## NPR Materials?

The previous post was on NLC materials that expand along some (but only some!) directions under an applied pressure. NLC, of course, stands for negative linear compressibility. The expansion along some directions is more than compensated by a shrinkage along the other directions, so that the overall volume does indeed decrease with pressure — a mandatory condition demanded by thermodynamic (specifically, mechanical) stability of the system.

A related property is Poisson’s ratio. Under a squeezing action, most materials shrink along the (axial or longitudinal) direction of squeezing , and expand along the two perpendicular (transverse) directions. In technical jargon, the negative of the ratio of the transverse strain to the longitudinal strain is called $\nu$, the Poisson’s ratio.

For most materials, Poisson’s ratio — as defined above — is positive. But it could be negative! There’s nothing fundamentally wrong with it, because the material is stable as long as its Poisson’s ratio is greater than -1 (i.e., $\nu > -1.0$. At the high end, $\nu$ has an upper limit of 0.5). Let’s call them NPR materials, with NPR standing for “Negative Poisson’s Ratio”.

To be sure, NPR materials are rarer than the “normal” kind. There has been quite a bit of effort to understand why some materials may exhibit NPR — see this short Nature article, for example; this article’s author also gave these materials a name: “auxetic materials”. I am not sure how popular this name is, though.

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Just a final aside. Cork has a Poisson’s ratio which is pretty close to zero. Here’s how Wikipedia explains its use as a wine stopper:

The use of cork as a stopper for wine bottles is the result of the fact that cork has a Poisson ratio of practically zero. This means that, as the cork is inserted into the bottle, the upper part which is not yet inserted will not expand as the lower part is compressed. The force needed to insert a cork into a bottle arises only from the compression of the cork and the friction between the cork and the bottle. If the stopper were made of rubber, for example, (with a Poisson ratio of about 1/2), there would be a relatively large additional force required to overcome the expansion of the upper part of the rubber stopper. 