Programmable Design of Self-Organized Patterns through a Precipitation Reaction.

Nature uses self-organized spatiotemporal patterns to construct systems with robustness and flexibility. Furthermore, understanding the principles underlying self-organization in nature enables programmable design of artificial patterns driven by chemical energy. The related mechanisms are however not clearly understood because most of these patterns form in reaction-diffusion (RD) systems consisting of intricate interaction between diffusion and reaction. Therefore, comprehensive understanding of the pattern formation may provide critical knowledge for developing novel strategies in both natural science and chemical engineering. Liesegang patterns (LPs) are one of the typical programmable patterns. This study demonstrates that appropriate tuning of gel concentration distribution is a key programming factor for controlling LP periodicities. The gel distribution was realized in bi- or multi-layered gels constructed by stacking agarose gels of different concentrations. Thus, exceptional LP periodicities were achieved locally in bi-layered gels. Furthermore, RD simulations revealed that the nucleation process modulated by the gel distribution determines the LP periodicity in bi-layered gels. Finally, based on this concept, desired LP periodicities were successfully realized by programming gel distributions in multi-layered gels. Thus, deep insights into the fundamental role of nucleation in designing LPs can lead to the practical applications of LPs and the understanding of self-organization in nature.