Periodic Patterning of Matter in Non-Equilibrium Liesegang-Type Structures

Bottom-up self-organization of unordered molecules into ordered, spatiotemporal patterns of complex structures through non-equilibrium reaction-diffusion (RD) processes is ubiquitous in nature across all scales. Unlike many RD processes that typically lead to transient patterns, periodic precipitation reactions governed by the Liesegang phenomenon are distinguished by the formation of stable, permanent structures. This unique characteristic makes them valuable tools in the development of hierarchical multifunctional materials, an area that has seen significant progress in recent decades. This review summarizes the fundamental aspects of the Liesegang phenomenon, focusing on the key characteristics, compositional features, inherent properties, and formation mechanisms of Liesegang patterns in chemical systems, while also highlighting their occurrence in biological and geological settings. We discuss recent advancements in applying periodic precipitation to address global challenges in microelectronics and environmental monitoring, concluding with a forward-looking perspective on the promising future applications of the Liesegang periodic precipitation in materials science, nanotechnology, medicine, and environmental engineering.