Complex amphiphilic structures are closely related to phase transitions, materials science, and mathematical biology. This project concentrates on the influence of nanoparticles, proteins and hydrophobic surfaces on the morphology of amphiphilic structures. This research greatly advances the understanding of the functionality of nanoparticles, bio-inspired materials, and biological membranes. It helps us understand essential processes like protein transportation, drug encapsulation, and drug delivery. It also provides new methods and techniques for the modeling and analysis of properties of other complex structures in polymeric materials. The educational activities include the supervision and training of graduate research. The educational goal is for graduate students to be trained in mathematical modeling, and in the analysis and numerical simulation of partial differential equations.
This research project concentrates on interdisciplinary research that combines applied mathematics and science, technology, and engineering. The PI is an applied mathematician, and the co-PI is a chemical experimentalist. The investigators model the encapsulation of nanoparticles in bilayer liposomes and polymeric micelles, the coating of biomaterials by amphiphilic copolymers, and the change of morphology caused by proteins, in the framework of the functionalized Cahn-Hilliard (FCH) energy, coupled with proper strong and weak anchoring conditions. This new mathematical framework translates the materials system into nonlinear PDEs coupled with proper boundary conditions. It has wide applications in the modeling of other physical, materials and biological systems. The PIs apply existing and new mathematical tools for the study of nonlinear PDEs. These tools lie in three areas: asymptotic analysis, variational methods, and numerical simulations. They are very useful in the study of other problems in applied mathematics related to nonlinear PDEs.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
