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Force-displacement curves have been obtained with a commercial atomic force microscope (AFM) at different temperatures and probe rates on a thick film of poly(n-butyl methacrylate) (PnBMA). The analysis of the force-displacement curves has been focused on the contact portion of the curves, giving information about the stiffness of the sample and its Young's modulus. A novel model of sample deformations that extends the basic equations of the elastic continuum contact theories to the plastic deformations is presented. This model gives several insights into the processes of deformation of soft samples and permits to calculate not only the parameters of the Williams-Landel-Ferry equation but also the Young's modulus and the yielding force of the polymer as a function of temperature and/or probe rate. These quantities have been measured in a wide range of temperatures (70 K) and probe rates (6 decades) for the first time with the AFM, and the results are in very good agreement with measurements performed with customary techniques, such as broadband spectroscopy and dynamic mechanical analysis.
Force-deformation curves have been acquired using nanoindentation and atomic force microscopy on two amorphous polymer samples. The shape and size of the indenter tip was characterized using a white light interferometer and AFM. The measured nanoindentation curves were fitted with the Hertz equation to calculate the Young's modulus of the polymers. Once the Young's moduli of the polymers were known, AFM was used to acquire force-distance-curves on the same samples. We also used the Hertz theory for the analysis in this case. As a result, the tip radius of the AFM cantilever tip could be measured.
This procedure is proposed as a method to determine the shape and size of AFM tips for the quantitative characterization of surface forces through force-distance curves.
Force–displacement curves have been acquired with a commercial atomic force microscope on thin films of poly(n-butyl methacrylate) on glass substrates in order to examine the so-called 'mechanical double layer' topic, i.e. the influence of the substrate on the mechanical properties of the film in dependence of the film thickness. The hyperbolic fit, a novel semi-empirical equation introduced in previous articles, has been further corroborated. The interpretation of this equation has been deepened, yielding a quantitative and demonstrative characterization of the mechanical properties of double layers. Provided that the Young's moduli of bulk polymer and substrate are measured from the deformation curves, this mathematical model permits to fit the deformationforce curves on the double layers and to determine the thickness of the polymer films in wide range (0200 nm).
Contact-resonance AFM (CR-AFM) has been used in recent years for the measurement of mechanical properties. Compared with other techniques, CR-AFM has a much shorter acquisition time, compensating the incomplete theoretical understanding of the underlying physical phenomena. In the present paper, we propose a procedure, which allows to determine the elastic modulus of the sample as a parameter of the fit of the CR frequency as a function of the load. It is concluded that CR measurements are not appropriate for polymer samples. Major drawbacks are the bad resolution for moduli lower than ca. 10 GPa and the lack of a comprehensive physical model.