Generic placeholder image

Micro and Nanosystems

Author(s): Stylianos-Vasileios Kontomaris* and Anna Malamou

DOI: 10.2174/1876402915666230209140024

DownloadDownload PDF Flyer Cite As
The Truncated Cone Effect in AFM Nanoindentation on Soft Materials

Page: [153 - 158] Pages: 6

  • * (Excluding Mailing and Handling)

Abstract

Background: Atomic Force Microscopy (AFM) nanoindentation is the principal method for the characterization of soft materials at the nanoscale. In most cases, pyramidal tips are used and approximated to perfect cones. However, the extended use of the AFM tip may alter its sharpness.

Objective: In many cases, a truncated cone shape is appropriate for tip modeling. In this technical note, the equation that relates the force with the indentation depth when indenting an elastic halfspace using a truncated cone is derived.

Methods: The nanoindentation equation for a truncated cone tip is derived using the fundamental differential equation that relates the sample’s contact stiffness with Young’s modulus.

Results: When fitting Sneddon’s equation (which is valid for a perfect cone) on data obtained using a truncated cone-shaped AFM tip, the results show a ‘pseudo-softening’ behavior.

Conclusion: The AFM tip's sharpness in nanoindentation experiments is a crucial parameter for obtaining the correct mechanical patterns of unknown samples.

