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.

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.

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.

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.