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Determining the spring constant of arbitrarily shaped cantilevers in viscous environments.

Payam, A. F. and Trewby, W. and Voïtchovsky, K. (2018) 'Determining the spring constant of arbitrarily shaped cantilevers in viscous environments.', Applied physics letters., 112 (8). 083101.


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.

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Publisher statement:© 2018 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://
Date accepted:07 February 2018
Date deposited:23 February 2018
Date of first online publication:20 February 2018
Date first made open access:20 February 2019

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