Hydrodynamic function and spring constant calibration of FluidFM micropipette cantilevers

Fluidic force microscopy (FluidFM) fuses the force sensitivity of atomic force microscopy with the manipulation capabilities of microfluidics by using microfabricated cantilevers with embedded fluidic channels. This innovation initiated new research and development directions in biology, biophysics, and material science. To acquire reliable and reproducible data, the calibration of the force sensor is crucial. Importantly, the hollow FluidFM cantilevers contain a row of parallel pillars inside a rectangular beam. The precise spring constant calibration of the internally structured cantilever is far from trivial, and existing methods generally assume simplifications that are not applicable to these special types of cantilevers. In addition, the Sader method, which is currently implemented by the FluidFM community, relies on the precise measurement of the quality factor, which renders the calibration of the spring constant sensitive to noise. In this study, the hydrodynamic function of these special types of hollow cantilevers was experimentally determined with different instruments. Based on the hydrodynamic function, a novel spring constant calibration method was adapted, which relied only on the two resonance frequencies of the cantilever, measured in air and in a liquid. Based on these results, our proposed method can be successfully used for the reliable, noise-free calibration of hollow FluidFM cantilevers.