Polymers are fascinating materials that can organise themselves into complex patterns, giving them highly desirable properties. The goal of this project is to understand how this self-assembly works using mathematical methods.
Studying pattern formation
Society’s growing demand for sustainable, high-performance products makes it extremely important to unravel the inner workings of the polymer materials of the future. These will have the ability to adapt, reshape, and self-repair. However, a deep understanding of the mechanisms behind such pattern formation is needed before this vision can become a reality. While heuristic arguments and computer simulations help, they often fall short in providing a complete understanding. This is where mathematical analysis becomes essential.
Challenges and goals
So far, only simple linear polymer structures have been studied mathematically, presenting interesting challenges for mathematicians. This project aims to go further by studying more complex polymer structures, both in bulk and in thin films, which are important for practical applications. This project will push the frontiers of mathematical investigations by considering, for the first time, more complex architectures of copolymers in the bulk and in thin films, which are cases of high interest for applications. We will provide a sound understanding of the mechanisms that regulate pattern formation in such complex systems by using rigorous mathematical tools.
Impact
The outcomes of this project will open new directions of mathematical research, which will inspire the future works of analysts. Furthermore, it will provide experimental scientists and simulation researchers with powerful mathematical insights to interpret their findings.