Graphical Abstract

[1]
Lekka, M.; Laidler, P. Applicability of AFM in cancer detection. Nat. Nanotechnol., 2009, 4(2), 72-73.
[http://dx.doi.org/10.1038/nnano.2009.004] [PMID: 19197298]
[2]
Plodinec, M.; Loparic, M.; Monnier, C.A.; Obermann, E.C.; Zanetti-Dallenbach, R.; Oertle, P.; Hyotyla, J.T.; Aebi, U.; Bentires-Alj, M.; Lim, R.Y.H.; Schoenenberger, C.A. The nanomechanical signature of breast cancer. Nat. Nanotechnol., 2012, 7(11), 757-765.
[http://dx.doi.org/10.1038/nnano.2012.167] [PMID: 23085644]
[3]
Stylianou, A.; Lekka, M.; Stylianopoulos, T. AFM assessing of nanomechanical fingerprints for cancer early diagnosis and classification: From single cell to tissue level. Nanoscale, 2018, 10(45), 20930-20945.
[http://dx.doi.org/10.1039/C8NR06146G] [PMID: 30406223]
[4]
Stylianou, A.; Kontomaris, S.V.; Grant, C.; Alexandratou, E. Atomic force microscopy on biological materials related to pathological conditions. Scanning, 2019, 2019, 1-25.
[http://dx.doi.org/10.1155/2019/8452851] [PMID: 31214274]
[5]
Krieg, M.; Fläschner, G.; Alsteens, D.; Gaub, B.M.; Roos, W.H.; Wuite, G.J.L.; Gaub, H.E.; Gerber, C.; Dufrêne, Y.F.; Müller, D.J. Atomic force microscopy-based mechanobiology. Nature Reviews Physics, 2019, 1(1), 41-57.
[http://dx.doi.org/10.1038/s42254-018-0001-7]
[6]
Pogoda, K.; Jaczewska, J.; Wiltowska-Zuber, J.; Klymenko, O.; Zuber, K.; Fornal, M.; Lekka, M. Depth-sensing analysis of cytoskeleton organization based on AFM data. Eur. Biophys. J., 2012, 41(1), 79-87.
[http://dx.doi.org/10.1007/s00249-011-0761-9] [PMID: 22038077]
[7]
Ding, Y.; Wang, J.; Xu, G.K.; Wang, G.F. Are elastic moduli of biological cells depth dependent or not? Another explanation using a contact mechanics model with surface tension. Soft Matter, 2018, 14(36), 7534-7541.
[http://dx.doi.org/10.1039/C8SM01216D] [PMID: 30152838]
[8]
Kontomaris, S.V.; Georgakopoulos, A.; Malamou, A.; Stylianou, A. The average Young’s modulus as a physical quantity for describing the depth-dependent mechanical properties of cells. Mech. Mater., 2021, 158103846.
[http://dx.doi.org/10.1016/j.mechmat.2021.103846]
[9]
Lee, J.J.; Rao, S.; Kaushik, G.; Azeloglu, E.U.; Costa, K.D. Dehomogenized elastic properties of heterogeneous layered materials in afm indentation experiments. Biophys. J., 2018, 114(11), 2717-2731.
[http://dx.doi.org/10.1016/j.bpj.2018.04.036] [PMID: 29874620]
[10]
Zemła, J.; Bobrowska, J.; Kubiak, A.; Zieliński, T.; Pabijan, J.; Pogoda, K.; Bobrowski, P.; Lekka, M. Indenting soft samples (hydrogels and cells) with cantilevers possessing various shapes of probing tip. Eur. Biophys. J., 2020, 49(6), 485-495.
[http://dx.doi.org/10.1007/s00249-020-01456-7] [PMID: 32803311]
[11]
Normand, A.C.; Charrier, A.M.; Arnould, O.; Lereu, A.L. Influence of force volume indentation parameters and processing method in wood cell walls nanomechanical studies. Sci. Rep., 2021, 11(1), 5739.
[http://dx.doi.org/10.1038/s41598-021-84994-0] [PMID: 33707500]
[12]
Kontomaris, S.V.; Malamou, A.; Stylianou, A. The Hertzian theory in AFM nanoindentation experiments regarding biological samples: Overcoming limitations in data processing. Micron, 2022, 155, 103228.
[http://dx.doi.org/10.1016/j.micron.2022.103228] [PMID: 35124406]
[13]
Kopycinska-Müller, M.; Geiss, R.H.; Hurley, D.C. Contact mechanics and tip shape in AFM-based nanomechanical measurements. Ultramicroscopy, 2006, 106(6), 466-474.
[http://dx.doi.org/10.1016/j.ultramic.2005.12.006] [PMID: 16448755]
[14]
Kontomaris, S.V.; Stylianou, A.; Malamou, A. Is it possible to directly determine the radius of a spherical indenter using force indentation data on soft samples? Scanning, 2022, 2022, 1-13.
[http://dx.doi.org/10.1155/2022/6463063] [PMID: 35265251]
[15]
Strahlendorff, T.; Dai, G.; Bergmann, D.; Tutsch, R. Tip wear and tip breakage in high-speed atomic force microscopes. Ultramicroscopy, 2019, 201, 28-37.
[http://dx.doi.org/10.1016/j.ultramic.2019.03.013] [PMID: 30925297]
[16]
Pharr, G.M.; Oliver, W.C.; Brotzen, F.R. On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation. J. Mater. Res., 1992, 7(3), 613-617.
[http://dx.doi.org/10.1557/JMR.1992.0613]
[17]
Mencík, J. Uncertainties and errors in nanoindentation; InTech: London, UK, 2012, pp. 53-86.
[http://dx.doi.org/10.5772/50002]
[18]
Gavara, N. A beginner’s guide to atomic force microscopy probing for cell mechanics. Microsc. Res. Tech., 2017, 80(1), 75-84.
[http://dx.doi.org/10.1002/jemt.22776] [PMID: 27676584]
[19]
Liu, M.; Sun, J.; Sun, Y.; Bock, C.; Chen, Q. Thickness-dependent mechanical properties of polydimethylsiloxane membranes. J. Micromech. Microeng., 2009, 19(3), 035028.
[http://dx.doi.org/10.1088/0960-1317/19/3/035028]
[20]
Hermanowicz, P.; Sarna, M.; Burda, K. Gabryś H. An open source software for analysis of force curves. Rev. Sci. Instrum., 2014, 85(6), 063703.
[http://dx.doi.org/10.1063/1.4881683]