The effect of adhesion on the contact radius in atomic force microscopy indentation

The effect of adhesion on nanoscale indentation experiments makes the interpretation of force-displacement curves acquired in these experiments very difficult. The indentation force results from the addition of adhesive and elastic forces at the indenter-sample contact. The evolution of the two forces during the indentation is determined by the variation of the indenter-sample contact radius. In the present work the variation of contact radius during atomic force microscopy (AFM) indentation of elastic and adhesive samples with conical indenters (AFM tips) is indirectly determined by measurements of the contact dynamic stiffness. For weak sample deformations, the contact radius is determined mainly by the adhesion force and indenter apex radius. For strong sample deformations, the contact radius increases linearly with the increase of the indenter displacement, the slope of this linear dependence being in agreement with Sneddon's theory of indentation (Sneddon 1965 Int. J. Eng. Sci. 3 47). Based on these results, a theoretical expression of indentation force dependence on displacement is found. This expression allows for determination of the thermodynamic work of adhesion at the indenter-sample interface and the sample elasticity modulus.