Outsmarting self-organization

A complex arrangement of microspheres (left) and the corresponding mathematical

A complex arrangement of microspheres (left) and the corresponding mathematical diagram (tessellation) that graphically highlights the structures (right). (Illustration: Laboratory for Soft Materials and Interfaces, ETH Zürich)

Researchers at ETH Zurich have coaxed tiny spheres made of polymer gels into forming complex patterns by themselves through a two-step process. Surfaces with tailor-made optical and mechanical properties could be realized in this way.

When retiling the bathroom or the terrace using, for instance, square, rectangular or hexagonal tiles, the result will be a simple and regular pattern - assuming one doesn’t make any mistakes. Similarly, using tiny spheres of different materials scientists can also produce simple regular patterns that have useful optical or mechanical properties. Those regular structures arrange themselves through the interplay between the forces among the spheres and actions exerted on them from the outside, such as pressure.

For some time now, researchers have tried to realize more complex versions of these structures, which are also known as colloidal crystals. So far, however, this has proved to be rather difficult. At ETH Zurich, Lucio Isa, professor at the Department of Materials, and his collaborators have managed to force simple microspheres to arrange themselves into complex colloidal crystals using a trick. The results of their work have recently been published in the scientific journal "Nature".

1 plus 1 doesn’t equal 2

"Simply speaking, we have shown that 1 plus 1 doesn’t necessarily equal 2", Isa explains. This is no disregard for elementary arithmetic, but rather a technique by which the researchers can bring tiny spheres, made of soft polymer gels and measuring only about a micrometre in diameter, to form more complex patterns than they would normally do of their own accord.

In the laboratory, they started with a standard experiment. They confined the polymer particles at the surface of a water bath covered by a layer of oil (hexane) floating on top of it. Using moveable barriers, the area of the water surface can be reduced and the particles are then squeezed together more and more, which causes them to arrange themselves into crystal-like structures. As these structures form, they are deposited onto a silicon support lifted through the water surface, very much like collecting them with a skimmer. Finally, the researchers remove the support from the water bath (see figure).

Two rounds

"If you repeat this procedure with a fresh silicon piece each time, in the end you’ll always find hexagonal structures on it, even if the spheres are exposed to increasing pressures and hence more strongly compressed", says Isa. However, if instead of a fresh silicon support, one takes one that has already been used and on top of which there is already a hexagonal pattern of microspheres, then the new spheres have to reckon with two boundary conditions during the second deposition: on the one hand, they repel each other while being corralled from the sides by the barriers, but on the other hand they also encounter the spheres of the first round, which are now in a fixed arrangement on the silicon support. Through the interplay between those two influences, the spheres of the second layer drive the formation of patterns that can be completely different from the first one - and also much more complex.

Complex patterns through frustration

Looking closely at that the combination between the two layers under a high-resolution microscope, one can see a variety of arrangements, depending on the packing density of the microspheres: interlocking’s patterns, hexagonal superlattices, or even herringbone patterns (see figure). "We have demonstrated that with simple building blocks - tiny spheres in our case - one can produce very complex arrangements in a two-step process", Isa says.

Using computer simulations, he and his team - among them two master’s students, who were involved in carrying out the experiments - were able to show that the complex patterns, indeed, resulted only from the repulsion between the tiny spheres. In particular, the repulsion between the spheres of the first, now fixed, layer and those of the second layer led to a phenomenon known as frustration. This means that the mobile spheres were no longer able to arrange themselves freely, but also had to respect the pattern of the first layer, even if naturally they would have preferred a different pattern.

Targeted structure design

Isa sees his method as an important step towards the targeted design of complex self-organized structures from simple basic building blocks. The shape of the building blocks and the degree of compression can be chosen in such a way as to result in a predetermined pattern. Those patterns can be regular crystals with more or less complex periodic lattice structures. His hope, however, is to extend the method to the fabrication of quasicrystals that exhibit local order, but whose patterns do not repeat themselves periodically in space. While Isa finds all of this highly interesting from a scientific viewpoint, he also sees concrete possibilities for applications. For instance, tailor-made surface patterns with particular optical properties or with a desired wetting or friction behaviour could be produced in this way. Those patterns could then be used for coatings of optical components or other materials.


Grillo F, Fernandez-Rodriguez MA, Antonopoulou M et al. Self-templating assembly of soft microparticles into complex tessellations. Nature 582, 219-224 (2020). doi: 10.1038/s41586-020-2341-6

Oliver Morsch

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