Effect of Diffusion Dimension on the Geometry of Precipitation Patterns in the Liesegang Phenomenon

Abstract

Liesegang patterns are one of the static patterns with regular periodicity, which have been used as chemical models for the similar static patterns in nature. However, the factors controlling their geometries are still not understood, particularly for system with a complex reaction medium. In this study, we focused on the effect of the diffusion dimension on the pattern geometry. Among pattern formations in (i) a rectangular gel for one-dimensional diffusion and (ii) a concentric gel for two-dimensional diffusion, the two-dimensional system exhibited an unexpected geometry, which did not follow the empirical law for Liesegang patterns. The difference in the pattern geometry between each dimensional system is discussed in terms of the diffusion behavior and concentration gradient of reaction components based on the Fick’s law. These findings show that it is necessary to consider the dimension of the reaction medium to construct a theoretical model and to design an experimental setup.