Study on viscoelastic contact mechanics by nanorheological atomic force microscopy

Abstract Nanorheological atomic force microscopy (AFM) enables us to measure nano-scale frequency-dependent dynamic moduli by oscillating the cantilever with a wide range of frequencies. However, the storage and loss moduli converted from dynamic stiffness obtained by nanorheological AFM with the contact area calculated by Johnson–Kendall–Roberts (JKR) contact mechanics, which is for elastic bodies with adhesion, exhibit difference compared to those by macroscopic dynamic mechanical analysis due to the different contact areas depending on frequencies. Herein, we modified one of the viscoelastic contact mechanics considering the extent of the relaxation of the bulk deformation, which was disregarded in the original theory, to improve the quantitative accuracy of the contact area. The modification was verified by several experiments. By implementing the theory, we successfully quantified frequency-dependent contact areas, and the nano-scale dynamic moduli by nanorheological AFM showed a better agreement with the macroscopic moduli.