Abstract
In an effort to improve the accuracy of force-separation curves obtained from atomic force microscope data, we compare force-separation curves computed using two methods to solve the Euler-Bernoulli equation. A recently introduced method using a direct sequential forward solution, Causal Time-Domain Analysis, is compared against a previously introduced Tikhonov Regularization method. Using the direct solution as a benchmark, it is found that the regularization technique is unable to reproduce accurate curve shapes. Using L-curve analysis and adjusting the regularization parameter, λ, to match either the depth or the full width at half maximum of the force curves, the two techniques are contrasted. Matched depths result in full width at half maxima that are off by an average of 27% and matched full width at half maxima produce depths that are off by an average of 109%.
Highlights
Force-separation curves are obtained indirectly from atomic force microscope measurements by applying a suitable model to convert photodetector voltages and z-piezo positions to forces and tip-sample separation distances
In an effort to improve the accuracy of force-separation curves obtained from atomic force microscope data, we compare force-separation curves computed using two methods to solve the Euler-Bernoulli equation
Resolution of these quantities increases the closer the probe tip is to the sample surface
Summary
Force-separation curves are obtained indirectly from atomic force microscope measurements by applying a suitable model to convert photodetector voltages and z-piezo positions to forces and tip-sample separation distances. The new approach chosen here, Causal Time-Domain Analysis, is based on direct application of the Euler-Bernoulli equation and integrating it in space (with a boundary condition that directly takes the measured signal into account) and in time (by starting from an early enough time that one is certain that the cantilever is in a quasistatic regime and there is a unique and simple connection between the signal, the force and the position of the hanging end of the cantilever) The benefit of this method is that it unveils information at large times, when the assumption of a static (or even quasistatic) regime is commonly no longer justifiable.
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