Theoretical Modeling of Polymeric and Biological Nanostructured Materials

Polymer coatings on periodic nanostructures have facilitated advanced applications in various fields. The performance of these structures is intimately linked to their nanoscale characteristics. Smart polymer coatings responsive to environmental stimuli such as temperature, pH level, and ionic strength have found important uses in these applications. Therefore, to optimize their performance and improve their design, precise characterization techniques are essential for understanding the nanoscale properties of polymer coating, especially in response to stimuli and interactions with the surrounding medium. Due to their layered compositions, applying non-destructive measurement methods by X-ray/neutron scattering is optimal. These approaches offer unique insights into the structure, dynamics, and kinetics of polymeric coatings and interfaces. The caveat is that scattering methods require non-trivial data modeling, particularly in the case of periodic structures, which result in strong correlations between scattered beams. The dynamical theory (DT) model offers an exact model for interpreting off-specular signals from periodically structured surfaces and has been validated on substrates measured by neutron scattering. In this dissertation, we improved the model using a computational optimization approach that simultaneously fits specular and off-specular scattering signals and efficiently retrieves the three-dimensional sample profile with high precision. In addition, we extended this to the case of X-ray scattering. We applied this approach to characterize polymer brushes for nanofluidic applications and protein binding to modulated lipid membranes. This approach opens new possibilities in developing soft matter nanostructured substrates with desired properties for various applications.