Abstract: The atomic force microscope has evolved from purely a qualitative apparatus that measures the topography of a sample into a quantitative tool that also measures mechanical properties of a sample at the nanoscale. Prior technologies that attempt to measure the bulk parameters must characterize the geometry of the atomic force microscope cantilever tip in a separate experiment before being able to measure the mechanical properties of the sample. This is the single biggest obstruction to the accuracy and expediency of quantitative atomic force microscopy methodologies. Present techniques are also unable to probe the full set of viscoelastic properties of a material as they do not include any method to measure the damping of samples. We propose a method herein that simultaneously circumvents the need for a separate experiment to characterize the tip geometry and measures the full set of viscoelastic properties of a material.

Abstract: A method for characterizing a nonlinear system using the system's steady state response including: exciting a transducer using a plurality of frequencies while decoupled from the nonlinear system, measuring the amplitude of response of each of the frequencies while decoupled from the nonlinear system, exciting the transducer using the plurality of frequencies while coupled to the nonlinear system, measuring the amplitude of response of each of the frequencies and the second harmonic of at least some of the frequencies, and solving for a set of phenomenological parameters characterizing the dynamics of the nonlinear system.