New model extends theory of pattern formation to the nano-cosmos

A new model developed by scientists from the Max Planck Institute for Dynamics and Self-Organization (MPI-DS) extends the theory of elastic phase separation towards nanoscopic structures. Such patterns are frequent in biological systems and also used in nano-engineering to create structural color. With their new insights, the scientists can predict the length scale of nanoscopic patterns and thus control them during production. The model is published in the journal Physical Review X.

Well-defined structural patterns are found all over the place in biological systems. A well-known example is the coloration of bird feathers and butterfly wings, which relies on the regular arrangement of nanoscopic structures, known as structural color. Such patterns often form by phase separation.

Different components separate from each other, similarly to how oil separates from water. However, it remains unclear how nature creates well-defined patterns leading to such colors. Generally, manufacturing synthetic materials on this submicron length scale is a common challenge.

One way to control structures made by phase separation relies on elasticity: Deformations of materials are well-described by elasticity theory on macroscopic scales, for example, to explain how a piece of rubber deforms under the effect of force. However, on a nanoscopic scale, materials are not homogeneous anymore and the macroscopic description of the material is insufficient.

Instead, the actual arrangement of molecules matters. Moreover, deforming any material requires energy, which thus impedes large deformations. Individual droplets formed by phase separation can thus not grow indefinitely. Depending on their arrangement, a regular pattern can emerge.

Scientists led by David Zwicker, head of the Max Planck Research Group “Theory of Biological Fluids” at MPI-DS, have now developed a model to address this aspect. They proposed a theory based on nonlocal elasticity to predict pattern formation by phase separation.

“With our new model, we can now take into account the relevant additional aspect to describe the system,” Zwicker says. “Modeling all molecular components in atomic detail would exceed the computational power. Instead, we extended the existing theory towards smaller structures comparable to the mesh size,” he explains.

The new theory predicts how material properties affect the formed pattern. It can thus help engineers to create specific nanoscopic structures, following physical principles of self-organization that nature exploits.