Regular-Type Liesegang Pattern of AgCl in a One-Dimensional System

Formation of Precipitation Ellipsoidal Disks and Spheres in the Wake of a Planar Diffusion Front

Pattern formation is one of the examples of self-organization. In the generation of patterns, the coupling between the mass transport of the chemical species and their chemical reactions plays an important role. Periodic precipitation (Liesegang phenomenon) is a type of pattern formation in which layered precipitation structures form in the wake of the diffusion front. Here, we show a new type of precipitation pattern formation in zeolitic imidazolate framework-67 in a solid hydrogel column in a test tube manifested in the generation of precipitation ellipsoidal disks and spheres in the wake of the planar diffusion front of the outer electrolyte (2-methylimidazole). To increase the probability of the emergence of ellipsoidal disks and spheres, the surfaces of the borosilicate test tubes were chemically treated and functionalized. To support the experimental findings, we developed a reaction-diffusion model that qualitatively describes the formation of precipitate ellipsoidal disks and spheres in a test tube.

Role of Stochasticity in Helical Self-Organization during Precipitation

Spontaneous pattern formation with a well-defined periodicity is ubiquitous in nature. The Liesegang phenomenon is a chemical model of such a spontaneous pattern formation. In this study, we investigated the role of stochasticity in reaction-diffusion precipitation processes by demonstrating the temperature dependence of spontaneous symmetry breaking and helix formation in the Liesegang pattern with CuCrO₄ precipitates; experimental analysis and numerical simulations based on reaction-diffusion equations were used. At high temperatures, helices with no, single, and double branches appeared in addition to the discrete parallel band characteristic of the Liesegang phenomenon. The probability of helix formation increased drastically when the experimental temperature during the pattern formation exceeded 20 °C. Moreover, the spacing coefficient, quantitatively representing the periodicity of obtained patterns, increased at high temperatures. Numerical simulations were performed to investigate the temperature dependence of the probability of helix formation and spacing coefficients. The stochasticity of the initial chemical reaction, which can trigger consequent nucleation and crystal growth, critically affected the probability of helix formation and the spacing coefficient. These features were explained in the framework of the prenucleation model by considering the degree of stochasticity in the initial chemical reaction step.