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Analytical equations to estimate the peak force will facilitate the interpretation and the planning of amplitude-modulation force microscopy (tapping mode) experiments. A closed-form analytical equation to estimate the tip-sample peak forces while imaging soft materials in liquid environment and within an elastic deformation regime has been deduced. We have combined a multivariate regression method with input from the virial-dissipation equations and Tatara's bidimensional deformation contact mechanics model. The equation enables to estimate the peak force based on the tapping mode observables, probe characteristics and the material properties of the sample. The accuracy of the equation has been verified by comparing it to numerical simulations for the archetypical operating conditions to image soft matter with high spatial resolution in tapping-mode AFM.

Scaling law to determine peak forces in tapping-mode AFM experiments on finite elastic soft matter systems