Polymer scientists from the University of Massachusetts at Amherst recently announced in a journal The nature of communication that they solved a long-standing mystery around a nanoscale structure formed by collections of molecules called a double hero. This form is one of the most desired for materials scientists, and has a wide range of applications; but, so far, a predictable understanding of how these forms are formed has not been provided by researchers.
“There is a wonderful interaction between pure mathematics and materials science,” says Greg Grasson, senior author and professor of polymer science and technology at UMass Amherst. “Our work explores how materials assemble themselves into natural forms.”
These forms can take different forms. They can be as simple as a layer, a cylinder or a sphere. “It needs to be like soap films,” adds Michael Dmitriev, a doctoral student in polymer science and technology at UMass Amherst and one of the co-authors. “There is an intuitive understanding of the shapes that molecules can create, such as soap. What we’ve done is uncover a hidden geometry that allows polymers to take the shape of a double hyroid.”
What does a double hyroid look like? It’s not intuitive. “They’re somewhere between a layer and a cylinder,” says Abhir Redi, a Northwestern doctoral student who completed this research as part of his postgraduate studies at UMass Amherst and lead author of the article. In other words, imagine a flat piece of window screen – a layer – and then roll it into a saddle-shaped layer that fits into a cubic box so that its surface area remains as small as possible. This is a hero. A double hyroid is when the second material, also twisted into a hyroid, fills in the gaps in the first hyroid. Each gyroid material forms a network of tubes that interpenetrate the other. Together they form an extremely complex material that is symmetrical on all sides, like many crystals, but imbued with a maze of channels, each formed of different molecular units. Since this material is a hybrid of two hyroids, it can be created to have conflicting properties.
These double gyroids have existed in nature and have been observed for a long time, but so far no one has understood how chain molecules known as block copolymers know how to form double hyroids. Reddy and his co-authors built on a previous theoretical model, adding a large dose of thermodynamics and a new approach to thinking about the packaging problem – or how best to fill a container container with material – borrowed from computational geometry and known as the medial map. Because copolymers must stretch to occupy each part of a self-assembled structure, understanding this formation requires knowing how molecules “measure the middle” of shapes, like hyroids, which are much more complex than spheres and cylinders. The updated theoretical model of the team not only explains the mysterious formation of double gyroids, but also promises to understand how the problem of packaging works in a much wider mass of self-assembled add-ons such as double diamonds and double primitives, or even structures not yet discovered.
Researchers funded by the U.S. Department of Energy plan to collaborate with synthetic chemists to begin refining their theory with experimental data. The ultimate goal is to be able to develop a wide range of materials that take advantage of the double hyroid structure and that can help advance a wide range of technologies from rechargeable batteries to reflective coatings.
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