Nonlinear dynamics as an essential tool for non-destructive characterization of soft nanostructures using tapping-mode atomic force microscopy

Tapping-mode atomic force microscopy provides a means for successful and non-intrusive characterization of soft physical and biological structures at the nanoscale. Its full potential can only be realized, provided that the response of the oscillating probe tip to the strongly nonlinear, near-field force interactions with the structure and the intermittency of contact can be accurately modelled, analysed, controlled and interpreted. To this end, this paper reviews some experimental observations of fundamentally nonlinear behaviour of the tip dynamics. It discusses the nonlinear phenomenology that explains their presence in the tapping-mode operation of the atomic force microscope. Particular emphasis is placed on the coexistence of different steady-state responses and their origin in transitions across regions of rapidly varying force characteristics. The heuristics of a recently developed method for treating such transitions are presented and insights into its implications are drawn from related micro- and nanoscale applications.