Determination of viscoelastic moduli at a submicrometric scale

From all analysis of the static friction regime of the tip of an atomic force microscope, a method is proposed for determining the viscoelastic modulus of materials which are viscoelastic at the temperature of the experiment. Present experiments consist in displacing the sample in its plane, periodically or at a constant velocity, while measuring the tangential force response of the contact to this shear solicitation. The proposed model permits to determine the relaxation and complex moduli at a sub-micrometric scale. Several experimental confirmations of the description are presented and it is shown that the local moduli measurements compare favorably with macroscopical results.