Figure 5. Scaling laws for dealloying kinetics and pattern length scales.

(a) Log–log plot of dealloying depth x_i versus time from simulations (lines) and experiments (dots) for different alloy composition. The dashed black line represents a power law with the characteristic 1/2 exponent of diffusion-limited kinetics. (b) Interface pattern scale at the dealloying front λ₀ versus dealloyed depth x_i showing agreement of simulations and experiments with theory (equation (3) is represented with a dashed line) over four decades of length scales for diffusion-coupled growth of lamellar/filamentary disconnected structures (c₀=15%). Topologically complex connected structures for higher c₀ exhibit an increase of λ₀ with dealloyed depth, but with λ₀ smaller than predicted by equation (3) that no longer holds. (c) Log–log plot of λ versus d where λ≥λ₀ denotes the structure scale at a distance d from the dealloying front increased by coarsening for connected structures. Simulations and experiments follow the predicted coarsening behaviour with a 1/2 exponent. (d) Simulation snapshot and cross-sections showing the coarsening of the connected structure obtained in 3D simulation for c₀=25%. Error bars on the experimental data points represent the s.d. obtained from 20 measurements.