Networks of triblock ellipses: from kagome order to disordered porous networks

In the world of tiny particles suspended in liquid, known as colloids, the way things stick together depends heavily on their shape and where they are sticky. Imagine a crowd of people trying to form a line; if everyone is perfectly round and equally friendly to everyone else, they will naturally pack together as tightly as possible, leaving no gaps. However, if you give these people a specific rule—say, they can only hold hands with two specific people standing on opposite sides of them, and they are shaped like long ovals instead of circles—the result is entirely different. Instead of a tight, solid block, they are forced to arrange themselves into open, porous networks with holes in the middle. Scientists have long been interested in these open structures because their unique shapes can control how light passes through them or how fluids move across them, properties that are vital for creating advanced materials. A famous example of such a structure is the kagome lattice, a pattern resembling a woven basket that is highly ordered yet full of empty space.

Researchers at the Technical University of Vienna recently explored how changing the shape of these sticky particles from spheres to elongated ellipses alters the way they build these networks. They used computer simulations to watch thousands of these oval-shaped particles, each with two sticky spots on opposite ends, as they assembled under different conditions of temperature and concentration. Their goal was to see if the change in shape would simply make the same patterns appear differently, or if it would fundamentally change the rules of how the particles find each other and lock into place. They discovered that while the particles still formed the beautiful, ordered kagome lattice, the path they took to get there was surprisingly direct. Unlike their round counterparts, which typically build long chains first and then rearrange them into the final pattern, these oval particles jumped straight to the finished structure.

The team observed that by adjusting the temperature and the density of the particles, they could tune the system to be either a perfectly ordered crystal or a messy, disordered network. When the conditions were just right, the particles formed a regular grid where every hole was a perfect loop of six particles. As they made the environment more crowded or colder, this order began to break down. The perfect loops started to distort, creating holes with five or seven sides, and eventually, the network became a chaotic mix of different shapes. To understand this chaos, the researchers developed a new way of mapping the connections. Instead of just counting how many particles were touching, they tracked exactly which sticky spots were connected. This allowed them to see that the oval particles had a unique flexibility; they could bend their connections more easily than round particles, which seemed to help them skip the intermediate step of forming chains and go straight to building the complex lattice.

The study also revealed that the way these networks break down is not random. As the order disappears, the holes in the network do not just get bigger; they change their character. The researchers found that the network developed a preference for five-sided holes over seven-sided ones, a specific imbalance that had been seen in other types of sticky particles but was now confirmed in these oval shapes. This shift suggests that the oval shape makes it easier for the particles to form certain types of defects while making others harder to achieve. The team also spotted some strange, ladder-like structures forming in the disordered regions, which might be competing with the kagome pattern for dominance, though they could not yet prove which structure was more stable.

Perhaps the most significant finding was how the particles assembled from scratch. In simulations of round particles, scientists had previously seen a two-step process: the particles would first clump together into long, stringy chains, and only later would these chains untangle and reorganize into the final lattice. The oval particles, however, did not do this. When the researchers lowered the temperature to trigger assembly, the particles formed the ordered loops immediately, without ever passing through a stage of long chains. This suggests that the elongated shape of the particles provides a different kind of freedom, allowing them to find their correct positions in the lattice much more directly. The researchers noted that at lower temperatures, the nuclei of these new structures became rougher and more branched, filled with more of the five-sided defects, indicating that the speed of assembly came at the cost of perfect smoothness.

This work provides a clear example of how a simple change in geometry—stretching a sphere into an ellipse—can rewrite the rules of self-assembly. It shows that the path a material takes to form is just as important as the final shape it ends up with. By introducing a new method to map the connections between sticky spots, the researchers gave themselves a powerful tool to see inside these networks, distinguishing between simple bonds and complex loops that were previously invisible to standard analysis. While the study was conducted entirely through computer simulations, the findings offer a compelling hypothesis for how shape influences the formation of complex materials. The results suggest that by designing particles with specific shapes and sticky spots, scientists might be able to guide the formation of materials with precisely controlled porosity and order, opening new doors for engineering materials that can filter, sense, or conduct light in ways that are currently impossible.