Dynamics Of Pattern Formation in Nonequilibrium Diffusion-Precipitation Systems

Abstract

Self-organization is a fascinating natural occurrence, yielding intricate structures and patterns under non-equilibrium conditions. One well-known example is the Liesegang phenomenon, which refers to the formation of parallel bands in 1D or concentric rings in 2D, via a diffusion-precipitation mechanism. Driven by a concentration gradient, the outer electrolyte diffuses into a gel medium impregnated with an inner electrolyte containing its coprecipitate ion. The precipitation gives rise to interesting patterns of rich and diverse morphological characteristics.

The present work studies several forms of such precipitation patterns and is composed of four main sections: (1) Investigation of the pattern and boundary formation in the chemical Voronoi framework, (2) Study of the influence of a temperature gradient on several characteristics of a 1D cobalt hydroxide system, (3) Dynamical study on novel three precipitate systems, (4) Studies on the chaotic behavior in 2D lead chromate system.

In the first project, we investigate the chemical analogues of the mathematical Voronoi diagrams. While the original (traditional) systems include sources of equal concentration and equal hole diameter, we vary, separately, the concentration or the hole diameter of these sources, in four different sets of systems. We try several different parameters to characterize the formation of such sectioned or tiled diagrams. Later, we perform kinetics experiments, where we study the evolution of the intensity and velocity of the fronts with time. Additionally, we examine the pattern formation in the presence of linear interfaces.

In the second project, we report the first ever application of a temperature gradient on a Liesegang system. We subject the monotonic cobalt hydroxide system to negative (upward), from 40˚C to 15˚C, and positive (downward), from 15˚C to 40˚C, temperature gradients. The latter are also compared to tubes placed at constant temperatures of 15˚C, 18˚C and 27.5˚C, considering variations in the position of the last band, the number of bands formed, as well as the position of all the bands with band number.

In the third project, we present two new three-precipitate systems. The mere introduction of cadmium and manganese cations, individually, into systems initially containing cobalt and nickel cations yields beautiful and fascinating precipitation patterns. Later, we perform atomic absorption spectrophotometry measurements for some selected systems to determine the composition of the bands.

Finally, in the fourth project, we carry out a preliminary investigation on the chaotic behavior exhibited by the lead chromate system in 2D as a result of variations in the flow rates of the outer electrolyte.