Stretching the limits
Most materials get thinner when stretched, but “auxetics” do the opposite and get thicker. Helen Gleeson describes her group’s discovery of a material that is auxetic at the molecular level, which could be used in everything from body armour to laminated glass
Take a rubber band, stretch it along its length, and it will shrink in the other two directions, getting narrower and thinner as you pull. The amount of “perpendicular contraction” that occurs is determined by the material’s Poisson ratio, which in such cases is a positive number. Some materials, however, do the exact opposite when stretched. Known as “auxetics”, they expand in one of the perpendicular directions and therefore have a negative Poisson ratio.
The first artificial auxetic materials were made about 40 years ago but they also exist in nature. Some are complex biomaterials, such as human tendons and cat, cow and salamander skin. There are also inorganic auxetics, including palladium, copper, gold and other face-centred cubic metals, as well as certain zeolites such as natrolite (Na2Al2Si3O10). When stretched, these materials undergo a clever internal reorganization, forming voids that lower the overall density.
Synthetic auxetics take the lead from nature’s elegance, being carefully engineered so that they have a similarly porous internal geometry. Their ability to get thicker when stretched makes auxetics fascinating from a scientific and theoretical point of view. But they also have some cool everyday applications. The sole on Nike’s Flyknit running shoe, for example, has a macroscopic auxetic geometric structure. It expands when a runner hits their foot on the ground, reducing uncomfortable pressure points in the process.
Despite such successes, it’s fair to say that applications of auxetics in other areas have been more limited. Part of the problem is that many artificial auxetic materials have a porous, foamy structure, with the individual pores usually being bigger than a micron in size. An auxetic material can therefore expand only by a certain amount: any more and it will weaken and possibly collapse. But in 2018 Devesh Mistry – who was then one of my PhD students at the University of Leeds, UK – made a ground-breaking and entirely unexpected discovery.
At the time, Mistry was studying the mechanical properties of liquid-crystal elastomers – a rubber-like material based on the standard liquid crystals found in flat-screen TVs and mobile-phone displays. Liquid crystals are curious in that they flow (like a liquid) yet still retain some order (like a crystal). Subtle differences in the amount of order in these fluids create many different phases of liquid crystal, the simplest being the “nematic” phase.
Nematic liquid crystals usually have elongated, rod-like molecules, which all line up so that their long axes point roughly in the same direction, like knives in a cutlery drawer. How well the molecules are aligned with that overall direction (known as the “director”) is quantified by the “order parameter” S = <3cos2θ – 1> / 2, where θ is the angle between the molecules and the director. This parameter can vary from 1 (for a perfect crystal) to 0 (corresponding to a randomly oriented liquid) and even as low as –0.5 (negative order, which we’ll return to later). Most nematic phases have an order parameter of S ≈ 0.6, meaning there’s some fluctuation in the overall alignment of the molecules around the director.
Now although most liquid crystals – including those in displays – contain small molecules, it’s also possible to obtain liquid-crystalline behaviour from long-chain polymers that have small, rod-like units strung out along their backbone (figure 1a) or stuck out from the side (figure 1b). When these rods line up, the polymers act like liquid crystals. What’s more, if the rods on one polymer chain are physically connected (or “cross-linked”) to more than one chain, you end up with the kind of liquid-crystal elastomer (LCE) that Mistry was studying.
Combining the elasticity of an ordinary elastomer (like rubber) with the self-organization of a liquid crystal, these soft materials have some unusual anisotropic mechanical properties. But because there was no chemist on our Leeds team at the time for him to draw on, Mistry decided to develop an LCE that he could easily synthesize himself using a known synthetic pathway and commercially available monomers – a “physicist-friendly” LCE as he put it. Using techniques borrowed from the liquid-crystal display industry, Mistry was able to make highly uniform thin films of his materials, in which the orientation of the rods can be controlled over large areas.
