Non-Linear Frequency Response of Atomic Force Microscope Cantilevers at the Solid-Liquid Interface

One significant advantage of atomic force microscopy (AFM) over other microscopy methods is its ability to characterize surfaces in liquid environments. However, operation in liquid is complicated by the large hydrodynamic loading, which leads to low quality factors, and in turn leads to many changes in the dynamics as opposed to air/vacuum environments. A thorough understanding of the dynamics is necessary for properly interpreting data from experiments. In this work, we study the non-linear dynamics of AFM micro-cantilevers interacting with hard surfaces in liquids. In comparison to prior works that have mostly examined the dynamics at a single drive frequency, we examine the full nonlinear frequency response. Two important results are highlighted. First, in addition to the primary resonance, there are also superharmonic resonances, which can distort tapping mode approach curves. Secondly, we point out that the layering (hydration forces) of liquid molecules at the solid-liquid interface, traditionally detected using small amplitude (linear) AFM, in fact has a significant effect on the nonlinear response. These results are shown by experiments and examined analytically. The effects of parameters such as cantilever stiffness and quality factors are studied using numerical simulation.