Time-varying tip-sample force measurements and steady-state dynamics in tapping-mode atomic force microscopy

Direct time-varying tip-sample force measurements by torsional harmonic cantilevers facilitate detailed investigations of the cantilever dynamics in tapping-mode atomic force microscopy. Here, we report experimental evidence that the mathematical relationships describing the steady-state dynamics are quantitatively satisfied by the independent measurements of tip-sample forces over a broad range of experimental conditions. These results confirm the existing understanding of tapping-mode atomic force microscopy and build confidence on the reliability of time-varying tip-sample force measurements by the torsional harmonic cantilevers.