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Amplitude-modulation (tapping mode) atomic force microscopy is a technique for high resolution imaging of a wide variety of surfaces in air and liquid environments. Here by using the virial theorem and energy conservation principles we have derived analytical relationships between the oscillation amplitude, phase shift, and average tip-surface forces. We find that the average value of the interaction force and oscillation and the average power dissipated by the tip-surface interaction are the quantities that control the amplitude reduction. The agreement obtained between analytical and numerical results supports the analytical method.This work has been supported by the Dirección General de Investigación Científica y Técnica (PB98-0471) and the\udEuropean Union (BICEPS, BIO4-CT-2112). A. S. P. acknowledges financial support from the Comunidad Autónoma de Madrid.Peer reviewe

Tip-surface forces, amplitude, and energy dissipation in amplitude-modulation (tapping mode) force microscopy