Rhythmic precipitate patterns and fractal structure

Liesegang patterns of parallel precipitate bands are obtained when solutions containing co-precipitate ions interdiffuse in a 1D gel matrix. The sparingly soluble salt formed, displays a beautiful stratification of discs of precipitate perpendicular to the 1D tube axis. The Liesegang structures are analyzed from the viewpoint of their fractal nature. Geometric Liesegang patterns are constructed in conformity with the well-known empirical laws such as the time, band spacing and band width laws. The dependence of the band spacing on the initial concentrations of diffusing (outer) and immobile (inner) electrolytes (A ₀ and B ₀, respectively) is taken to follow the Matalon-Packter law. Both mathematical fractal dimensions and box-count dimensions are calculated. The fractal dimension is found to increase with increasing A ₀ and decreasing B ₀. We also analyze mosaic patterns with random distribution of crystallites, grown under different conditions than the classical Liesegang gel method, and report on their fractal properties. Finally, complex Liesegang patterns wherein the bands are grouped in multiplets are studied, and it is shown that the fractal nature increases with the multiplicity.