How simple geometry gives rise to complex materials

Utrecht University researchers Rodolfo Subert and Marjolein Dijkstra show in their latest study that complex three-dimensional networks in materials can emerge from nothing more than particle shape. In Nature Communications they describe how simple geometries, aided by entropy, can give rise to layers, networks and even spontaneous left- and right-handed twisting, which is a phenomenon previously linked mainly to highly complex molecules.

Materials are good at organising themselves. Molecules can assemble into membranes, and crystals can arrange into regular lattices. These structures are nice to look at, but they are also useful, forming the basis of technologies behind displays, medical materials and smart sensors.

The usual assumption is that such order requires complex causes, like electric charges, chemical reactions and interactions between particles. But Rodolfo Subert and Marjolein Dijkstra show that it can sometimes be much simpler. In their latest study, they show that the shape of building blocks alone can be enough to generate intricate, organised patterns.

Order without attraction

The researchers worked with computer simulations of virtual particles. In these simulations, they used hard, polyhedral shapes with just one rule: particles were not allowed to overlap. Even so, when the particles were packed closely enough, they began to organise spontaneously. First into layers, then into columns and three-dimensional networks. Entropy, the natural tendency of systems to move toward their most likely state, plays an important role here. Some ordered structures turn out to be simply more probable for particles than disorder.

Spontaneous twisting

Eventually, the simulations even produced structures with a clear left- or right-handed twist. That the particles started to twist at all came as a surprise, says Marjolein Dijkstra. “The particles themselves are not twisted, but together they form a pattern with a preference for left or right twist. That direction is not built in anywhere.”

When structures develop such handedness, physicists call it chirality. Chiral structures play an important role in biological systems and liquid crystals. Until now, such effects were thought to require complex, asymmetric, twisted molecules. This study shows that geometry alone can sometimes be enough.

The particles themselves are not twisted, but together they form a pattern with a preference for left or right twist. That direction is not built in anywhere

Geometry

Because of their specific shape, particles have a slight preference for how they align with their neighbours. But when these local preferences are extended to larger scales, they no longer fit together. The system effectively jams. To resolve this, the material bends, twists or deforms, and from that, complex patterns emerge.

Materials by design

Although the work is based on simulations, it is not only relevant as fundamental research. The particle shapes used in this study can in principle be manufactured using existing techniques in colloid science. That means the insights could help researchers design new materials with, for example, unusual optical or mechanical properties. 

According to the scientists, a few simple design rules apply: elongated shapes tend to produce twisted structures, flatter shapes favour columnar patterns, and intermediate forms give rise to network-like materials. Researcher Rodolfo Subert explains that these kinds of simple rules are important for further developing our understanding of material behavior. "In our research, we show that sometimes surprisingly simple principles underlie complex patterns," he says.