Nonlinear dynamic perspectives on dynamic force microscopy.

Dynamic force microscopy (DFM) utilizes the dynamic response of a resonating probe tip as it approaches and retracts from a sample to measure the topography and material properties of a nanostructure. We present recent results based on nonlinear dynamical systems theory, computational continuation techniques and detailed experiments that yield new perspectives and insights into DFM.A dynamic model including van der Waals and Derjaguin-Müller-Toporov contact forces demonstrates that periodic solutions can be represented as a catastrophe surface with respect to the approach distance and excitation frequency. Turning points on the surface lead to hysteretic amplitude jumps as the tip nears/retracts from the sample. New light is cast upon sudden global changes that occur in the interaction potential at certain gap widths that cause the tip to "stick" to, or tap irregularly the sample. Experiments are performed using a tapping mode tip on a graphite sample to verify the predictions.