A robust AFM-based method for locally measuring the elasticity of samples

Investigation of the local sample elasticity is of high importance in many scientific domains. In 2014, Herruzo et al. published a new method based on frequency-modulation atomic force microscopy to locally determine the elasticity of samples (Nat. Commun.2014, 5, 3126). This method gives evidence for the linearity of the relation between the frequency shift of the cantilever first flexural mode Δf₁ and the square of the frequency shift of the second flexural mode Δf₂². In the present work, we showed that a similar linear relation exists when measuring in contact mode with a certain load F and propose a new method for determining the elastic modulus of samples from this relation. The measurements were performed in non-dry air at ambient temperature on three different polymers (polystyrene, polypropylene and linear low-density polyethylene) and a self-assembled monolayer of 1H,1H,2H,2H-perfluorodecyltrichlorosilane (FDTS) on a silicon oxide substrate perforated with circular holes prepared by polymer blend lithography. For all samples the relation was evidenced by recording Δf₁, Δf₂ and F as a function of the Z-displacement curves of the piezoelectric scanner. The occurence of a plastic deformation followed by an elastic deformation is shown and explained. The necessary load F for measuring in the elastic domain was assessed for each sample, used for mapping the frequency shifts Δf₁ and Δf₂ and for determining the elastic modulus from Δf₂²/Δf₁. The method was used to give an estimate of the Young's modulus of the FDTS thin film.