This study examines the nonlinear dynamics in tapping-mode atomic force microscopy (AFM) with tip-surface interactions that include van der Waals and Derjaguin-Muller- € Toporov contact forces. We investigate the periodic solutions of the hybrid system by performing numerical pseudo-arclength continuation. Through the use of bifurcation locus maps in the set of parameters of the discontinuous model, the overall dynamical response scenario is assessed. We demonstrate the influence of various dissipation mechanisms that are related with the AFM touching or lacking contact with the sample. Local and global analyses are used to investigate the stability of the stable solution in the repulsive regime. The impacting nonsmooth dynamics framed within a higher-mode Galerkin discretization is able to capture windows of irregular and complex motion.

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Most physical phenomena be it mechanical, chemical or biological are inherently nonlinear in nature. In fact, it is the linear phenomenon that is the exception rather than the rule. By harnessing these nonlinearities one can obtain far greater information about the underlying physics and develop more sensitive and efficient devices. This is especially true at the micro and nanoscale world where the forces tend to be highly nonlinear and the go-to tool for studying such forces is the atomic force microscopy (AFM). Ever since its inception, AFMhas revolutionized theworld of nanotechnology through its ability to manipulate and characterize matter with atomic resolution. With the gradual development of novel characterization techniques, AFM has slowly transitioned from a traditional imaging technique to a powerful nanomechanical characterization tool capable of estimating material properties of wide variety of samples with ease. This transition is fueled by the greater interest in understanding the highly nonlinear tip-sample interaction forces that exist between an AFM probe and the sample of interest. However, in order to advance our understanding of nanoscale interactions, one must fully embrace the nonlinear nature of the system and develop parameter identification techniques based on nonlinear dynamics. In this regard, this thesis focusses on both fundamental and applied nonlinear dynamical studies to develop novel identification techniques for dynamic AFM applications.@en

Modal interactions are pervasive effects that commonly emerge in nanomechanical systems. The coupling of vibrating modes can be leveraged in many ways, including to enhance sensing or to disclose complex phenomenologies. In this work we show how machine learning and data-driven approaches could be used to capture intermodal coupling. We employ a quasi-recurrent neural network (QRNN) for identifying mode coupling and verify its applicability on experimental data obtained from tapping mode atomic force microscopy (AFM). Hidden units of the QRNN are monitored to trace fingerprints of modes activation and to quantify their contributions over the global distortion of orbits in the phase space. To demonstrate the broad applicability of the method, the trained model is re-applied over different experiments and on diverse materials. Over a range of tip-sample configurations, dynamic AFM possesses features general enough to be seized by the QRNN and it is not required an ad-hoc re-training for the identification of interacting modes. Our study opens up a route for utilizing established machine learning techniques for rapid recognition of nonlinear complex effect such as internal resonances in nanotechnology. The QRNN analysis is meant to assist AFM sensing operations when exploiting modal interaction to enhance the signal-to-noise ratio of higher harmonics and provide high resolution compositional contrast in multi-frequency AFM applications.

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This paper investigates the nonlinear dynamics in tapping-mode atomic force microscopy (AFM) with tip-surface interactions that include Van der Waals and Derjaguin-Müller-Toporov contact forces. We study the periodic solutions of the hybrid system by performing numerical pseudo-arclength continuation. The overall dynamical response scenario is evaluated via bifurcation loci maps in the set of parameters of the discontinuous model. We showcase the influence of different dissipation mechanisms activated when the AFM is in contact or out-of contact with the sample. The robustness of the stable solution in the repulsive regime is studied via local and global analyses. The impacting non-smooth dynamics framed within a higher-mode Galerkin discretization is able to capture windows of irregular and complex motion.

