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"Honeycomb
Lattice"
Triangle Lattice
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Torquato and colleagues have published a paper
in the Nov. 25 issue of Physical Review Letters, the leading physics
journal, outlining a mathematical approach that would enable them to
produce desired configurations of nanoparticles by manipulating the
manner in which the particles interact with one another.
This may not mean much to the man on the street,
but to the average scientist it is a fairly astounding proposition.
"In a sense this would allow you to play God,
because the method creates, on the computer, new types of particles
whose interactions are tuned precisely so as to yield a desired
structure," said Pablo Debenedetti, a professor of chemical
engineering at Princeton.
The standard approach in nanotechnology is to come
up with new chemical structures through trial and error, by letting
constituent parts react with one other as they do in nature and then
seeing whether the result is useful.
Nanotechnologists rely on something called "self-assembly."
Self-assembly refers to the fact that molecular building blocks do not
have to be put together in some kind of miniaturized factory-like
fashion. Instead, under the right conditions, they will spontaneously
arrange themselves into larger, carefully organized structures.
As the researchers point out in their paper,
biology offers many extraordinary examples of self-assembly, including
the formation of the DNA double helix.
But Torquato and his colleagues, visiting research
collaborator Frank Stillinger and physics graduate student Mikael
Rechtsman, have taken an inverse approach to self-assembly.
"We stand the problem of self-assembly on its head,"
said Torquato, a professor of chemistry who is affiliated with the
Princeton Institute for the Science and Technology of Materials, a
multidisciplinary research center devoted to materials science.
Instead of employing the traditional
trial-and-error method of self-assembly that is used by
nanotechnologists and which is found in nature, Torquato and his
colleagues start with an exact blueprint of the nanostructure they
want to build.
''If one thinks of a nanomaterial as a house, our
approach enables a scientist to act as architect, contractor, and day
laborer all wrapped up in one," Torquato said. "We design the
components of the house, such as the 2-by-4s and cement blocks, so
that they will interact with each other in such a way that when you
throw them together randomly they self-assemble into the desired house."
To do the same thing using current techniques, by
contrast, a scientist would have to conduct endless experiments to
come up with the same house. And in the end that researcher may not
end up with a house at all but rather – metaphorically speaking --
with a garage or a horse stable or a grain silo.
While Torquato is a theorist rather than a
practitioner, his ideas may have implications for nanostructures used
in a range of applications in sensors, electronics and aerospace
engineering.
"This is a wonderful example of how asking deep
theoretical questions can lead to important practical applications,"
said Debenedetti.
So far Torquato and his colleagues have
demonstrated their concept only theoretically, with computer modeling.
They illustrated their technique by considering
thin films of particles. If one thinks of the particles as pennies
scattered upon a table, the pennies, when laterally compressed, would
normally self-assemble into a pattern called a triangular lattice.
But by optimizing the interactions of the "pennies,"
or particles, Torquato made them self-assemble into an entirely
different pattern known as a honeycomb lattice (called that because it
very much resembles a honeycomb).
Why is this important? The honeycomb lattice is the
two-dimensional analog to the three-dimensional diamond lattice – the
creation of which is somewhat of a holy grail in nanotechnology.
Diamonds found in nature self-assemble the way they
do because the carbon atoms that are the building blocks of diamonds
interact with each other in a specific way that is referred to as
covalent bonding. This means that each carbon atom has to bond with
exactly four neighboring atoms along specific directions.
One surprising and exciting feature of the
Princeton work is that the researchers were able to achieve the
honeycomb with non-directional bonding rather than covalent, or
directional, bonding.
"Until now, people did not think it was possible to
achieve this with non-directional interactions, so we view this as a
fundamental theoretical breakthrough in statistical mechanics,"
Torquato said. Statistical mechanics is a field that bridges the
microscopic world of individual atoms with the macroscopic world of
materials that we can see and touch.
To create the honeycomb lattice, the researchers
employed techniques of optimization, a field that has burgeoned since
World War II and which is essentially the science of inventing
mathematical methods to make things run efficiently.
Torquato and his colleagues hope that their efforts
will be replicated in the laboratory using particles called colloids,
which have unique properties that make them ideal candidates to test
out the theory. Paul Chaikin, a professor of physics at New York
University, said he is planning to do laboratory experiments based on
the work.
The paper appearing in Physical Review Letters is a
condensed version of a more detailed paper that has been accepted for
publication in Physical Review E and which will probably appear
sometime before the end of the year.
Torquato said that he and Stillinger initially had
trouble attracting research money to support their idea. Colleagues "thought
it was so far out in left field in terms of whether we could do what
we were claiming that it was difficult to get funding for it," he said.
The work was ultimately funded by the Office of Basic Energy Sciences
at the U.S. Department of Energy.
"The honeycomb lattice is a simple example but it
illustrates the power of our approach," Torquato said. "We envision
assembling even more useful and unusual structures in the future." |
