It's not magic, but new materials designed by two Northwestern University researchers seem to exhibit magical properties. Some contract when they should expand, and others expand when they should contract.

When tensioned, ordinary materials expand along the direction of the applied force. The new metamaterials (artificial materials engineered to have properties that may not be found in nature) do the opposite when tensioned - they contract. Other materials designed by the researchers expand when compressed.

"Materials are networks of connected constituents, and when you apply tension or pressure, they can respond in surprising ways," said Adilson E. Motter, the Harold H. and Virginia Anderson Professor of Physics and Astronomy at Northwestern's Weinberg College of Arts and Sciences.

"Think of a piece of rod that you tension by pulling its ends with your fingers," he said. "It would normally get longer, but for these materials it will get shorter."

Motter and Zachary G. Nicolaou applied network concepts to design the new materials, all of which exhibit negative compressibility transitions. Their results are published this week in Nature Materials. Nicolaou, an undergraduate physics student at Northwestern when the work was done, now is a first-year graduate student at Caltech.

Different types of metamaterials already have led to interesting applications such as superlenses, visibility cloaks and acoustic shields. But no existing material or metamaterial was previously shown to exhibit negative compressibility transitions.

These metamaterials may enable new applications, including the development of new protective mechanical devices and actuators (a type of assembly for operating or controlling a system), and the enhancement of microelectromechanical systems.

The materials also exhibit force amplification, a phenomenon in which a small increase in deformation leads to an abrupt increase in the response force. The latter can be useful for the design of micro-mechanical controls, ratchets and force amplifiers.

All known materials deform along the direction of a constant applied force by expanding when they are tensioned and contracting when they are compressed. Owing to stability considerations, such contraction of a material in the same direction of an applied tension (in response to tension) cannot occur continuously.

Possibly because of this, most people would intuitively expect that contraction in response to tension would be impossible.

The important point of the Northwestern study is that such a counterintuitive response can occur discontinuously, namely, through something known by physicists as a phase transition. A familiar form of phase transition is the transformation of water into ice or vapor. Phase transitions allow for abrupt changes in the physical properties of a material. Yet, all conventional materials are such that phase transitions will lead to ordinary compressibility.

"This research shows that new materials, in fact, can be created to exhibit a phase transition during which the material undergoes contraction when tensioned or expansion when pressured," Motter said. "We refer to such transformations as 'negative compressibility transitions.'"

Materials with such properties have not been discovered in nature, but they can be constructed as metamaterials. Metamaterials are engineered materials that gain their properties from structure rather than composition. The relevant building blocks of such materials are not necessarily microscopic, atomic-sized objects, but may in fact be composed of a large number of atoms and hence be mesoscopic or macroscopic in size.

A key step for the discovery of the materials in this study was the representation of the material as a network of interacting particles.

"We were inspired by the observation that the realized equilibrium is not necessarily optimal in a decentralized network," Motter said. "A conceptual precedent to this is the now 45-year-old insight from German mathematician Dietrich Braess that adding a road to a traffic network may increase rather than decrease the average travel time."

Analogous effects also have been identified in physical networks, including an increase of current upon the removal of an intermediate conductor in electric networks. These are examples in which the equilibrium realized by the system can be brought closer to the optimum by constraining the structure of the network.

"Our materials are devised such that an analogous phenomenon occurs spontaneously, in response to a change in the external force rather than in the structure of the network," Motter said.

The article, "Mechanical Metamaterials With Negative Compressibility Transitions," is available here