Mathematics of Self-Assembled Materials

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The ability of systems to assemble and organize without direct control or intervention is fundamental to biological and non-biological systems. Materials such as complex polymers may self-assemble into a wide variety of forms, and have many nanotechnology and biomedical applications. This project studies models of material self-assembly to develop theoretical insight and predictive capabilities. Formulas are developed that connect microscopic molecular properties to mechanical and morphological behaviors at larger scales. Computations are employed for predicting novel behaviors and custom-tailoring inputs for engineered nanostructures. The award provides research and educational opportunities for both graduate and undergraduate students.This project broadly investigates polymer, amphiphilic, and particle-based systems, and processes fundamental to the creation of nanoscale materials. Models describing formation of nanoparticles and amphiphilic structures in heterogeneous polymer systems are examined using a mixture of analytical and computational approaches that quantify equilibria, morphology, and dynamics. In conjunction with these models, algorithms for inverse problems will be developed for purposes of parameter identification and engineering design. Self-assembled systems involving a large number of interacting particles are studied within the same framework, leading to predictions of pattern formation and collective behavior. Byproducts of the research include the development of numerical and inverse problem algorithms.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.