Density, fractal angle, and fractal dimension in linear Zn electrodeposition morphology

In this paper, we explore some aspects of the formation of tree-like structures (dendrites) with branching and ramifications in Zn electrodeposition systems. A special cell is designed wherein dendrites are grown between two parallel electrodes. All measurements are carried out at fixed voltage (9.5 V). As the concentration is varied at that fixed potential, the fractal box-count dimension is exactly anti-correlated with the pattern density. The latter is measured by the fraction covered by the electrodeposits, of a total area delimited by the cathode and the farthest dendritic tip. At relatively high concentration, the obtuse angle of lateral branching and the box dimension show a good correlation. The pattern density decreases with interelectrode distance, thus displaying a perfect correlation with the dependence of the current on the latter parameter. The time evolution of the pattern density exhibits an interesting oscillation caused by the preferential growth of individualized trees.