Abstract
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 FN 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 FN 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 FN 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.
Highlights
Knowledge of the local elasticity of samples is of high interest in many scientific domains, as many processes and physical quantities are correlated with the elastic modulus
The results obtained with these methods are in good agreement with theoretical data and data obtained from macroscopical experiments, difficulties in the precise determination of the elastic modulus based on the theoretical model, or during the use of the method may be encountered when using dynamicmode atomic force microscope (AFM)
In Hurley and Turner’s [6] method, the stated equations for the computation of the normal sample stiffness by numerical methods used to determine sample elasticity are based on the equations established by Rabe [9] and Rabe et al [10] for atomic force acoustic microscopy (AFAM) [11,12,13,14]
Summary
Knowledge of the local elasticity of samples is of high interest in many scientific domains, as many processes and physical quantities are correlated with the elastic modulus. The method is based on the theoretical model developed by Herruzo et al [7] for the computation of the effective elastic modulus of samples Eeff ranging from 1 MPa to 3 GPa from the measured frequency shifts of the two flexural modes of a cantilever operated in intermittent-contact mode: (1) (b) Effective spring constant keff and values of the ratio between measured applied normal force FN,meas and Z-displacement Δz as a function of the sample stiffness.
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