Model reduction techniques for quantitative nano-mechanical AFM mode

A recently developed atomic force microscope process, the PeakForce quantitative nanomechanical mapping (PF-QNM) mode, allows us to probe over a large spatial region surface topography together with a variety of mechanical properties (e.g. apparent modulus, adhesion, viscosity). The resulting large set of data often exhibits strong coupling between material response and surface topography. This letter proposes the use of a proper orthogonal decomposition (POD) technique to analyze and segment the force-indentation data obtained by the PF-QNM mode in a highly efficient and robust manner. Two examples illustrate the proposed methodology. In the first one, low-density polyethylene nanopods are deposited on a polystyrene film. The second is made of carbonyl iron particles embedded in a polydimethylsiloxane matrix. The proposed POD method permits us to seamlessly identify the underlying phase constituents in both samples and decouple them from the surface topography by compressing voluminous force-indentation data into a subset with a much lower dimensionality.

Automated summary

The study introduces a new atomic force microscope technique, PeakForce quantitative nanomechanical mapping, which allows the detection of surface topography and various mechanical properties. The use of proper orthogonal decomposition technique is proposed to analyze and segment experimental data efficiently and robustly. This method can effectively identify the underlying phase constituents in materials and decouple them from surface topography.