BioEd Online

Physicists have made a bizarre discovery: the concept of temperature is meaningless in some tiny objects. Although the concept of temperature is known to break down on the scale of individual atoms, research now suggests that it may also fail to apply in rather larger entities, such as carbon nanotubes.

The blossoming field of nanotechnology relies on being able to manipulate materials that are made from just a few thousand atoms. Carbon nanotubes, for example, are tiny cylinders that could be used to make miniature electronic devices.

Ortwin Hess from the University of Surrey, Guildford, UK and colleagues say that if you took the temperature at one end of a 10-micrometre nanotube, it would not necessarily have the same temperature as the other end, no matter how long it was left to reach a thermal equilibrium. Such a nanotube is about as long as a sheet of paper is thick.

"If you're down to a scale where temperature is not relevant, the fluctuations in physical properties of that system could be unpredictable, and that is potentially bad for any device," says Peter Atkins, a physical chemist at University of Oxford, UK.

The idea that temperature breaks down somewhere between the real world and the atomic scale is not necessarily surprising, says Hess. The breakthrough is in pinpointing exactly the size at which it happens, he says.

The location of that boundary also depends on the material in question, and the amount of heat energy it holds. And it may be difficult to measure the temperature of larger objects in particular circumstances.

For example, he says, a 10 centimetre-long silicon crystal cannot have a measurable temperature that is less than 1°C above absolute zero, the point at which an entity contains no heat energy. The size of the object in this example brings the effect crashing into the everyday world, he adds. The work is due to be published Physical Review Letters¹.

Statistical approach

"Our everyday experience of temperature is as a signpost for the flow of energy as heat," Atkins explains. In the real world, heat flows from objects of a higher temperature to objects of a lower temperature, so a mug feels warm when heat flows from it to our fingertips.

On the atomic scale, temperature is also a description of the distribution of heat energy among the many billions of atoms and molecules that make up the world around us.

Crucially, this is a statistical approach that assumes you are dealing with very large numbers of particles. For just one atom, such an approach is not meaningful, says Atkins. The statistics only start to make sense when considering dozens, or even hundreds of atoms. The big question is, how many?

Little Boxes

The team imagined how a series of separate compartments all joined together in a line would behave under different thermal conditions. In the real world, a compartment's temperature has some meaning because it can tell you in which direction heat energy will flow along the line. Eventually, the compartments should reach equilibrium and all have the same temperature.

But the physicists divided the compartments into smaller and smaller boxes, until they reached a point where the chain could never reach thermal equilibrium because of the statistical fluctuations inherent in the quantum world.

At this size limit, hot spots can sit next to cooler spots, without any energy flowing between the two. Moreover, the temperature of one compartment may fluctuate unpredictably over time. "It all boils down to the quantum uncertainty principle," says Hess.

"They're using some subtle arguments, but it looks about right," adds Atkins.

Size matters

The finding could shock some scientists working on nanoscale devices, who may not expect temperature to behave in this way.

Philip Moriarty, a nanotechnology expert at the University of Nottingham, UK, says that the idea of a size limit to temperature is fair enough, although the implications that it holds for nanotechnology remain to be shown in the laboratory. He adds that the model is quite a simple approximation.

Conversely, Hess argues that carbon nanotubes are a good match for their mathematical model. A 10-micrometre string of carbon atoms might contain fewer than 100,000 atoms. This is sufficiently few for temperature to become a little fuzzy, agrees Atkins.

"Now that we are making these nanodevices, we have to rethink the way we look at temperature," Hess concludes.