Determining the spring constant of arbitrarily shaped cantilevers in viscous environments

Payam, A.F.; Trewby, W.; Voïtchovsky, K.

doi:10.1063/1.5009071

Determining the spring constant of arbitrarily shaped cantilevers in viscous environments

Payam, A.F.; Trewby, W.; Voïtchovsky, K.

Authors

A.F. Payam

W. Trewby

Professor Kislon Voitchovsky kislon.voitchovsky@durham.ac.uk
Professor

Abstract

Accurate calibration of the flexural spring constant of microcantilevers is crucial for sensing devices, microactuators, and atomic force microscopy (AFM). Existing methods rely on precise knowledge of cantilever geometry, make significant simplifications, or require potentially damaging contact with the sample. Here, we develop a simple equation to calculate the flexural spring constants of arbitrarily shaped cantilevers in fluid. Our approach, verified here with AFM, only requires the measurement of two resonance frequencies of the cantilever in air and in a liquid, with no need for additional input or knowledge about the system. We validate the method with cantilevers of different shapes and compare its predictions with existing models. We also show how the method’s accuracy can be considerably improved, especially in more viscous liquids, if the effective width of the cantilever is known. Significantly, the developed equations can be extended to calculate the spring constants of the cantilever’s higher eigenmodes.

Citation

Payam, A., Trewby, W., & Voïtchovsky, K. (2018). Determining the spring constant of arbitrarily shaped cantilevers in viscous environments. Applied Physics Letters, 112(8), Article 083101. https://doi.org/10.1063/1.5009071

Journal Article Type	Article
Acceptance Date	Feb 7, 2018
Online Publication Date	Feb 20, 2018
Publication Date	Feb 20, 2018
Deposit Date	Feb 7, 2018
Publicly Available Date	Feb 23, 2018
Journal	Applied Physics Letters
Print ISSN	0003-6951
Electronic ISSN	1077-3118
Publisher	American Institute of Physics
Peer Reviewed	Peer Reviewed
Volume	112
Issue	8
Article Number	083101
DOI	https://doi.org/10.1063/1.5009071

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Copyright Statement
© 2018 Author(s). All article content, except where
otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://
creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5009071