Having developed his new LCE material, which had rods as side groups, Mistry and a group of technicians from Leeds started building a special piece of equipment for testing its mechanical properties. The equipment was designed so that it could fit onto the stage of a polarizing microscope – one of the tools-of-the-trade in liquid-crystal physics. Using the rig, Mistry was able to measure the angle of the director at a chosen point in the LCE, which indicates the amount of local liquid-crystalline order, and monitor how this changes as the strain is increased.
When he pulled the film in the x direction – perpendicular to the director, which pointed in the y direction (figure 1c) – nothing of note initially happened. The material simply stretched in a soft elastic fashion and the director remained about 90° to the stretching direction. However, once it was stretched beyond a threshold strain of 0.9, the director rapidly began to line up with the strain axis – in other words, the angle between the director and the stretching direction fell to 0°. By simultaneously measuring the dimensions of the LCE film, Mistry concluded that it was behaving as an auxetic material – it was getting thicker in the z direction, at 90° to the direction in which it was being stretched.
There were two possible explanations for this unexpected auxetic behaviour. The first, rather mundane, option was that the strain on the sample had simply lowered the material’s density, meaning that pores had formed in it as with all other ordinary auxetics. But when Mistry carried out further mechanical studies using cryo-scanning electron microscopy and atomic-force microscopy, it appeared that the volume – and hence density – remained unchanged, which meant that no nanometre-sized pores had formed.
That therefore left the other, more exciting, option, which was that the LCE’s auxetic behaviour was occurring at the molecular scale. Incredibly, Mistry had discovered a material that, when strained beyond a certain threshold value (0.9), thickened perpendicular to the direction in which it was being stretched without the formation of voids. Somehow the polymer was rearranging itself at a local molecular level to trigger auxetic behaviour (figure 1d).
What’s more, Mistry soon noticed that the threshold strain dictating the onset of auxetic behaviour coincided with what appeared to be an order parameter of zero – and potentially even less than zero. An order parameter less than zero might seem odd, but in this case it means that the rod-like units are randomly oriented in the x–y plane of the material, while the director itself points in the z-direction, out of the plane.
Further insights have been uncovered by Thomas Raistrick, one of my current PhD students. His quantitative Raman-scattering measurements have shown that the uniaxial order of the material (meaning it has only one axis of anisotropy) falls to zero as the material is stretched. But just before the threshold strain, biaxial behaviour emerges (meaning the material now has two axes of anisotropy). As the strain increases further, the material begins to return to a uniaxial state. We need to do more work, but it’s clear that a complex interchange of order and symmetry causes the auxetic response, with further insights hopefully emerging soon.
What’s so interesting about this LCE’s auxetic behaviour is that it occurs at the molecular scale rather than relying on the behaviour of macroscopic pores found in other “first-generation” synthetic auxetic materials. It therefore does not become inherently weaker when stretched, which means it could be used, say, as body armour, where you need a material that is likely to come under a lot of impact. The material would then act as a shock absorber – thickening in response to the force, rather than becoming thinner like a standard positive-Poisson-ratio material.
These transparent molecular auxetics could also be useful in the automotive industry to protect car windows, which usually have several layers of glass separated by layers of polymer. When hit, the induced strain makes all the layers shrink and so can become unstuck or “delaminate”. But if you had an auxetic material with a negative Poisson ratio, it would – if hit – expand against each layer of glass and stop any delamination from occurring. Molecular auxetics could also, for the same reason, be used in solar cells, which usually come with a 25-year warranty and need to stay robust for long periods.
Our team at Leeds, including Mariam Hussain, Richard Mandle, Ethan Jull, Keith Rollins and Peter Hine, is currently exploring these protection and delamination prevention applications. We believe that molecular auxetic LCEs could be game-changers – not just because they’re robust, transparent and thicken when stretched, but also because we can effectively tune these materials at the molecular level simply by adjusting their chemical make-up.
- The author thanks Ethan Jull of the University of Leeds for the original draft of this article