Random Spacing between Metal Tree Electrodeposits in Linear DLA Arrays.

Jaad Tannous,Lina Anouti,Rabih Sultan

doi:10.3390/e20090643

Abstract

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.

Highlights

Fractals are tree-like ramification structures that appear in a variety of physico-chemical systems [1].They replicate on different length scales and are essentially self-similar [2,3]
Just as trees grow naturally along a linear array, trees of metal deposits can be grown by electrolysis or via a mere redox reaction
Molecular dynamics simulations were performed [29] to study the diffusion of Thouy and Jullien fractal aggregates as a function of their mass and fractal dimension

Summary

Introduction

Fractals are tree-like ramification structures that appear in a variety of physico-chemical systems [1] They replicate on different length scales and are essentially self-similar [2,3]. Just as trees grow naturally along a linear array, trees of metal deposits can be grown by electrolysis or via a mere redox reaction. The former ones are known as electrodeposits, while the latter are coined electroless fractals. The growth of zinc electrodeposits was studied experimentally in both linear [14,20] and circular [31] geometries, and simulated using a stochastic model based on the dielectric breakdown model (DBM). Using a mathematical model of coupled agglomeration and growth, Al2 O3 monomer and agglomerated inclusion particles of hydrodynamic diameter between 6 μm and 9 μm were demonstrated [31] to accumulate, driven by a large swirl of flow in both inlet and outlet zones

Methods

Results

Conclusion