  In a recent paper [1] we developed a theoretical model to describe current
transients arising during electrochemical deposition experiments performed at
the bottom of sub-micrometric cylindrical vessels with permeable walls. In the
present work we extended the model for describing the current transients
observed during electrodeposition through porous networks produced by colloidal
crystals. Instead of considering a cylindrically shaped membrane with a
constant cross sectional radius, the membrane will have a corrugated surface,
with a radius that changes periodically with z, the vertical axis of the
cylindrically corrugated vessel. According to the model, the porous network is
formed by the replication of those units, put side by side in close contact,
and impregnated by an electrolytic solution. Through the lateral surface of
those cylinders we allow for a selective flux of species. The inward or outward
flux obeys a complex dynamics regulated by the competition between the
diffusion kinetics and the chemical kinetics that answer for the reduction of
species at a reactive surface located at the bottom of the cylindrical
cavities. The analytical expression for the current transient is complemented
by a random prescription for the influx or outflux of matter through the
lateral surface plus a modulation in its intensity that follows the surface
corrugation. The theoretical data are compared with the current transients
obtained in nanosphere lithography experiments.
