Viscoelasticity is a material property that is relevant in a variety of nanoscale materials and interfaces in medicine and industry. Therefore, a method of mechanical quantification has become exceedingly desired. In this thesis the Atomic force microscope (AFM) is applied to accurately characterize the mechanical behavior of viscoelastic samples. The goal is to enhance viscoelastic characterization using the so-called Intermodulation AFM (ImAFM) technique by applying, adapting and improving multiple modelling and optimization methods. In ImAFM force reconstruction is performed by extracting intermodulations around resonance in the cantilever response. These intermodulations present new observables that can be used for characterization. This thesis investigates the potential of this technique in combination with an up-and-coming model describing viscoelastic interaction. A toolbox has been developed for numerical simulations of the model to resemble the experiments. The model has been evaluated in a variety of situations using sensitivity analysis in a large feasibility range, encompassing many complex dynamics. Because of the diversity in model dynamics a global optimization has been performed for experimental reconstruction.

Suspended microfluidic resonators enable detection of fluid density and viscosity with high sensitivity. Here, a two-legged suspended microchannel resonator that probes pico-litres of liquid is presented. The higher resonant modes (flexural and torsional) were explored for increased sensitivity and resolution. Unlike other reported microchannel resonators, this device showed an increase in the quality factor with resonant frequency value. The performance of the resonator was tested by filling the channel with three liquids, one at a time, over a density range of 779 - 1110 Kg/m^3 and a viscosity range of 0.89 - 16.2 mPa.s. The highest resolution obtained was 0.011% change in density. Measurements with torsional mode showed an improvement of about six times in sensitivity and about fifteen times in resolution compared to the first flexural mode. When the empty channel was filled with liquids of different viscosity, the quality factor of the first flexural mode remained overall constant with a variation below 3.3% between the fluids, and confirming the inherent property of suspended microchannel resonators. However, it significantly decreased for second flexural and torsional modes. No noticeable difference was observed in the quality factor between different liquid viscosities for all modes.@en

Dynamic Atomic Force Microscopy (dAFM) is an extremely powerful tool for exploring surface topology and nanoscale manipulation and characterization. A feature of dAFM is the existence of highly nonlinear forces between a cantilever tip and sample. One of these forces that plays a large role in operation of AFM is the van der Waals (vdW) force. This force is characterized in part by the Hamaker constant H and cantilever tip radius R. Measuring these two properties quickly and accurately can facilitate further characterization methods in dAFM. This research will focus on creating methods in which H and R can be extracted using the dynamic response of a cantilever. The vdW force was used to extract H by analyzing the softening behavior of Frequency Response Curves (FRCs). Electrostatic forces were used to extract R by applying a simplified Kelvin Probe Force Microscopy (KPFM) technique. The method to extract H was demonstrated numerically, and the method to extract R was proven experimentally and validated using a Scanning Electron Microscopy (SEM) image.

Diamond is a highly desirable material for state-of-the-art micro-electromechanical (MEMS) devices, radio-frequency filters and mass sensors, due to its extreme properties and robustness. However, the fabrication/integration of diamond structures into Si-based components remain costly and complex. In this work, a lithography-free, low-cost method is introduced to fabricate diamond-based micro-resonators: a modified home/office desktop inkjet printer is used to locally deposit nanodiamond ink as ∅50–60 µm spots, which are grown into ≈1 µm thick nanocrystalline diamond film disks by chemical vapor deposition, and suspended by reactive ion etching. The frequency response of the fabricated structures is analyzed by laser interferometry, showing resonance frequencies in the range of ≈9–30 MHz, with Q-factors exceeding 10⁴, and (f₀ × Q) figure of merit up to ≈2.5 × 10¹¹ Hz in vacuum. Analysis in controlled atmospheres shows a clear dependence of the Q-factors on gas pressure up until 1 atm, with Q ∝ 1/P. When applied as mass sensors, the inkjet-printed diamond resonators yield mass responsivities up to 981 Hz fg⁻¹ after Au deposition, and ultrahigh mass resolution up to 278 ± 48 zg, thus outperforming many similar devices produced by traditional top-down, lithography-based techniques. In summary, this work demonstrates the fabrication of functional high-performance diamond-based micro-sensors by direct inkjet printing.

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Despite numerous theoretical investigations on the mechanical properties of graphene, an accurate identification of its material behavior is still unattained. One hypothesis for this uncertainty is that modeling graphene as a static membrane cannot describe the strong coupling between mechanics and thermodynamics of this structure. Therefore, characterization methods built upon static models could not capture these effects. In this paper, we propose a new method for building a reduced order model for the dynamics of thermalized graphene membranes. We apply the proper orthogonal decomposition algorithm on time responses obtained from molecular dynamics simulations. As a result, a set of orthogonal modes is obtained which are then employed to build a reduced order model. The proposed model can describe the motion of the suspended graphene membrane over the whole spatial domain accurately. Moreover, due to its computational efficiency, it is more versatile for exploring the nonlinear dynamics of the system. This model is then employed for studying the nonlinear dynamics of graphene membranes at large amplitudes to extract Young's modulus. The obtained Young's modulus incorporates the effects of nano-scaled thermally induced dynamic ripples and hence, is temperature and size dependent. Our proposed atomistic modal order reduction method provides a framework for studying the dynamics and extracting the mechanical properties of other nano-structures at the molecular level.

