Have you ever wondered how nature manages to create such intricate and resilient structures? Researchers at the University of Michigan are diving into this very question. By studying the unique geometries of coccolithophore shells, they’re uncovering how mismatched building blocks can lead to complex structures with remarkable properties. These natural mismatches, known as geometric frustrations, are the secret behind protective shells and strong yet flexible bones. Through clever mathematical modeling, the team hopes to mimic these natural strategies to craft advanced materials for things like medical devices and eco-friendly construction.
Xiaoming Mao, a physics professor and the senior author of the study, sees immense potential in using frustration as a design tool. ‘Frustration—using these mismatched building blocks—gives rise to wonderful complexity, and that complexity can be useful in providing superior material properties,’ she explained. This insight, sparked by the geometric shells of coccolithophores, has opened the door to discovering similar strategies throughout nature.
The researchers are tapping into graph theory to figure out how structures can hit that sweet spot of frustration. By creating phase diagrams, they can predict material properties based on the arrangement of building blocks. It’s all about understanding two types of frustration: noncumulative, where irregular shapes just won’t line up neatly, and cumulative, where shapes can’t pack together perfectly.
Take tiling a surface with pentagons, for example—it’s a classic case of geometric frustration. The study found that while some organization in block and void structures is crucial, too much order can actually weaken material properties. Mao points out, ‘A simple crystal doesn’t give you what you want, but something completely disorganized won’t work either.’ The trick is finding that perfect balance.
Published in Physical Review Letters, this research includes contributions from Nicholas Kotov, a professor of chemical engineering, and graduate students José Ortiz-Tavárez and Zhen Yang. The team is continuing their work at COMPASS, a National Science Foundation research center, aiming to bring their models to life in real-world materials. They’re connecting complexity with functionality through AI and data analysis.
