A paper in the online journal Physical Review Letters unveils an elegant formula by Rice University physicist Boris Yakobson and his colleagues that defines the energy of a piece of graphene cut at any angle.
Yakobson said it would be a real game-changer if they could, for instance, grow batches of pure armchair nanotubes for use in such projects as armchair quantum nanowire (AQW). As imagined by Rice’s late Nobel Laureate Richard Smalley, AQW could revolutionize the nation’s power grid by carrying 10 times the amount of electricity as copper at only one-sixth the weight.
Yakobson’s work may open a path to do so. A nanotube’s chirality is determined by the combination of energies at play in its nucleation. “When it just emerges from the ‘primordial soup’ of carbon, the edge of the tube is essentially the same as the edge of graphene,” he said.
“At first, it’s just a cap. There’s no stem yet. You’re frying these caps on a skillet, and they’re bubbling,” he said. “The probability for different bubbles to emerge is controlled by energy around the edge.”
Yakobson, a professor in mechanical engineering and materials science and of chemistry, said this alone is significant because the way graphene handles energy depends upon the angle — or chirality — of its edge, and solving that process for odd angles has been extremely challenging. But, he wrote, the research has “profound implications in the context of nanotube growth, offering rational ways to control their chiral symmetry, a tantalizing yet so far elusive goal.”
Graphene is the single-atom-thick form of carbon that has become of tremendous interest for its potential to revolutionize electronics, optics, sensing and mechanical devices. Getting a handle on how this chicken-wire-shaped sheet of carbon atoms transports electricity has been the focus of intense study.
A sheet of graphene with zigzag or armchair edges squares up nicely. Zigzags are metallic, armchairs are semiconductors, and their atoms march in rank, evenly spaced, along the edges. A full 30 degrees of rotation separates one from the other.
But if the hexagons that make up a sheet are offset less than 30 degrees, atoms along a straight edge are unevenly spaced. “That makes analysis of the energy very complicated, because it’s a large irregular structure. It’s like noise,” Yakobson said. “We’ve found a way to calculate the energies in these arbitrary angles,” he said.
The energy of an arbitrary graphene edge, from armchair (A) to zigzag (Z) orientation, is derived in analytical form. It contains a “chemical phase shift” determined by the chemical conditions at the edge. Direct atomistic computations support the universal nature of the relationship, definitive for graphene formation, and shapes of the voids or ribbons. It has further profound implications for nanotube chirality selection and possibly control by chemical means, at the nucleation stage.
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