Model reduction techniques for quantitative nano-mechanical AFM mode

International audience ; A recently developed atomic force microscope (AFM) process, the Peak-Force Quantitative Nanomechanical Mapping (PF-QNM) mode, allows 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 samples 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 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.