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The Ideal Shape

Researchers from São Paulo and Minas Gerais show how to build carbon nanotubes that slide almost without friction

SERGIO LEGOAS / UNICAMP Virtual dumbbells: the best format for a nano-oscillator, working without any loss of energySERGIO LEGOAS / UNICAMP

The two structures on the right are reminiscent of a pair of dumbbells, but they would never be of any use in doing exercises. Actually, they represent tubes made up of 6,000 carbon atoms, the same chemical element that makes up pencil leads – that is very small, even compared with a simple pinhead, which is made up of a quantity of atoms that corresponds to the number 1 followed by 18 zeroes.

Visible here only because they were magnified 30 million times, these cylinders are part of a microscopic world in which phenomena are by laws that often escape from day to day logic, in which the unit of measurement is the nanometer, which is one billionth part of a meter. Made from a random association of carbon atoms from graphite vapor bombarded by a laser, the dumbbells, or nanotubes, as they are called, measure 1.4 nanometers in diameter – about 100,000 times less than the thickness of a strand of hair – and 8.2 nanometers in length. Actually, each dumbbell consists of two nanotubes: an outer one, and, inside it, a smaller one, represented in yellow in the diagram.

In an article that made the cover of the February 7 issue of the most important scientific magazine on physics, Physical Review Letters, a team made up of physicists from the State University of Campinas (Unicamp) and from Federal University of Juiz de Fora (UFJF) showed that the dumbbell format is the simplest shape to make it possible for this set of two nanotubes to work like a nano-oscillator: a mechanism in which, after an initial impulse, the smaller tube moves from one extremity to the other in an interminable oscillatory movement, capable of lasting a practically indefinite period of time.

Nanotubes are something like the Lilliputians, the tiny inhabitants of Lilliput, the city created by Irish writer Jonathan Swift in Gulliver’s Travels, in the eyes of the giant who gives the book its name. The role of Gulliver is played by today’s electronic oscillators, 10 million times bigger. It is nowadays with these devices that one manages to generate or to capture electromagnetic waves, like those used in transmissions by radio, television and mobile telephony. Another example in daily life of devices with oscillators is the computer, in which the clock, which indicates speed, registers the average number of operations that the processor (chip) is capable of carrying out each second.

In ten years, nano-oscillators may lead to a new generation of electronic equipment, with carbon instead of silicon as the raw material. They would make it possible to generate new telecommunications transmission bands and electrical and electronic equipment that would be quicker and more durable, since the material is extremely resistant. For the time being, the dumbbells exist only in a virtual environment, but they already symbolize an economical and versatile alternative, capable of operating at frequencies almost 40 times higher than today’s oscillators, reaching up to 38 gigahertz (GHz) – one hertz, the unit of measurement of frequency, corresponds to one oscillation per second. “The great merit of this work was to have surpassed the gigahertz barrier”, says physicist Douglas Soares Galvão, from Unicamp, who coordinated the study, which was done using simulations on a computer.

Nanotubes are becoming viable as the technology for their manufacture, now at the initial stage, is mastered and production costs fall – something that is a little closer to happening, as in a few years a set of international patents expires, which would make the price of nanotubes plummet from today’s US$ 1,000 a milligram to less than US$ 100 a kilo. Once these obstacles have been overcome, nanotubes gain military applications. Without the cylinders at their ends, they would work like nanocannons. Launched at over 1,500 meters a second, equivalent to the speed of a rifle bullet, the inner nanotube would be a sort of nanobullet, overcoming the force that keeps it inside the larger tube, called the Van der Waals force, which explains the reciprocal attraction between neutral molecules (without any electric charge), like the nanotubes.

The idea of using simulations on a computer to assess whether nanotubes would work as oscillators arose last June at Unicamp’s Physics Institute, when the suspicion was raised that the results of a study published a few months before could be wrong. In January 2002, Quanshui Zheng, from Tsinghua University, in China, and Qing Jiang, from the University of California, in the United States, suggested in the Physical Review Letters that carbon nanotubes could generate nano-oscillators capable of operating at several frequencies in the order of gigahertz. They proposed the use of somewhat different nanotubes – the larger of them without any cylinders at the ends and with one of the extremities closed. Furthermore, they had done the calculations for a set of static nanotubes, without taking into consideration the effects of the increase in temperature – which makes the atoms vibrate more intensely – nor the passage of time, which makes it possible to get to know how the tubes interact during movement.