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Micro and Nano-mechanical resonators are becoming increasingly ubiquitous in the areas of particle characterization and biological sensing. For biological sensing, however, the presence of a liquid environment is a pre-requisite. Hollow cantilevers, which allow fluids to be transported inside the resonator, often have high quality factors even when the channels are filled with fluids. This makes them attractive for both sensing mass and determining fluid properties in small volumes. This work aims at determining the density of fluids in picoliter volumes with high resolution using hollow cantilevers. In order to achieve this, we obtain the resonance frequencies of the vibrating microstructure linked to three different modes: the first two flexural modes and the first torsional mode. The first torsional mode is unique to our device and is enabled by the specific geometry of the hollow cantilever. Our approach involves filling the resonator channels with three different fluids in vacuum and monitoring the resonance frequencies and quality factors of the three modes. As the mode number increases, we observe that the shifts in resonance frequency and quality factor for each liquid also increase. This implies that as we approach higher mode numbers there is an improvement in the sensitivity and resolution of the density measurement technique. The quality factors for the three fluids for a specific mode are not significantly different. It is found that in order to achieve higher sensitivities and improved resolution in determining fluid properties, studying higher modes of hollow cantilevers in improved vacuum could indeed be an effective solution.

The bending rigidity of two-dimensional (2D) materials is a key parameter for understanding the mechanics of 2D NEMS devices. The apparent bending rigidity of graphene membranes at macroscopic scale differs from theoretical predictions at micro-scale. This difference is believed to originate from thermally induced dynamic ripples in these atomically thin membranes. In this paper, we perform modal analysis to estimate the effective bending rigidity of graphene membranes from the frequency spectrum of their Brownian motion. Our method is based on fitting the resonance frequencies obtained from the Brownian motion in molecular dynamics simulations, to those obtained from a continuum mechanics model, with bending rigidity and pretension as the fit parameters. In this way, the effective bending rigidity of the membrane and its temperature and size dependence, are extracted, while including the effects of dynamic ripples and thermal fluctuations. The proposed method provides a framework for estimating the macroscopic mechanical properties in other 2D nanostructures at finite temperatures.

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Biomechanics of cells have been identified as an important factor relating to their functionalities. Consequently, the need for sensitive measurement methods for mechanical analysis on the nano- and microscale is high. Micro-cantilever resonators can have a large impact in material determination at the nanoscale. When adding a material, the resulting shift in resonance frequency is associated with its mass and stiffness properties. The goal of this project is to exploit the contribution of higher flexural modes on the determination of both the density and Young's modulus of an added polymer on a micro-cantilever.
The identification of mass and stiffness is, in this thesis, restricted to the deposition of a two-photon polymerized layer on micro-cantilevers. A polymeric material is used, since cells are complex systems with viscoelastic properties, where polymers are less complex and mimic biological matter very well. Two configurations are investigated: an added polymer near the tip of the cantilever and a polymeric layer near the base of the beam. Experimentally and theoretically derived multi-modal analysis are linked, to decouple the mass and stiffness properties.
The added polymeric layer affects the resonance frequency of the system, which is found to be location and mode related. Decoupling of the mass and stiffness properties based on the modes with the largest frequency shift, lead to different outcomes compared to considering modes with the largest deflection and curvature at a specific location. The use of higher modes does affect the outcomes of the decoupling of mass and stiffness. Whether it leads to an increase on accuracy is yet elusive.

Linear and non-linear vibrations of a U-shaped hollow microcantilever beam filled with fluid and interacting with a small particle are investigated. The microfluidic device is assumed to be subjected to internal flowing fluid carrying a buoyant mass. The equations of motion are derived via extended Hamilton's principle and by using Euler-Bernoulli beam theory retaining geometric and inertial non-linearities. A reduced-order model is obtained applying Galerkin's method and solved by using a pseudo arc-length continuation and collocation scheme to perform bifurcation analysis and obtain frequency response curves. Direct time integration of the equations of motion has also been performed by using Adams-Moulton method to obtain time histories and analyze transient cantilever-particle interactions in depth. It is shown that exploiting near resonant non-linear behavior of the microcantilever could potentially yield enhanced sensor metrics. This is found to be due to the transitions that occur as a matter of particle movement near the saddle-node bifurcation points of the coupled system that lead to jumps between coexisting stable attractors.

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The accuracy of measurements in Amplitude Modulation Atomic Force Microscopy (AFM) is directly related to the geometry of the tip. The AFM tip is characterized by its radius of curvature, which could suffer from alterations due to repetitive mechanical contact with the surface. An estimation of the tip change would allow the user to assess the quality during imaging. In this work, we introduce a method for tip radius evaluation based on the nonlinear dynamic response of the AFM cantilever. A nonlinear fitting procedure is used to match several curves with softening nonlinearity in the noncontact regime. By performing measurements in this regime, we are able to maximize the influence of the tip radius on the AFM probe response, and this can be exploited to estimate with good accuracy the AFM tip radius.@en