Nonlinear Dynamics of Microcantilevers Interacting with Nanostructures: New Paradigms for Ultrasensitive Atomic Force Microscopy

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This project investigates the dynamics of new ultrasensitive modes for nanoscale imaging and force sensing in the Atomic Force Microscope (AFM) that could impact significantly its considerable applications in nanotechnology, material science, biology, condensed matter physics, and data storage technology. Continuous rod models of AFM microcantilevers driven at parametric and nonlinear resonances (sub-, superharmonic and combination) are systematically discretized about their equilibrium position under the action of tip-sample interaction forces. The dynamics of the discretized model are studied using (1) analytical asymptotic techniques to accommodate non-smoothness of tip-sample interaction forces, and (2) accurate numerical simulations for non-smooth systems. A focus is placed on identifying regions in parameter space with greatest sensitivity to tip-sample interaction forces as well as regions corresponding to bifurcations and unstable dynamics. Careful experiments are performed on different microcantilevers and sample materials with a custom built AFM with dual lock-in amplifiers that allow for different excitation and response frequencies, a typical situation for parametric and nonlinear resonance. The Atomic Force Microscope (AFM) has become one of the most important tools for nanotechnology with its remarkable ability to measure nanoscale forces and image and manipulate atoms and molecules with nanometer resolution. Efforts are ongoing around the world to improve the sensitivity of this key enabling tool for nanotechnology; however, under ambient conditions this sensitivity is fundamentally limited by the nature of excitation and the quality factor (Q-factor) of the resonance. Greater sensitivity to nanoscale interaction forces could enable the AFM to reveal material property contrast and detect nanoscale forces that are otherwise hidden in background noise. The proposed research aims to create entirely new AFM modes by oscillating the AFM probes using (a) parametric and (b) nonlinear resonances that could bypass the current limits on sensitivity in conventional AFM systems. In doing so, the research could open the door to scientific breakthroughs in diverse AFM applications including the imaging and spectroscopy of biological molecules, probe-based data storage, and synthesis and characterization of nanomaterials. Given the explosion of AFM's in University campuses and research labs around the world, there is a rapidly growing body of AFM experimentalists who are not trained in dynamics and little realize its importance in this "microscope". The project uses the existing framework of the NSF supported nanoHUB (www.nanohub.org) to create online simulation tools for AFM dynamics that would be accessible to hundreds of experimentalists and educators worldwide. Created by the Network for Computational Nanotechnology (NCN), this is a NSF-funded initiative connecting theory, experiment, and computation one of NSF's success stories in the use of cyberinfrastructure to spur scientific research. Not only is the use of these tools expected to aid the interpretation of AFM data and reduce AFM training time for graduate students and researchers worldwide, it also serves as an excellent resource for teaching fundamental and advanced concepts of scanning probe microscopy in both undergraduate and graduate classes.