The effective determination of the hydrodynamic sizes of nanomaterials functionalized with various coatings is a topic of intense research. Analytical ultracentrifugation, a lesser known characterization method that provides hydrodynamic size via a parameter termed the sedimentation coefficient, provides this information in a manner unsurpassed by alternative methods. In the first part of this thesis, I present the application of analytical ultracentrifugation to ligand-stabilized nanocrystals of cadmium selenide, iron oxide, and gold in organic solvents. This method was able to provide distinct sedimentation coefficients for these model nanocrystals, some of which were different in diameter by only an ångstrom. Further, we show that the sedimentation coefficient has a significant dependence on the density of the composite material, which is based on the size of the nanomaterial and surface coating. Therefore, we introduced a descriptive size-dependent term into conventional models that accounts for both the inorganic core and organic coating to more accurately represent the overall density. We also explored the effects of different approaches for analytical ultracentrifugation data analysis on the sedimentation coefficients obtained and found that all methods yielded the same value. Finally, we elucidated experimental parameters for the ultracentrifuge that specifically affect nanomaterial samples and established best practices for studying sedimentation for these types of materials. The results from this work allow for better agreement between experimental and theoretical sedimentation coefficients, which is useful for accurately evaluating hydrodynamic sizes of nanomaterials.

In the second part of this thesis, the relationship between protein surface charge and gold nanoparticle aggregation is explored by using pH variation and chemical modification. Lysozyme and α-lactalbumin share a common three-dimensional fold but have significantly different isoelectric points (pI) and surface charge distributions. Myoglobin is also a small globular protein with a pK intermediate between α-lactalbumin and lysozyme, and a variant with a specific sulfhydryl group has been generated. These proteins have been conjugated to gold nanoparticles under varying pH conditions and following chemical modifications that impact the protein's pI. Changes in UV-visible spectra, TEM distribution, and dynamic light scattering indicate that significant aggregation depends on a positively charged protein surface.