Determination of complex modulus by atomic force microscopy

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Abstract
The static friction regime of an atomic force microscope tip on a soft material is analyzed. A mechanical model shows that the experimental response is characteristic of the complex modulus of the sample. Moduli deduced from experiments on styrene-butadiene films compare favorably with macroscopically determined ones. Small discrepancies can be attributed to the imprecise knowledge of the mechanical properties of the cantilever. Relative measurements should, however, be accurately made. Spatial resolution depends on mechanical and adhesive properties of the material. For the experiments shown, the resolution is a few microns. Contrary to others, this method is little dependent on the geometrical properties of the tip end since in this regime the tip is deeply intruded in the material. It applies on thin films and heterogeneous materials and provides a new method for determining the mechanical properties at a local scale.