Analysis of hysteresis effect on the vibration behavior of AFM intelligent MC in the vicinity of sample surface by considering the size effect in air and liquid

Abstract

Nowadays, scientists consider AFM as a powerful Nanorobot for the measurement of inter-molecular forces as well as identification and topography of sample surfaces. In order to enhance the performance of this Nanorobot, the modified couple stress (MCS) theory in the air and the liquid environment has used to reduce the error resulting from the modeling of AFM microcantilever (MC) based on classic continuum mechanic theory. In this paper, using the Hamiltonian principle and based on the Euler Bernoulli beam theory, motion equations are extracted taking into account the capillary, van der Waals and contact forces between the tip and the sample, as well as the hydrodynamic and the squeeze force in the liquid environment. Modeling is carried out for two dagger and rectangular geometries considering the geometric discontinuities due to the presence of a piezoelectric layer enclosed between the two sides of the electrode and the change in the cross-section of the MC when connecting the probe to the MC. Galerkin method is employed for the discretization of equations. In order to analyze the effects of geometry and environment on the MC vibration behavior, the time and frequency response are obtained at distances away from the surface for both MC geometries in the air and liquid environment. Comparison results suggest that the natural frequency is reduced due to the added mass of the dagger MC. This reduction is more tangible in the liquid environment because of the added mass. Also, the effect of the hysteresis phenomenon caused by the ferromagnetic property of materials is analyzed in order to approximate the theoretical model to the real model using the PI, Bouce-van and Duhem models. Surface topography is illustrated considering the hysteresis effect on rectangular and dagger MC. According to the results, the amplitude is amplified by using the three models. This amplification is higher in the PI model.