The intricate geometries of shells made by single-celled plankton called coccolithophores inspired University of Michigan researchers to understand how mismatched building blocks can yield complex behaviors and desirable material properties. Image credit: F. M. Monteiro et al. Sci. Adv. (2016) DOI: 10.1126/sciadv.1501822 (Used under a CC BY-SA 4.0 license)

Anyone who’s ever tried tiling a floor, a backsplash or even an arts-and-crafts project probably knows the emotional frustration of working with pieces whose shapes don’t perfectly complement each other.

It turns out, though, that some creatures may actually rely on similar mismatches to create geometric frustrations that result in complex natural structures with remarkable properties, such as protective shells and sturdy yet flexible bones.

Now, researchers at the University of Michigan have developed mathematical models showing one way that nature achieves this. These models, in turn, could help design advanced materials for medical devices, sustainable construction and more.

“Frustration—using these mismatched building blocks—gives rise to wonderful complexity and that complexity can be useful in providing superior material properties,” said Xiaoming Mao, U-M professor of physics and senior author of the new study.

Mao’s research group has always been interested in the relationship between a material’s structures and its properties. But this particular project was inspired by a picture she saw of single-celled organisms called coccolithophores that make beautiful geometric shells out of calcium carbonate.

That got her wondering how these simple organisms could use basic ingredients to create complex structures. As the researchers dug into the problem, they found this strategy was not confined to the coccolithophores.

“There are many, many examples in nature,” Mao said. “And geometric frustration is one of the pathways that leads to these incredible structures.”

You may read the rest of the story on the University of Michigan News website.

More information: 

Xiaoming Mao

Study: Statistical mechanics of frustrated assemblies and incompatible graphs (DOI: 10.1103/PhysRevLett.134.147401)