Atomic force microscope cantilever spring constant evaluation for higher mode oscillations: A kinetostatic method

Abstract

Our previous study of the particle mass sensor has shown a large ratio (up to thousands) between the spring constants of a rectangular cantilever in higher mode vibration and at the static bending or natural mode vibration. This has been proven by us through the derived nodal point position equation. That solution is good for a cantilever with the free end in noncontact regime and the probe shifted from the end to an effective section and contacting a soft object. Our further research shows that the same nodal position equation with the proper frequency equations may be used for the same spring constant ratio estimation if the vibrating at higher mode cantilever's free end has a significant additional mass clamped to it or that end is in permanent contact with an elastic or hard measurand object (reference cantilever). However, in the latter case, the spring constant ratio is much smaller (in tens) than in other mentioned cases at equal higher (up to fourth) vibration modes. We also present the spring constant ratio for a vibrating at higher eigenmode V-shaped cantilever, which is now in wide use for atomic force microscopy. The received results on the spring constant ratio are in good (within a few percent) agreement with the theoretical and experimental data published by other researchers. The knowledge of a possible spring constant transformation is important for the proper calibration and use of an atomic force microscope with vibrating cantilever in the higher eigenmodes for measurement and imaging with enlarged resolution.

Flexural vibrations of a thin clamped steel bar

“…This indicates that the elastic constant of the thin bar increases considerably when one goes to higher normal modes. This is in qualitative agreement with a theory of vibrating cantilevers [22]. The amplitude of the forced vibrations of the third normal mode was below the threshold of detection by our optical sensor, nevertheless around a drive frequency of 320 Hz we could hear a sharp increase in the sound generated by the vibrating bar.…”

The additive effect of harmonics on conservative and dissipative interactions

“…(14) by simply calibrating the spring constant, Q factor, and natural resonant frequency for the corresponding mode and inserting the corresponding values in the equation. 10,11,53,54 The instantaneous force F ts (d) during tip approach (_ z 1 < 0) and tip retraction (_ z 1 > 0) as recovered for n ¼ 10 ( Fig. 3(a)), n ¼ 30 (Fig.…”

Investigation on the surface free energy of a single flax fiber through adhesion measurement by atomic force microscopy

“…Several methods are available for calculating the spring constant of the AFM probe, such as the thermal fluctuation measurement method, the kinetostatic method, the heterodyne interferometry method, and the extended added micro-drop method. [22][23][24] The Sader method 25 was used here for determining the spring constant and calculated to be 37.5 N/m. The tip of the cantilever was characterized by Field Emission Scanning Electron Microscopy (FESEM) (JEOL JSM-7600F).…”