Frequency Function in Atomic Force Microscopy Applied to a Liquid Environment

Abstract

Scanning specimens in liquids using commercial atomic force microscopy (AFM) is very time-consuming due to the necessary try-and-error iteration for determining appropriate triggering frequencies and probes. In addition, the iteration easily contaminates the AFM tip and damages the samples, which consumes probes. One reason for this could be inaccuracy in the resonant frequency in the feedback system setup. This paper proposes a frequency function which varies with the tip-sample separation, and it helps to improve the frequency shift in the current feedback system of commercial AFMs. The frequency function is a closed-form equation, which allows for easy calculation, as confirmed by experimental data. It comprises three physical effects: the quasi-static equilibrium condition, the atomic forces gradient effect, and hydrodynamic load effect. While each of these has previously been developed in separate studies, this is the first time their combination has been used to represent the complete frequency phenomenon. To avoid “jump to contact” issues, experiments often use probes with relatively stiffer cantilevers, which inevitably reduce the force sensitivity in sensing low atomic forces. The proposed frequency function can also predict jump to contact behavior and, thus, the probe sensitivity could be increased and soft probes could be widely used. Additionally, various tip height behaviors coupling with the atomic forces gradient and hydrodynamic effects are discussed in the context of carbon nanotube probes.

Tip Pressure on Semicircular Specimens in Tapping Mode Atomic Force Microscopy in Viscous Fluid Environments

“…When the tip shifts to the left ( Figure 4 b–d), the vorticity increases on the right side of the specimen because the geometric gap between the tip and specimen is irregular, which results in complex vorticity. This phenomenon was also found for a planar specimen, as shown in Figure 2b of [ 5 ].…”

“…Notably, this distortion of surface morphology is different from the geometric effect between tip and specimen in air [ 4 ]. Numerous studies have discussed probe hydrodynamics [ 1 , 5 , 6 ], which are known to affect a probe’s natural frequencies [ 1 , 7 ]; however, few studies have focused on the specimen pressure caused by tips [ 8 ]. The authors of the present study demonstrated that the liquid pressure varies with the tip geometry; furthermore, the maximum hydrodynamic pressure caused by a cone-shaped tip is approximately 0.5 Pa, and this can predeform a membrane by several nanometers before the tip taps its surface [ 9 ].…”

“…Kim et al [ 11 ] found that when a standard grating sample was scanned using AFM in different fluids, the images were significantly distorted and the additional pressure between the cantilever and sample was strongly dependent on the kinematic viscosity of the fluid. Moreover, the additional pressure from the probe was dependent on the tip–specimen distance, probe width, tip shape, vibration frequency, and Reynolds number [ 5 ]. The maximum hydrodynamic pressure exerted by a tip is approximately 180 pN [ 12 ], which is 1.8 times larger than the peak force, the maximum contact force when the tip contacts the specimen.…”

Parameter Identification and Adaptive Control Of Carbon Nanotube Resonators

“…In such studies, researchers have mainly focused on the vibrational properties of the CNTs in order to design different types of sensors [2]. CNT resonators have been used so far in many instruments for sensing very small mass [1], force [3], detection of gas atoms [4], and AFM in fluid environments [5]. CNT resonators have been used so far in many instruments for sensing very small mass [1], force [3], detection of gas atoms [4], and AFM in fluid environments [5].…”

Tip Effect of the Tapping Mode of Atomic Force Microscope in Viscous Fluid Environments

“…However, the vibrating probe produces pressure and vorticity at the edges between the tip and the beam, and these affect the pressure on the specimen. Many studies have discussed the dynamics of probes in a liquid environment [1,4], but few have focused on pressure caused by these tips. We believe the liquid pressure and vorticity induced by the vibrating tip may deform the geometric surface of the specimen, especially when the tip and specimen are close.…”