In 2013, materials scientists at the Wyss Institute of Biologically Inspired Engineering and the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) grew a garden of self-assembled crystal microstructures. Now, applied mathematicians at the Wyss Institute and SEAS have developed a framework to better understand and control the fabrication of these microstructures.
Together, the researchers used that framework to grow sophisticated optical microcomponents. The research is published in Science.
When it comes to the fabrication of multifunctional materials, nature has humans beat by miles. Marine mollusks can embed photonic structures into their curved shells without compromising shell strength; deep sea sponges evolved fiber optic cables to direct light to symbiotically living organisms; and brittlestars cover their skeletons with lenses to focus light into the body to “see” at night. During growth, these sophisticated optical structures tune tiny, well-defined curves and hollow shapes to better guide and trap light.
Manufacturing complex bio-inspired shapes in the lab is often time consuming and costly. The breakthrough in 2013 was led by materials scientists Joanna Aizenberg, Ph.D., the Amy Smith Berylson Professor of Materials Science and Chemistry and Chemical Biology and Core Faculty member of the Wyss Institute and former Postdoctoral Fellow Wim L. Noorduin. The research allowed researchers to fabricate delicate, flower-like structures on a substrate by simply manipulating chemical gradients in a beaker of fluid. These structures, composed of carbonate and glass, form a bouquet of thin walls.
What that research lacked then was a quantitative understanding of the mechanisms involved that would enable even more precise control over these structures.
Enter the theorists.
Inspired by the theory to explain solidification and crystallization patterns, L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, Physics, and Organismic and Evolutionary Biology, and Postdoctoral Fellow C. Nadir Kaplan, Ph.D., developed a new geometrical framework to explain how previous precipitation patterns grew and even predicted new structures.
Mahadevan is also Core Faculty member of the Wyss Institute.
In experiments, the shape of the structures can be controlled by changing the pH of the solution they are formed in.
“At high pH, these structures grow in a flat manner and you get flat shapes, like the side of a vase,” says Kaplan, co-first author of the paper. “At low pH, the structure starts to curve and you get helical structures.”
When Kaplan solved the resulting equations as a function of pH, with a mathematical parameter standing in for the chemical change, he found that he could recreate all the shapes developed by Noorduin and Aizenberg — and come up with new ones.