Science | DOI: 10.1145/1610252.1610259
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
The researchers find their optimal
potential functions using an iterative