Experimental and theoretical investigation of the transition from bands to 2d squares-hexagons and 3d Turing patterns in the cadmium sulfide precipitation reaction-diffusion system -

Abstract

Spatiotemporal pattern formation in precipitation reaction-diffusion (RD) systems was first observed as concentric rings by R. E. Liesegang in 1896. Later on, other structures have been reported, including: directly spaced rings, the unusual revert spacing, secondary structures, fractals, spirals (2D), helices (3D) and other features. In our work, we study for the first time the formation of new precipitation patterns in two and three dimensions. Our system consists of diffusing sodium sulfide into a gel matrix containing dissolved cadmium (II) ions. When performed in a planar reactor (2D), the white cadmium hydroxide Cd(OH)₂precipitation occurs parallel to the diffusion front and takes the form of spaced dots with squared-hexagonal symmetry. A yellow back front follows the evolution of the system due to the formation of the yellow cadmium sulfide CdS resulting from the anionic exchange between OH⁻ and S²⁻ ions. On the other hand, in (3D) the system exhibits more complex patterns due to the stacking of layers of the (2D) patterns along the third dimension. These (3D) patterns exhibit Turing-like behavior. We intend to study the effect of different variables on the morphology of the patterns, including the concentration of inner and outer electrolytes, temperature, thickness of the gel, addition of capping agents, variation of ionic strength, and application of a static electric field. We also plan to investigate theoretically and numerically the spatiotemporal dynamics of the obtained patterns. In that regard, we will invoke the Cahn-Hilliard equation in the description of the precipitate pattern formation whereby the colloidal product resulting from the reaction of the diffusing electrolytes undergo spinodal decomposition followed by an Ostwald ripening scenario. The resulting evolution equations will be solved numerically using the Finite Element Method (FEM), which provides flexibility to solve these equations on domains with complex geometries.