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Dynamic atomic force microscopy (AFM) is a key platform that enables topological and nanomechanical characterization of novel materials. This is achieved by linking the nanoscale forces that exist between the AFM tip and the sample to specific mathematical functions through modeling. However, the main challenge in dynamic AFM is to quantify these nanoscale forces without the use of complex models that are routinely used to explain the physics of tip–sample interaction. Here, we make use of machine learning and data science to characterize tip–sample forces purely from experimental data with sub-microsecond resolution. Our machine learning approach is first trained on standard AFM models and then showcased experimentally on a polymer blend of polystyrene (PS) and low density polyethylene (LDPE) sample. Using this algorithm we probe the complex physics of tip–sample contact in polymers, estimate elasticity, and provide insight into energy dissipation during contact. Our study opens a new route in dynamic AFM characterization where machine learning can be combined with experimental methodologies to probe transient processes involved in phase transformation as well as complex chemical and biological phenomena in real-time.@en

Quantifying the nanomechanical properties of soft-matter using multi-frequency atomic force microscopy (AFM) is crucial for studying the performance of polymers, ultra-thin coatings, and biological systems. Such characterization processes often make use of cantilever's spectral components to discern nanomechanical properties within a multi-parameter optimization problem. This could inadvertently lead to an over-determined parameter estimation with no clear relation between the identified parameters and their influence on the experimental data. In this work, we explore the sensitivity of viscoelastic characterization in polymeric samples to the experimental observables of multi-frequency intermodulation AFM. By performing simulations and experiments we show that surface viscoelasticity has negligible effect on the experimental data and can lead to inconsistent and often non-physical identified parameters. Our analysis reveals that this lack of influence of the surface parameters relates to a vanishing gradient and non-convexity while minimizing the objective function. By removing the surface dependency from the model, we show that the characterization of bulk properties can be achieved with ease and without any ambiguity. Our work sheds light on the sensitivity issues that can be faced when optimizing for a large number of parameters and observables in AFM operation, and calls for the development of new viscoelastic models at the nanoscale and improved computational methodologies for nanoscale mapping of viscoelasticity using AFM.

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Increasing the signal-to-noise ratio in dynamic atomic force microscopy plays a key role in nanomechanical mapping of materials with atomic resolution. In this work, we develop an experimental procedure for increasing the sensitivity of higher harmonics of an atomic-force-microscope cantilever without modifying the cantilever geometry but instead by utilizing dynamical mode coupling between its flexural modes of vibration. We perform experiments on different cantilevers and samples and observe that via nonlinear resonance frequency tuning we can obtain a frequency range where strong modal interactions lead to 7-fold and 16-fold increases in the sensitivity of the 6th and 17th harmonics while reducing sample indentation. We derive a numerical model that captures the observed physics and confirms that nonlinear mode coupling is the reason for the increase of the amplitude of higher harmonics during tip-sample interactions.

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In this work, we perform a comprehensive analysis of the robustness of attractors in tapping mode atomic force microscopy. The numerical model is based on cantilever dynamics driven in the Lennard–Jones potential. Pseudo-arc-length continuation and basins of attraction are utilized to obtain the frequency response and dynamical integrity of the attractors. The global bifurcation and response scenario maps for the system are developed by incorporating several local bifurcation loci in the excitation parameter space. Moreover, the map delineates various escape thresholds for different attractors present in the system. Our work unveils the properties of the cantilever oscillation in proximity to the sample surface, which is governed by the so-called in-contact attractor. The robustness of this attractor against operating parameters is quantified by means of integrity profiles. Our work provides a unique view into global dynamics in tapping mode atomic force microscopy and helps establishing an extended topological view of the system.

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In the field of nanomechanics, parametric excitations are of interest since they can greatly enhance sensing capabilities and eliminate cross-talk. Above a certain threshold of the parametric pump, the mechanical resonator can be brought into parametric resonance. Here we demonstrate parametric resonance of suspended single-layer graphene membranes by an efficient opto-thermal drive that modulates the intrinsic spring constant. With a large amplitude of the optical drive, a record number of 14 mechanical modes can be brought into parametric resonance by modulating a single parameter: The pre-tension. A detailed analysis of the parametric resonance allows us to study nonlinear dynamics and the loss tangent of graphene resonators. It is found that nonlinear damping, of the van der Pol type, is essential to describe the high amplitude parametric resonance response in atomically thin membranes.

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