New model extends pattern formation theory to nanoscale universe

A new model developed by scientists at the Max Planck Institute for Dynamics and Self-Organization (MPI-DS) extends elastic phase separation theory to nanoscale structures. Such patterns are common in biological systems and are also used in nanoengineering to produce structural colors. With their new insights, scientists can predict the length scale of nanoscale patterns and thereby control them during production.The model was published in the journal Physical ReviewX.

Well-defined structural patterns are ubiquitous in biological systems. A well-known example is the coloration of bird feathers and butterfly wings, which relies on the regular arrangement of nanostructures, called structural color. This pattern is usually formed through phase separation.

The different components separate from each other, similar to the separation of oil and water. However, it’s not clear how nature creates the clear patterns to produce this color. Generally speaking, fabricating synthetic materials with such submicron lengths is a common challenge.

One way to control the structure of phase separation relies on elasticity: elastic theory can well describe the deformation of materials at the macroscale, explaining, for example, how a piece of rubber deforms under the action of force. However, at the nanometer scale, materials are no longer homogeneous and macroscopic descriptions of materials are insufficient.

Rather, the actual arrangement of the molecules matters. Furthermore, deforming any material requires energy, thus preventing large deformations. Therefore, a single droplet formed through phase separation cannot grow indefinitely. Depending on their arrangement, regular patterns can emerge.

Scientists led by David Zwicker, head of the Max Planck “Biofluids Theory” research group at MPI-DS, have now developed a model to solve this problem. They proposed a theory based on nonlocal elasticity to predict the pattern formation of phase separation.

“With our new model, we can now describe the system taking into account relevant additional aspects,” Zwicker said. “Modeling all the molecular components in atomic detail would be beyond computational capabilities. Instead, we extended the existing theory to smaller structures comparable to the grid size,” he explains.

The new theory predicts how material properties affect the patterns formed. Therefore, it helps engineers create specific nanostructures following the physical principles of self-organization exploited by nature.