  Knowledge of surface forces is the key to understanding a large number of
processes in fields ranging from physics to material science and biology. The
most common method to study surfaces is dynamic atomic force microscopy (AFM).
Dynamic AFM has been enormously successful in imaging surface topography, even
to atomic resolution, but the force between the AFM tip and the surface remains
unknown during imaging. Here, we present a new approach that combines high
accuracy force measurements and high resolution scanning. The method, called
amplitude-dependence force spectroscopy (ADFS) is based on the
amplitude-dependence of the cantilever's response near resonance and allows for
separate determination of both conservative and dissipative tip-surface
interactions. We use ADFS to quantitatively study and map the nano-mechanical
interaction between the AFM tip and heterogeneous polymer surfaces. ADFS is
compatible with commercial atomic force microscopes and we anticipate its
wide-spread use in taking AFM toward quantitative microscopy.
