A new quasiparticle called the "wrinklon" could help explain why materials as diverse as graphene and household curtains wrinkle in much the same way – despite their very different length scales. The particle has been introduced by researchers in Belgium, France and the US as a result of measurements on a wide range of materials on length scales from micrometres to metres. While the work may not lead to more attractive curtains, wrinkles do turn out to affect the electronic properties of graphene and the analysis could therefore influence the development of graphene-based devices.

Wrinkles can appear whenever a sheet of material is fixed along one or more edges. In the case of a fabric curtain, the wrinkles are close together at the top and the space between wrinkles increases continuously further down the curtain. The emergence of wrinklons – by Pascal Damman and colleagues at the universities of Mons, Paris and California Riverside, as well as the Massachusetts Institute of Technology – reflects this change and defines the patterns of wrinkles seen in such materials.

Self-similar patterns

Physicists have enjoyed great success in describing complex systems in terms of quasiparticles – collective excitations that behave much like discrete particles. This latest wrinklon quasiparticle describes a localized region with a high degree of stretching where two wrinkles merge into one (see figure). Indeed, if you happen to be sitting next to a curtain, then you can probably see a few wrinklons, which may appear depending on the tension in the material and its physical properties such as thickness and elasticity.

By studying images of wrinkled materials, the team led by Damman found that the patterns are self-similar. This means that the same pattern occurs in different regions of the material but on different length scales. As Damman explains, "If you look at a photograph of a region of the curtain without knowing the length scale, you can't know where it was taken."

The team demonstrated the universal nature of wrinkling by studying materials as diverse as graphene (a sheet of carbon just one atom thick), curtains made of fabric and rubber, as well as paper and plastic sheets. For each material the team measured the distance between neighbouring wrinkles (the wavelength) as a function of the distance from the fixed edge of the material (the top of a curtain, for example). They also measured the tension on the material – in the case of curtains this is supplied by the downward pull of gravity. The Young modulus (or elasticity) and thickness of the material were also measured.

One power law for all

The team found that the "normalized wavelength" (the wavelength divided by the thickness of the material) of ripples in a number of materials have the same power-law relationship with the "normalized distance" from the fixed edge. This distance includes a term that is a function of the tension, thickness and elasticity of the material.

When plotted on a log–log graph, measurements on materials ranging from graphene to fabric curtains fall on the same line. "This is the best evidence yet that wrinkling occurs in the same way over a wide range of length scales," says Benjamin Davidovitch of the University of Massachusetts, Amherst, who was not involved with the experiment. "It has never been demonstrated with such clarity," he adds.

According to Damman, the findings could be important to those studying graphene. As the wrinklons are affected by the thickness of the material, it should be possible to determine the thickness of a sample simply by looking at its wrinkles. Researchers could therefore distinguish between graphene that is one atom thick and samples that are two or three atoms thick – something that can be difficult to do.

These latest results could also be used to ensure that graphene devices are made wrinkle-free, or with specific patterns of wrinkles. This could be important for those developing electronic devices based on graphene, because the electronic properties of the material are affected by wrinkles. According to Damman's colleague Chun Ning Lau of the University of California, Riverside, devices with desirable properties could be created by "straintronics" – whereby specific wrinkle patterns are created by controlling the strain on graphene.

The work is describe in Phys. Rev. Lett. 106 224301.