Sergio Legoas, Scheila Braga and Vitor Coluci, from Galvão’s team, created the programs that generated the structures automatically, carried out the simulations of the nanooscilators, and, finally, showed that there was a mistake in the model used by the Chinese. As it had been proposed, the nanotube system would not work: simulations showed that the inner tube, when it started to oscillate, would bang into the closed off wall and start to vibrate, which would prevent the continuation of movement. The indication that led to the dumbbell shape arose from work published in Science two years previously, by Alexander Zettl and John Cumings, from the University of California at Berkely.

In it, it was shown in experiments that nanotubes made up of multiple layers showed an oscillatory movement: when a nanotube was pushed further inside, it moved outwards until almost escaping, but would return to the inside of the larger nanotube by moving in the opposite direction – evidence of the action of the Van der Waals force, which increases in proportion to the area of the inner tube exposed outside the larger tube.

Adding the articles to the simulations, the Brazilian team concluded that the most important thing in order to let the inner tube slides without any friction inside the larger nanotube was the free space between them. Using a series of calculations, the group found that the radius of the outer tube should be 3.4 ångströms (one ångström corresponds to one tenth of a nanometer) larger than the inner one. But the problem was only partly resolved. If they assembled the nanooscillator on the basis of this information alone, the nanotube would look like pipe with the two extremities open, containing a capsule in the inside. They had to get a shape that would prevent the entry of free atoms, which would act as impurities and hamper the movement of the smaller tube. “In three months, we arrived at the dumbbell format, the simplest configuration possible”, says Galvão. “Nobody believed that there existed in nature a system like this, capable of working almost without any friction.”

With this shape and this distance between the tubes, the oscillator was capable of functioning practically without losing any energy in the form of heat caused by attrition between the walls. It was still not enough, though. A mechanism like this has to be capable of working at room temperature, 25° Celsius.

Repeating the simulations, Galvão found that the system of nanotubes worked in a stable manner not only at the temperature of 0 kelvin, which corresponds to -273º Celsius, and was adopted in the calculations for representing one of the conditions in which atoms practically stop vibrating. It would also remain efficient at a temperature of 400 kelvin (127º Celsius), vibrating at a frequency of up to 38 GHz. “In the simulation, the nanooscillator would work over an indefinite period, without needing to be given a new impulse”, says Galvão. “In the real world, though, as there are small disturbances, the system would need to be fed with a very small amount of energy.”

The team of researchers from São Paulo and Minas is now working to discover a practical manner of setting the internal nanotube of the oscillator into movement. The initial proposal, suggested by physicians Pablo Coura and Sócrates Dantas, from Juiz de Fora, in Minas Gerais, would be to use the magnetic field of a sort of electromagnet, to give the initial push in the oscillator. To do so, the inner tube, albeit made of carbon, would have to act like a metal, and the outer one, like an insulating material. In the tests in which they assessed the maximum speed at which the inner nanotube could move without escaping from the dumbbell, the physicists discovered that when it reached a speed of 1,500 meters a second the inner nanotube wold be violently shot out of the oscillator.

It was from this result that the idea arose of using the nanotubes as a nanocannon. Galvão’s team managed to create equations that were capable of foreseeing the impact of a nanobullet, and it is now doing experiments – always in a virtual environment – to increase the projectile’s firepower. The best results obtained happened when cubane molecules are encapsulated inside the inner tube. Cubanes are molecules made up of eight carbon atoms and eight hydrogen atoms which are bound together to form a cube – hence the name.

Anyhow, to provide an effective military application – something that still belongs to the field of fiction -, billions of nanocannons would have to be gathered together in a few centimeters. Like this, if they were put into a satellite, the nanotubes could be fired against an enemy satellite, thus recalling the hypothetical scenario of the Star Wars, the American defense program revived in the 80’s by former president Ronald Reagan. “But a very large quantity of nanocannons would be needed to produce a significant impact, because a single nanocannon would only be effective against a nanosatellite”, Galvão jokes.

The Project
Theoretical Systematic Mapping of the Structure-Function Relationship in Conjugated Polymers of Technological Interest (nº 99/07339-4); Modality Thematic project; Coordinator Marília Junqueira Caldas – Physics Institute/Unicamp; Investment R$ 384,613.83