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 deformation-force curves on the double layers and to determine the thickness of the polymer films in wide range (0-200 nm).
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