Liesegang Rings Engineered from Charged Nanoparticles

The study of spatial patterns that are formed from reacting and diffusing chemicals has been central to the development of nonlinear chemical kinetics1,2 and has provided mechanistic understanding of natural phenomena ranging from the formation of stalactites and striated minerals3 through intracellular oscillations4 to cardiac rhythms.5,6 Although virtually all artificial pattern-forming chemical systems [Liesegang rings (LRs),6,7 Belousov-Zhabotinsky (BZ) oscillations and waves,8 and discharge filaments9] have been serendipitously discovered rather than systematically designed, subsequent developments have led to remarkable control of these patterns. Nowadays, BZ waves can be propagated controllably,10 Turing patterns can be designed rationally from first principles,11 and Liesegang-like structures can be crafted with desired shapes and interband spacings in the presence12 or absence13 of external fields. In the context of Liesegang structures, however, it must b