Growth kinetics of a nanoprotuberance under the action of an oscillating nanotip

The atomic force microscope is a versatile tool that allows many routes to be used for investigating the mechanical properties of soft materials on the nanometer scale. In the present work, experiments were performed on polystyrene polymer films of various molecular weight by approaching a vibrating nanotip towards the surface. The variation of the oscillating amplitude of the cantilever is interpreted as the result of the growth process of a nanoprotuberance. The growth rate is found to be dependent of the magnitude of the oscillating amplitude and of the molecular weight. A model is developed describing in a very simple way the action of the tip and a viscoelastic response of the polymer. The numerical simulation helps in understanding the nonlinear relation between the growth rate and the vibrating amplitude of the microlever and describes qualitatively most of the experimental features. For the softer material, experimental situations are found that allow the experimental results to be amenable with an analytical solution. The analytical solution provides a fruitful comparison with the experimental results showing that some of the nanoprotuberance evolution cannot be explained with the approximation used. The presents results show that there exists a new and fascinating route to better understand the mechanical response at the local scale. PUBLISHED IN Phys. Rev. B 59(3), 2407-2416 (1999) @S0163-29~99!03003-9#