Modeling and Simulation of Tapping-mode Atomic Force Microscopy in Liquid

Abstract

Application of atomic force microscopy (AFM) in liquid is necessary for imaging and manipulation of biological specimens. In this paper, we have simulated a tapping-mode AFM tilted cantilever in liquid environment near a surface by well defining the contact forces and extracting frequency response and amplitude versus separation diagrams. Contact forces have some differences in liquid in comparison to air or vacuum in magnitude or formulation. Hydrodynamic forces are also applied on the cantilever due to the motion in liquid. For modeling we have used a continuous beam model with its first mode and forward-time simulation method for simulation of its hybrid dynamics. Then we have extracted frequency response and amplitude versus diagrams in liquid. The results show good agreement with experiments. The resonance frequency in liquid is so smaller in comparison to air due to additional mass and additional damping. The results show that the effect of separation on free vibration amplitude and resonance frequency is considerable.

Theoretical model and experimental study on environmental dissipation mechanism of tapping mode atomic force microscope

“…When the probe gradually approaches a certain distance from the sample, the air under the cantilever beam will be blocked by the sample and cannot be freely arranged as shown in Figure 6. At this time, the influence of air squeeze film damping on the cantilever dynamics should be considered 20 …”

“…As the probe gradually moves down until it approaches the surface of the sample, the interaction mechanism between the probe and the sample also needs to be considered. Based on Reynolds equation, the response function of cantilever under the influence of the squeeze film damping is given, 18–20 and the actions of the squeeze film damping under different parameters are discussed 21–23 . In ambient air conditions, one kind of dissipation energy due to adhesion hysteresis comes from the capillary forces between the AFM tip and the sample 24,25 .…”

Modeling and simulation of AFM cantilever with two piezoelectric layers submerged in liquid over rough surfaces

“…where [14], (e) Response obtained from the vibration of cantilever by magnetic excitation in liquid [15]. In Eq.…”

Новый Метод Описания Затухающих Колебаний Балки С Одним Заделанным Концом

“…Задачи о колебаниях тел с распределенной массой, в частности балок, возникают во многих областях науки и техники -от строительной механики [1] до кремниевой микромеханики и зондовых нанотехнологий [2][3][4][5]. Математически эти задачи сводятся к краевым задачам для уравнений в частных производных параболического типа четвертого порядка.…”