The measurement of nanomechanical properties is of great interest to science and industry. Key to progress in this area is the development of new techniques and analysis methods to identify, measure, and quantify these properties. In this dissertation, new data analysis methods and experimental techniques for measuring nanomechanical properties with the atomic force microscope (AFM) are considered. These techniques are then applied to the study of cellulose nanoparticles, an abundant, plant derived nanomaterial. Quantifying uncertainty is a prerequisite for the manufacture of reliable nano-engineered materials and products. However, rigorous uncertainty quantification is rarely applied for material property measurements with the AFM. A framework is presented to ascribe uncertainty to local nanomechanical properties of any nanoparticle or surface measured with the AFM by taking into account the main uncertainty sources inherent in such measurements. This method is demonstrated by quantifying uncertainty in force displacement AFM based measurements of the transverse elastic modulus of tunicate cellulose nanocrystals. Next, a more comprehensive study of different types of cellulose nanoparticles is undertaken with contact resonance (CR) AFM. CR-AFM is a dynamic AFM technique that exploits the resonance frequency of the AFM cantilever while it is permanent contact with the sample surface to predict nanomechanical properties. This technique offers improved measurement sensitivity over static AFM methods for some material systems. The effects of cellulose source material and processing technique on the properties of cellulose nanoparticles are compared. Finally, dynamic AFM cantilever vibration shapes are studied. Many AFM modes exploit the dynamic response of a cantilever in permanent contact with a sample to extract local material properties. A common challenge to these modes is that they assume a certain shape of cantilever vibration, which is not accessible in standard AFM measurements. A method is presented to measure these vibrational shapes. This method is then used to study CR-AFM, providing unique insight into CR-AFM modeling and experiments. The methodologies discussed in this dissertation provide improved capability to measure nanomechanical properties with the AFM.
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