Nonlinear Dynamics of Atomic Force Microscopy with Viscoelastic Term and Casimir force interactions: An Overview

Atomic force microscopy (AFM) is an important tool for analyzing the atomic surface of synthetic or biological samples. The atomic force microscopy device consists of a built-in microcantilever that contains a nano tip at its free end. This nano tip finds the surface of the sample which is scanned for data collection. Vibrations caused by irregularities on the sample surface are collected using a laser that reflects from the microcantilever to a photodiode. In this work, we explore the nonlinear dynamics of the mathematical model, which describes the one-dimensional torsional behavior of the microcantilever motion. The term viscoelasticity and the Casimir force were considered, and we established the set of parameters that present chaotic behavior and thus, proposed control techniques to suppress chaos. However, we explored the nonlinear dynamics behavior of a one-dimensional nonlinear AFM model with the twist of the tip of the microbeam containing the analysis tip. And so, we analyze the contribution of the Casimir Force and the viscoelasticity term in the model considered. The aim of this work was to analyze the regions in which the system is in a chaotic and periodic regime, choosing the initial conditions, using classical tools (Lyapunov Exponent, Bifurcation Diagram, Poincare Map, etc.). Determining such regions supports improvements and proposals for future control projects to suppress chaos. Such suppression allows irregularities in the movement of the microcantilever to be periodic, which can reduce noise in sample analyses.