Quantitative force measurements using frequency modulation atomic force microscopy—theoretical foundations

Use of the atomic force microscope (AFM) in quantitative force measurements inherently requires a theoretical framework enabling conversion of the observed deflection properties of the cantilever to an interaction force. In this paper, the theoretical foundations of using frequency modulation atomic force microscopy (FM-AFM) in quantitative force measurements are examined and rigorously elucidated, with consideration being given to both ‘conservative’ and ‘dissipative’ interactions. This includes a detailed discussion of the underlying assumptions involved in such quantitative force measurements, the presentation of globally valid explicit formulae for evaluation of so-called ‘conservative’ and ‘dissipative’ forces, discussion of the origin of these forces, and analysis of the applicability of FM-AFM to quantitative force measurements in liquid.