Euler-Bernoulli Theory Accurately Predicts Atomic Force Microscope Shape During Non-Equilibrium Snap to Contact Motion.

Abstract

We find that the Euler-Bernoulli theory is an appropriate framework to predict the kinematics of the cantilever during the far-from-equilibrium snap-to-contact event. We show by direct comparison with Doppler Vibrometry experiments the validity of the force-separation reconstruction algorithm based on the Euler- Bernoulli equation. Specifically, we did this comparison for the case of a cantilever undergoing far-fromequilibrium motion driven by nonlinear forces during the snap-to-contact event. The relevance of our result is that, unlike in the experiment used here, conventional atomic force microscopy experimental conditions allow collection of the slope or position versus time at only a single point on the cantilever. However, as seen in the Methods section, a distinct algorithm can be formulated to deal with this data as well. While our rendering of the Euler-Bernoulli-based algorithm allows for the reconstruction of the full shape of the cantilever at all times, the reliability of these shapes rests ultimately on the validity of the model used. Our proof thus paves the way to use our reconstruction algorithm under conventional atomic force microscopy operating conditions. The time-consuming multiple Doppler Vibrometry measurement, while central to our test, is shown here to be no longer needed when running conventional atomic force microscopy experiments. Indeed, once one knows that Euler-Bernoulli can be used during snap-to-contact to predict the shape of the cantilever, the bending forces are readily attainable. In other words, our results should extend the ability to produce accurate force-separation curves from conventional voltage-time traces into far-from-equilibrium motion and nonlinear interactions. (from Conclusion)