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Force-displacement curves have been acquired with a commercial atomic force microscope on a thin film of poly(n-butyl methacrylate) on glass substrates. The film thickness is nonuniform, ranging in the measured area from 0 to 30 nm, and gives the possibility to survey 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 stiffness and the deformation for each force-distance curve were determined and related to the film thickness. We were able to estimate the resolution of the film thickness that can be achieved by means of force-distance curves. By exploiting the data acquired in the present and in a previous experiment, a novel semiempirical approach to describe the mechanical properties of a mechanical double-layer is introduced. The mathematical model, with which deformation-force curves can be described, permits to calculate the Young's moduli of film and substrate in agreement with literature values and to determine the film thickness in agreement with the topography.
Forcedisplacement curves have been acquired with a commercial atomic force microscope on thin films of poly(n-butyl methacrylate) on glass substrates. Different film thicknesses, from 10 up to 430 nm, were chosen to examine in detail the so called mechanical double-layer topic, i.e., the influence of the substrate on the determination of the mechanical properties of thin films. Taking advantage of the Hertz theory we calculated for all films the contact radius between tip and sample as a function of the applied load. Further Young's modulus of the samples was derived from the experimental data as a function of the applied load and, alternatively, of the deformation. The results of this analysis for 10 different film thicknesses were fitted with several half empirical equations proposed by several researchers. The focus of this work is to evaluate such existing half empirical theories for mechanical double-layers and to show the need for an alternative consistent approach.
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).
Force–distance curves have been acquired with an Atomic Force Microscope on polymethyl methacrylate with embedded glass spheres. The glass spheres provide a stiff substrate with an irregular and complex topography hidden underneath a compliant and even polymer film. This situation is a special case of a mechanical double-layer, which we examined in detail in previous experiments. Up to now uniform and non-uniform polymer films on an even substrate were examined. The film thickness on each point of the sample surface was known and force–distance curves could be averaged in groups according to the film thickness. In this way we were able to develop a semi empirical approach which allows describing the shape of averaged force–distance curves depending on the Youngs moduli of the involved materials and on the film thickness. In this experiment we reconstruct a hidden topography, i.e., we determine the polymer thickness on each point of the sample by analyzing single force–distance curves with our semi empirical equation. The accuracy reached by this approach permits to obtain a reconstruction of the shape and position of the embedded particles limited by a maximum detection depth. Single curves are also analyzed qualitatively in order to locate areas where the adhesion at the polymer/glass interface is weak or the two phases are detached.