Two- and three-dimensional chemical waves in the reaction-diffusion system of mercuric iodide in hydrogel media -

Abstract

In our study, we will investigate a simple reaction-diffusion process that embraces a pattern formation of traveling chemical waves in an “excitable” system based on the simple precipitation reaction between mercuric chloride and potassium iodide in a solid hydrogel media. The reaction involves a redissolution of the precipitate upon excess outer concentration. In the gel media, we observe three different polymorphs: orange (tetragonal), β-yellow (orthorhombic) and α-red (tetragonal). Amongst these polymorphs, the orange and yellow are the kinetically favored and appear early in the reactions, yet they are both metastable and transform readily to the most stable and thermodynamically favored red polymorph. We first report a 2D system that incorporates superdiffusive radially propagating waves exhibiting unusual cusp-like borders. These waves result from a leading precipitation reaction (wavefront) and a trailing redissolution (waveback) between the initially separated reactants to produce the HgI₂ precipitate in a thin sheet of the solid hydrogel (agar) medium. The propagation dynamics is accompanied by the continuous polymorphic transformations between the metastable orange-yellow crystals and the stable red crystals of HgI₂. We study the dynamics of wavefront and waveback propagation, which reveals interesting anomalous superdiffusive behavior without the involvement of external enhancement of motion. We predict that the dynamics are dependent on the outer iodide concentration in which a transition from superdiffusive to subdiffusive transport occurs. Inner mercuric concentrations apply an impact on the structure of the precipitation band where it converts from the unusual cusp-like form to the cusp-free regular form. While gel concentration affects the speed of propagation of the wave, it has no effect on its shape or on its superdiffusive dynamics. Microscopically, we show that the macroscopic wave propagation and polymorphic transformations are accompanied by an Ostwald