First Material with Longitudinal Negative Compressibility
Authors: Zachary G. Nicolaou1,2 and Adilson E. Motter1
1Department of Physics and Astronomy, Northwestern University, USA
2Department of Physics, California Institute of Technology, USA
Conventional materials deform along the direction of the applied force in such a way that they expand when the force is tensional and contract when it is compressive. But our new paper  published this month in Nature Materials demonstrates that not all materials have to be that way. We explored network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). This effect is achieved through destabilizations of metastable equilibria of the constituents of the material. These destabilizations give rise to a stress-induced phase transition associated with a twisted hysteresis curve for the stress-strain relationship. The proposed materials are the first to exhibit longitudinal negative compressibility at zero frequency.
|Negative compressibility surface. When pressured, the surface expands instead of contracting [Image copyright: Adilson E Motter]|
The motivation for this work comes from our previous research on networks. It has been known that some networks respond in a surprising way to various types of perturbations. For example, in previous research our group has shown that the removal of a gene from the metabolic network of a living cell can often be compensated by the removal (not addition) of other genes . Our hypothesis was that, with the right design, similarly counter-intuitive responses could occur in materials as well, which are essentially networks of interacting particles. The idea of using network concepts to design a material that could contract longitudinally when tensioned was particularly attractive because no existing material (natural or engineered) had been found to exhibit that property.
|Negative compressibility cube. When tensioned, the cube contracts instead of expanding [Image copyright: Adilson E Motter].|
There are numerous potential applications for materials with negative compressibility transitions. They include the development of new actuators, microelectromechanical systems, and protective devices---from ordinary ones, such as seat belts, to devices that reduce the consequences of equipment failure. These materials may also lead to force amplification devices, which could be used to sense minute forces and transform them into large ones. Indeed, the strain-driven counterpart of negative compressibility transitions is a force amplification phenomenon, where an increase in deformation induces a discontinuous increase in response force. Other potential applications would be to improve the durability of existing materials, such as in crack closure of fractured materials. In fact, we expect other researchers to come up with yet different applications that we have not even thought about.
|Negative compressibility material. The material at the center of the image expands vertically as it is squeezed [Image copyright: Adilson E Motter].|
The most surprising aspect of this research is the very finding that you can create a material that contracts when it would be expected to expand and expands when it would be expected to contract. Think of a piece of rod that you tension by pulling its ends with your fingers. It would normally get longer, but for these materials it can get shorter. This has been generally assumed not to be possible for the excellent reason that no known material behaves that way. Moreover, it is easy to show that this is indeed impossible if we assume that the material will respond continuously to the applied force. Our work shows, however, that this unfamiliar form of compressibility can occur by means of an abrupt change---a phase transition. A posteriori, perhaps another surprising aspect of our research was the simplicity of the system once we understood how it works, and this can have practical implications for the fabrication of the material.
This work illustrates rather dramatically how deceiving it is to assume that a material’s property will be limited by those of existing ones, the reason being that existing materials explore only a tiny fraction of the space of all possibilities. Previous research has pushed the boundaries of electromagnetic properties and led, for example, to materials with negative refractive index . Our research shows that even mechanical properties that have no immediate analogs in electromagnetic metamaterials can be tailored and even inverted. At the end, the material’s properties are only limited by how different interacting parts can be assembled together. For a related discussion in the context of networks, see Ref. .
 Z. G. Nicolaou and A. E. Motter, Mechanical metamaterials with negative compressibility transitions, Nature Materials 11, 608-613 (2012). Abstract.
 A. E. Motter, "Improved network performance via antagonism: From synthetic rescues to multi-drug combinations", BioEssays 32, 236-245 (2010). Full Article.
 R. A. Shelby, D. R. Smith and S. Schultz, "Experimental verification of a negative index of refraction", Science 292(5514), 77-79 (2001). Abstract.
 A. E. Motter and R. Albert, "Networks in motion", Physics Today 65(4), 43-48 (2012). Abstract.