Routes to fractality and entropy in Liesegang systems

Tunability of Self-Organized Structures Based on Thermodynamic Flux

Nature establishes structures and functions via self-organization of constituents, including ions, molecules, and particles. Understanding the selection rule that determines the self-organized structure formed from many possible alternatives is fundamentally and technologically important. In this study, the selection rule for the self-organization associated with a reaction-diffusion system was explored using the Liesegang phenomenon, by which a periodic precipitation pattern is formed as a model system. Experiments were conducted by systematically changing the mass flux. At low mass fluxes, a vertically periodic pattern was formed, whereas at high mass fluxes, a horizontally periodic pattern was formed. The results inferred that a structural vertical-to-horizontal periodicity transition occurred in the self-organized periodic structure at the crossover flux at which the entropy production rate reversed. Numerical analyses attributed the as-observed flux-dependent structural transition to the selection of the self-organized pattern with a higher entropy production rate. These findings contribute to our understanding of how nature controls self-organized structures and geometry, potentially facilitating the development of novel designs, syntheses, and fabrication processes for well-controlled organized functional structures.

Random Spacing between Metal Tree Electrodeposits in Linear DLA Arrays

When we examine the random growth of trees along a linear alley in a rural area, we wonder what governs the location of those trees, and hence the distance between adjacent ones. The same question arises when we observe the growth of metal electro-deposition trees along a linear cathode in a rectangular film of solution. We carry out different sets of experiments wherein zinc trees are grown by electrolysis from a linear graphite cathode in a 2D film of zinc sulfate solution toward a thick zinc metal anode. We measure the distance between adjacent trees, calculate the average for each set, and correlate the latter with probability and entropy. We also obtain a computational image of the grown trees as a function of parameters such as the cell size, number of particles, and sticking probability. The dependence of average distance on concentration is studied and assessed.