale dissipation processes by dynamic atomic force microscopy. Physical Rewiew Letters, 2006, vol. 97, no. 1, pp. 016103-1–4. https://doi.org/10.1103/PhysRevLett.97.016103

The authors declare that there are no conflicts of interest present.