ELECTRODEPOSIT TREE PATTERNS IN LINEAR CELLS - EXPERIMENT AND COMPUTER-MODELS

Fractal tree patterns are generated experimentally in electrodeposits of CuSO4 in thin linear cells with relatively high voltages (15-30 V across two copper electrodes of separation 3.8 cm). The tree separations, tree widths and heights, and tree statistics are analysed. Tree pattern from two two-dimensional computer models, the three-directions biased random walk (BRW) model and the dielectric breakdown model (DBM) with probability cut-off, are produced. The BRW model compares very well with our experimental data. There is a minimum in the N(m) versus m curve where N(m) is the number of trees with mass m. For m small, N(m) approximately m(-tau) with 0 < tau < 1, in contrast to the DLA result that 1- < tau < 2. The fractal dimension of the tree D varies linearly with the fractal dimension of the walker D(w), which also differs from the DLA results of Matsushita et al. The DBM with cut-off gives trees with too much ramification compared to the experimental results, and fails to produce the sharp structure transition lines observed in previous electrodeposit experiments.