Analysis of dynamic characteristics of cantilevers excited at the fixed end in dynamic atomic force microscopy in liquid environments

Dynamic atomic force microscopy (AFM) is commonly employed for the analysis of material morphology and mechanical properties at the micro and nanoscale in liquid environments. A comprehensive understanding of the dynamic characteristics of AFM cantilevers in liquid environments is crucial for the development of quantitative methods to assess mechanical properties accurately. In this study, we investigate the dynamical behaviors of AFM cantilevers in liquid environments by introducing added mass and added damping to simulate the effects of fluid on the cantilever using the finite difference method (FDM). The time-domain response and spectrum of the cantilever are investigated, as well as the dynamic characteristics of the cantilever in bimodal AFM. The results demonstrate that the thickness of the cantilever has a greater impact on the cantilever's natural frequency and quality factors in liquids. The fluid density dominates the natural frequency, and the fluid viscosity dominates the quality factor. In the presence of tip-sample interaction, the vibration shape curves in liquids tend to incline upwards, and the displacement response no longer takes the form of a sine/cosine curve, according to time domain and spectrum analysis. The squeeze damping decreases the displacement response of the cantilever and inhibits the amplification of higher harmonics of the displacement and interaction force. The continuous beam model based on FDM is suitable for evaluating the dynamics of bimodal AFM in liquid, and it overcomes the constraints on detection position and modal parameters compared to the mode coupling method.