Computational modeling of the template-assisted deposition of nanowires

In the present paper we developed and simulated a two-dimensional model for the electrodeposition inside the porous anodic alumina template, which deals with one only potentiostatic pulse applied to one pore. The potential distribution within the oxide is described by Laplace equation and the diffusion equation takes into account the transport of the metal ions in the solution. These equations are coupled by time-dependent boundary conditions at the deposition interface. The charge transfer process is described by a Butler–Volmer relationship. Two limit situations corresponding, respectively, to a completely insulating template and to a metallic cavity are described by the model. The first case corresponds to the ideal condition for a truly one-dimensional deposition because there is no current on the pore wall. In the second limit situation, the reacting interface is treated as an equipotential and the deposition kinetic is limited by the charge transfer process. Furthermore, in this case one has a bi-dimensional electrodeposit growth. Between these limit situations, the charge transfer process and the voltage drop inside the oxide are equally significative. In this case, the model captures the dynamic interaction between the concentration gradients and the potential distribution inside the oxide which allows us to explain several experimental observations.