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An analytic model for accurate spring constant calibration of rectangular atomic force microscope cantilevers.

ABSTRACT: Spring constant calibration of the atomic force microscope (AFM) cantilever is of fundamental importance for quantifying the force between the AFM cantilever tip and the sample. The calibration within the framework of thin plate theory undoubtedly has a higher accuracy and broader scope than that within the well-established beam theory. However, thin plate theory-based accurate analytic determination of the constant has been perceived as an extremely difficult issue. In this paper, we implement the thin plate theory-based analytic modeling for the static behavior of rectangular AFM cantilevers, which reveals that the three-dimensional effect and Poisson effect play important roles in accurate determination of the spring constants. A quantitative scaling law is found that the normalized spring constant depends only on the Poisson's ratio, normalized dimension and normalized load coordinate. Both the literature and our refined finite element model validate the present results. The developed model is expected to serve as the benchmark for accurate calibration of rectangular AFM cantilevers.

SUBMITTER: Li R

PROVIDER: S-EPMC4625185 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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An analytic model for accurate spring constant calibration of rectangular atomic force microscope cantilevers.

Li Rui R Ye Hongfei H Zhang Weisheng W Ma Guojun G Su Yewang Y

Scientific reports 20151029

Spring constant calibration of the atomic force microscope (AFM) cantilever is of fundamental importance for quantifying the force between the AFM cantilever tip and the sample. The calibration within the framework of thin plate theory undoubtedly has a higher accuracy and broader scope than that within the well-established beam theory. However, thin plate theory-based accurate analytic determination of the constant has been perceived as an extremely difficult issue. In this paper, we implement ...[more]

PMID: 26510769

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Project description:The fluidic force microscope (FluidFM) can be considered as the nanofluidic extension of the atomic force microscope (AFM). This novel instrument facilitates the experimental procedure and data acquisition of force spectroscopy (FS) and is also used for the determination of single-cell adhesion forces (SCFS) and elasticity. FluidFM uses special probes with an integrated nanochannel inside the cantilevers supported by parallel rows of pillars. However, little is known about how the properties of these hollow cantilevers affect the most important parameters which directly scale the obtained spectroscopic data: the inverse optical lever sensitivity (InvOLS) and the spring constant (k). The precise determination of these parameters during calibration is essential in order to gain reliable, comparable and consistent results with SCFS. Demonstrated by our literature survey, the standard error of previously published SCFS results obtained with FluidFM ranges from 11.8% to 50%. The question arises whether this can be accounted for biological diversity or may be the consequence of improper calibration. Thus the aim of our work was to investigate the calibration accuracy of these parameters and their dependence on: (1) the aperture size (2, 4 and 8 µm) of the hollow micropipette type cantilever; (2) the position of the laser spot on the back of the cantilever; (3) the substrate used for calibration (silicon or polystyrene). It was found that both the obtained InvOLS and spring constant values depend significantly on the position of the laser spot. Apart from the theoretically expectable monotonous increase in InvOLS (from the tip to the base of the cantilever, as functions of the laser spot's position), we discerned a well-defined and reproducible fluctuation, which can be as high as ±30%, regardless of the used aperture size or substrate. The calibration of spring constant also showed an error in the range of -13/+20%, measured at the first 40 µm of the cantilever. Based on our results a calibration strategy is proposed and the optimal laser position which yields the most reliable spring constant values was determined and found to be on the first pair of pillars. Our proposed method helps in reducing the error introduced via improper calibration and thus increases the reliability of subsequent cell adhesion force or elasticity measurements with FluidFM.

Dataset Information

An analytic model for accurate spring constant calibration of rectangular atomic force microscope cantilevers.

Publications

An analytic model for accurate spring constant calibration of rectangular atomic force microscope cantilevers.

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