Spatiotemporal and Microscopic Analyses of Asymmetric Liesegang Bands: Diffusion-Limited Crystallization of Calcium Phosphate in a Hydrogel

In the more than 100 years since the Liesegang phenomenon was discovered, intensive studies have been conducted to understand and control the characteristics of the periodic precipitation patterns in which the outer electrolyte diffuses into a hydrogel containing the inner electrolyte. Between fields of physics and chemistry, the periodicity of the precipitate has been investigated restrictively by spatial analyses and numerical simulations at macroscopic scales and it has been considered as a result of simple precipitation. In this work, calcium ion diffusion into gelatin hydrogels containing phosphate ions, a biomimetic system for bone formation, resulted in typical Liesegang patterns at macroscopic scales, but the asymmetric growth of the crystal was found in every single band at microscopic scales, which has not been observed or overlooked in the previous reports. The pattern consists of three characteristic bands: a continuous band, a split-fin band, and an intact-fin band. While the continuous band has a uniform crystal density, the split-fin and intact-fin bands have asymmetric crystal densities along the single band. We investigate the formation process of individual bands as well as the whole pattern by combining microscopic and spatiotemporal analyses based on the nucleation theory. Formation processes of asymmetric bands are explained by the unique stability and the diffusive property of amorphous precursors depending on the rate of calcium ion delivery. This is the first study to focus on the inhomogeneity of a single band in Liesegang patterns and the time-dependent mechanism of its growth.