Determination of the Resonance Frequency and Spring Constant of FluidFM Cantilevers with Numerical Simulations

The robotized version of the nanofluidic force-microscope, FluidFM BOT, is a versatile tool utilized for single-cell force-spectroscopy, micropatterning, and fluid injection or extraction. It can manipulate fluids with an embedded nano-channel in the core of its special silicon-nitride cantilever by having a fluid reservoir connected to a pressure control system. The precise determination of the spring constant is essential for any cantilever. The aim of our current work is to lay the bases of a spring constant calibration method that requires knowing the first two resonance frequencies of the cantilever in air and in a viscous medium. For this purpose, we used finite element method (FEM) numerical simulation on a CAD model, which was created based on SEM images made on the FluidFM micropipette cantilever. The resonance frequencies of the cantilever in air and in a viscous medium were calculated from the simulations. The resonance frequencies of the cantilever were determined in air and water, with respect to changes in the mesh size, Young’s modulus of the cantilever, the aperture size, and the volume of surrounding media. The relevance of the data is discussed in light of experimentally determined resonance frequencies and technological limitations.