Analytical methods to derive the elastic modulus of soft and adhesive materials from atomic force microcopy force measurements

We present new DMT-based and JKR-based methods to derive the elastic modulus of sample surfaces from an atomic force microscope force-distance curve (DMT: Derjaguin-Muller-Toporov, JKR: Johnson-Kendall-Roberts). Application of the methods to the Maugis-Dugdale curves revealed that the JKR-based method determines very accurate moduli for Maugis' transitional parameter lambda > 0.3; however, the DMT-based method generally estimates much less accurate moduli. The new JKR-based method has advantages over the two-point method, which has been often used for the JKR analysis, in capabilities to select the fitting range and to involve more than two points in curve fitting. Utilizing the advantages, for example, one can limit the fitting range to the attractive force zone to reduce the contact area of soft and adhesive materials. The method consists of algebraical calculation and optionally linear fitting; hence, the computational cost is low enough to be applicable to a real-time JKR analysis method of fast force mapping. The detailed procedure of the method is explained using a force-distance curve on a poly(dimethylsiloxane) surface. The advantages of the method are demonstrated using a force mapping data on a vulcanized rubber blend. (c) 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019