Abstract
In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale.
Highlights
Atomic force microscopy (AFM) has been developed to a nearly ubiquitous tool for studying physics, chemistry, biology, medicine and engineering at the nano-scale [1,2,3,4,5]
Rutzel et al [9] used the Lennard-Jones (LJ) potential to model the tip-surface interactions and carried out a comprehensive investigation to the nonlinear dynamics and stability of the tapping mode (TM)-AFM, and the results showed that considering the LJ interaction potential in modeling the dynamics of AFM could improve the qualitative prediction of the real system response
This section aims at numerically investigating the characteristics and nonlinear dynamics of a TMAFM cantilever-sample system driven by the harmonic excitation
Summary
Atomic force microscopy (AFM) has been developed to a nearly ubiquitous tool for studying physics, chemistry, biology, medicine and engineering at the nano-scale [1,2,3,4,5]. Using nonlinear analysis methods and numerical simulations, Basso et al [12] found that the chaotic behavior may occur via a cascade of period doubling bifurcations In their studies [11,12], Melnikov theory was used to predict the existence of chaos in AFM. Lee et al [6] carried out numerical analysis using modern continuation tools for computational nonlinear dynamics and bifurcation problems where the tip-surface interaction was represented by the van der Waals and DMT contact forces. A rational connection of the tip-sample-interaction and the nonlinear dynamics analysis of the cantilever where the coupled effects of squeeze film damping and hydrodynamic loading are considered has not been presented and addressed satisfactorily.
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