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In attempting to perform frequency modulationatomic force microscopy (FM-AFM) in liquids, a non-flat phase transfer function in the self-excitation system prevents proper tracking of the cantilever natural frequency. This results in frequency-and-phase modulation atomic force microscopy (FPM-AFM) which lies in between phase modulationatomic force microscopy (PM-AFM) and FM-AFM. We derive the theory necessary to recover the conservative force and damping in such a situation, where standard FM-AFM theory no longer applies. Although our recovery procedure applies to all cantilever excitation methods in principle, its practical implementation may be difficult, or even impossible, if the cantilever is driven piezoacoustically. Specifically, we contrast the piezoacoustic excitation method to the photothermal method in the context of force spectroscopy of hydration structures at the mica-water interface. The results clearly demonstrate that photothermal excitation is superior to piezoacoustic excitation, as it allows for accurate quantitative interpretation of the acquired data.


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