Nnews

Science | DOI: 10.1145/1610252.1610259
Gary Anthes

Blueprints for
Self-assembly

Researchers are using tools from information theory and computer science to facilitate the automatic creation of nanoscale structures.

SelF-ASSeMBly, By which atoms, molecules, or other nanoscale components pontaneously organize into something useful, sounds so simple. Just mix a few chemicals and wait for a new plastic, drug, or electronic component to form at the bottom of your test tube.

Unfortunately, it’s not so easy. Coaxing tiny particles to arrange themselves in an orderly way, with desirable and repeatable properties, is enormously complex, typically involving a great deal of trial and error in the laboratory.

But now two mathematicians, using tools from information theory and computer science, have found a new and relatively simple way to orchestrate the assembly of nanostructures. And they have devised algorithms that can produce mathematical proofs that their structures are optimum.

Henry Cohn, a principal researcher at Microsoft Research New England and Abhinav Kumar, an assistant professor of mathematics at Massachusetts Institute of Technology, have employed a rich mix of techniques—including heuristic algorithms, linear programming, search optimization, and error-correc-

the Schlegel diagram for a regular 120-cell structure (with a dodecahedral facet in red) from henry Cohn and abhinav Kumar’s self-assembly research.

tion theory—to produce their results.

Writing in a recent issue of Proceedings of the National Academy of Sciences, Cohn and Kumar describe their success in designing a system to direct 20 randomly placed particles on a sphere to form into a perfect dodecahedron with 12 pentagonal faces, a structure that minimizes potential energy and, hence, maximizes stability.

Although the methods have yet to be implemented in a lab, they may ultimately find use in such diverse fields

as electronics, communications, and medicine. For example, Cohn says, a drug company might produce a time-release drug by encapsulating tiny drug droplets in structures, such as dodecahedrons, that have certain desired properties. The idea is to simplify the search for the proper materials and conditions for self-assembly of such things.

The forces between particles determine whether or not they will organize into a stable and desired configuration. Cohn and Kumar’s blueprints for self-assembly specify the required inter-particle forces and distances via formulas called potential functions.

Traditional approaches to this problem use complex potential functions with multiple potential wells, local energy minima that cause the particles to settle into certain positions. But Cohn and Kumar devised a way to find potential functions that cause the particles to organize themselves more directly, without relying on local minima. The resulting formulas are simpler and, hence, would be much easier to implement in a lab or manufacturing line, they say.

In the second part of the problem, Cohn and Kumar go on to mathematically prove that the dodecahedron and several other structures built by their methods are in fact the unique ground states, or globally energy-min-imizing arrangements of particles. They do that using linear programming bounds, a tool borrowed from error-correction theory.