Characterising visco-elastic response

A viscoelastic surface has a characteristic delay time between applied load and material response. When this delay time becomes longer than the period of cantilever oscillation, the force quadrature curves become hysteretic. Using a moving surface model one can extract the characteristic time constants for tip penetration in to the surface, and relaxation of the free surface.

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Simulated force quadrature curves using the moving surface model show excellent agreement with experimental data.  Simulation reveals the surface motion, which can not be measured with the AFM.  The time evolution of the envelope of rapid cantilever oscillation (blue) and surface oscillation (orange), shows that the adhesion force lifts the soft surface.  The surface does not have time to fully relax between successive taps of the tip, giving rise to a time-average lifted surface and hysteresis in the force quadrature curves.

Machine learning to map mechanical response

Intermodulation AFM gives some 60 amplitude and phase images, in one scan at normal speed (2 min. for 256 x 256 pixels). Each pixel represents a single point in a abstract 60-dimensional 'feature' space. Machine learning attempts to group or cluster the pixels in this space. The ImAFM Software Suite comes with functionality for k-means clustering. Other clustering algorithms are easily programmed using the scripting interface and the Python module scikit-learn.

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A map showing regions of similar mechanical response on a dynamically vulcanized thermal plastic alloy (DVA).  Pixels were grouped in to 5 clusters using the k-means algorithm.   The x-y location of the pixel is not a feature of the data, so the method blindly reconstructs the map.  Force quadrature curves are shown for the pixel closest to the centroid of each cluster, thus giving the characteristic mechanical response of the region with corresponding color on the map.