Effect of tip mass on frequency response and sensitivity of AFM cantilever in liquid

Hydrodynamic function and spring constant calibration of FluidFM micropipette cantilevers

Fluidic force microscopy (FluidFM) fuses the force sensitivity of atomic force microscopy with the manipulation capabilities of microfluidics by using microfabricated cantilevers with embedded fluidic channels. This innovation initiated new research and development directions in biology, biophysics, and material science. To acquire reliable and reproducible data, the calibration of the force sensor is crucial. Importantly, the hollow FluidFM cantilevers contain a row of parallel pillars inside a rectangular beam. The precise spring constant calibration of the internally structured cantilever is far from trivial, and existing methods generally assume simplifications that are not applicable to these special types of cantilevers. In addition, the Sader method, which is currently implemented by the FluidFM community, relies on the precise measurement of the quality factor, which renders the calibration of the spring constant sensitive to noise. In this study, the hydrodynamic function of these special types of hollow cantilevers was experimentally determined with different instruments. Based on the hydrodynamic function, a novel spring constant calibration method was adapted, which relied only on the two resonance frequencies of the cantilever, measured in air and in a liquid. Based on these results, our proposed method can be successfully used for the reliable, noise-free calibration of hollow FluidFM cantilevers.

Scanning Probe Microscopy Facility for Operando Study of Redox Processes on Lithium ion Battery Electrodes

An Atomic Force Microscope (AFM) is combined with a special designed glovebox system and coupled to a Galvanostat/Potentiostat to allow measurements on electrochemical properties for battery research. An open cell design with electrical contacts makes it possible to reach the electrode surface with the cantilever so as to perform measurements during battery operation. A combined AFM-Scanning Electro-Chemical Microscopy (AFM-SECM) approach makes it possible to simultaneously obtain topological information and electrochemical activity. Several methods have been explored to provide the probe tip with an amount of lithium so that it can be used as an active element in a measurement. The “wet methods” that use liquid electrolyte appear to have significant drawbacks compared to dry methods, in which no electrolyte is used. Two dry methods were found to be best applicable, with one method applying metallic lithium to the tip and the second method forming an alloy with the silicon of the tip. The amount of lithium applied to the tip was measured by determining the shift of the resonance frequency which makes it possible to follow the lithiation process. A FEM-based probe model has been used to simulate this shift due to mass change. The AFM-Galvanostat/Potentiostat set-up is used to perform electrochemical measurements. Initial measurements with lithiated probes show that we are able to follow ion currents between tip and sample and perform an electrochemical impedance analysis in absence of an interfering Redox-probe. The active probe method developed in this way can be extended to techniques in which AFM measurements can be combined with mapping electrochemical processes with a spatial resolution.

Dynamic analysis of flexural vibration mode of an atomic force microscope cantilever with a sidewall probe in liquid

In this paper, dynamic behavior and the resonance frequencies of flexural vibration modes of an atomic force microscope cantilever with sidewall probe immersed in liquid to surface stiffness variations have been investigated and a closed-form expression is derived. Using numerical analysis, the flexural resonance frequencies of microcantilever immersed in liquid are calculated and the results are compared with the air environment. Then, the effect of sidewall length and normal stiffness on the frequency is investigated. Moreover, the surface-coupled effect between the cantilever and simple surface when the cantilever is close to the surface is considered and its effect on the quality factors of the first to fourth modes is studied.

Vibration response of piezoelectric microcantilever as ultrasmall mass sensor in liquid environment

The present study aims to analyze the vibrating behavior of a piezoelectric microcantilever (MC) as a mass nanosensor. The vibrating behavior of the MC as well as its sensitivity as a mass nanosensor are investigated and compared in both air and liquid environments. To this end, Euler-Bernoulli theory was used to model the vibrating behavior of piezoelectric MC with added mass at its free end. Frequency analysis was conducted by considering geometric discontinuities and taking added mass into account. The effect of liquid environment applied to the MC (as hydrodynamic forces) was based on a string of spheres model. Since changes in resonance frequency are used as the measurement parameter in mass sensors, changes in resonance frequency during absorption of nanoparticles was selected as the main parameter to be investigated in this study. Ultimately, with the aim to achieve optimal geometric dimensions for the piezoelectric MC, sensitivity analysis was additionally performed in order to increase the frequency sensitivity. According to the results, frequency sensitivity of the piezoelectric MC decreased in liquid environment compared to air environments. Moreover, increases in fluid density and viscosity caused a decreased frequency sensitivity. Simulation results indicate that the second vibrating mode in air and liquid environments is the appropriate operating mode for this type of MC.

Simultaneous viscosity and density measurement of small volumes of liquids using a vibrating microcantilever

Many industrial and technological applications require precise determination of the viscosity and density of liquids. Such measurements can be time consuming and often require sampling substantial amounts of the liquid. These problems can partly be overcome with the use of microcantilevers but most existing methods depend on the specific geometry and properties of the cantilever, which renders simple, accurate measurement difficult. Here we present a new approach able to simultaneously quantify both the density and the viscosity of microliters of liquids. The method, based solely on the measurement of two characteristic frequencies of an immersed microcantilever, is completely independent of the choice of a cantilever. We derive analytical expressions for the liquid's density and viscosity and validate our approach with several simple liquids and different cantilevers. Application of our model to non-Newtonian fluids shows that the calculated viscosities are remarkably robust when compared to measurements obtained from a standard rheometer. However, the results become increasingly dependent on the cantilever geometry as the frequency-dependent nature of the liquid's viscosity becomes more significant.

Sensitivity analysis of rectangular atomic force microscope cantilevers immersed in liquids based on the modified couple stress theory

The modified couple stress theory is adopted to study the sensitivity of a rectangular atomic force microscope (AFM) cantilever immersed in acetone, water, carbon tetrachloride (CCl4), and 1-butanol. The theory contains a material length scale parameter and considers the size effect in the analysis. However, this parameter is difficult to obtain via experimental measurements. In this study, a conjugate gradient method for the parameter estimation of the frequency equation is presented. The optimal method provides a quantitative approach for estimating the material length scale parameter based on the modified couple stress theory. The results show that the material length scale parameter of the AFM cantilever immersed in acetone, CCl4, water, and 1-butanol is 0, 25, 116.3, and 471 nm, respectively. In addition, the vibration sensitivities of the AFM cantilever immersed in these liquids are investigated. The results are useful for the design of AFM cantilevers immersed in liquids.