Determining the spring constant of arbitrarily shaped cantilevers in viscous environments

Amir Farokh Payam, W Trewby, Kislon Voitchovsky

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
40 Downloads (Pure)


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.
Original languageEnglish
Article number083101
Pages (from-to)1-4
Number of pages4
JournalApplied Physics Letters
Issue number8
Early online date20 Feb 2018
Publication statusPublished online - 20 Feb 2018


  • Electrical properties and parameters
  • Cantilever
  • Lasers
  • Lab-on-a-chip
  • Signal processing
  • Atomic force microscopy
  • Viscous liquid
  • Electronic noise
  • Organic compounds
  • Microactuators


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