Fractal structures in two-metal electrodeposition systems I: Pb and Zn

Abstract

Pattern formation in two-metal electrochemical deposition has been scarcely explored in the chemical literature. In this paper, we report new experiments on zinc-lead fractal co-deposition. Electrodeposits are grown in special cells at a fixed large value of the zinc ion concentration, while that of the lead ion is increased gradually. A very wide diversity of morphologies are obtained and classified. Most of the deposited domains are almost exclusively Pb or Zn. But certain regions originating at the base cathode, ranging from a short grass alley to dense, grown-up bushes or shrubs, manifest a combined Pb-Zn composition. Composition is determined using scanning electron microscopy/energy dispersive x ray measurements as well atomic absorption spectroscopy. Pb domains are characterized by shiny leaf-like and dense deposits as well as flowers with round, balloon-like corollas. The Zn zones display a greater variety of morphologies such as thick trunks and thin and fine branching, in addition to minute "cigar flower" structures. The various morphologies are analyzed and classified from the viewpoint of fractal nature, characterized by the box-count fractal dimension. Finally, macroscopic spatial alternation between two different characteristic morphologies is observed under certain conditions.

Coefficients of Reaction‐Diffusion Processes Derived From Patterns in Rocks

“…This process is known as “spinodal decomposition.” For the Liesegang patterning, it has been interpreted as a discrete scenario of competing dynamics between spin‐flip (i.e., reaction) and spin‐exchange (i.e., diffusion) (Antal et al., 1999), evolving toward the final stationary pattern. It is worth noting that this category of generalized approach has gained significant success in diverse disciplines, including those involving morphogenesis in a system of natural materials (Arguello, Gumulya, et al., 2022; Arguello, Labanda, et al., 2022; Arguello et al., 2023; Christoph et al., 1999; Cooper, 2012; Nakouzi & Sultan, 2011), and those focusing on digital pattern recognition in for example, (Bertozzi et al., 2007; Theljani et al., 2020), due to the striking similarity in the essential force‐flux interactions of thermodynamic nature. Here, the concept of phase separation is employed for interpretation and parameter inversion of the rhythmically banded and spotted patterns of East Kimberley Zebra rocks, which can be extended to the general classification of Mississippi Valley Type deposits (L’Heureux, 2013; Kelka et al., 2017).…”

Self-organization in precipitation reactions far from the equilibrium

“…In addition, reaction-diffusion–type equations have been used to model neural signals ( 8 ), cardiac arrhythmias ( 9 , 10 ), uterine contractions ( 11 ), and a broad range of other dynamical processes ( 12 ). Similar examples from chemistry include pattern formation in the autocatalytic Belousov-Zhabotinsky reaction ( 13 , 14 ), the CO oxidation on platinum catalysts ( 15 ), gas discharge systems ( 16 ), corrosion processes ( 17 , 18 ), electrochemical deposition ( 19 , 20 ), and frontal polymerization ( 21 ). Many of these systems create self-propagating reaction zones that, in two or three dimensions, organize more complex patterns ranging from labyrinthine shapes ( 22 ) to spiral waves and, in some cases, create unique materials in their wake.…”

Random Spacing between Metal Tree Electrodeposits in Linear DLA Arrays

“…We observe random oscillations in the spacing sequence, and compute the entropy of this self-organizing system, which is shown to be consistent in all the considered sets. The present work is an extension of our previous work on electrolytic fractal growth in Zn [ 20 ], and two-metal [ 21 , 22 ] systems, and electroless growth of Ag by reduction of Ag + with Cu [ 23 ].…”