Modelling competitive coadsorption in electrochemical growth processes

We present analytical and numerical results for models of electrodeposition of ZnO films with organic additives, with a special focus on the growth of hybrid films with eosin Y. First we propose a rate equation model which assumes that the additives form branches with an exposed part above the ZnO deposit. The branches grow with larger rate than the pure film, and it is assumed that the rate of production of ZnO near them is proportional to the height exposed to the solution. This accounts for the generation of OH− ions from the reduction of dissolved oxygen near those branches and the reactions with Zn ions to form ZnO molecules. The steady state solution of this model shows both species growing with the rate of the branches, and qualitatively explains their catalytic effect. Subsequently, we propose a more realistic statistical model which represents the basic features of the formation of the hybrid deposits from Zn ions, a hydroxide precursor and eosin in solution. It avoids the description of the role of several species, such as the Zn ions, by using simple probabilistic rules for the reactions of eosin and oxygen, and takes into account diffusion from solution along the same lines of the diffusion-limited aggregation models. The catalytic effect is represented by the preferencial production of OH− ions near eosin branches, which form ZnO species. Simulations of the model were performed with concentrations in solution corresponding to the typical experimental values. It is shown that an improvement of the growth rate is possible only with a rather large diffusion coefficient of eosin in solution compared to that of hydroxide precursors, which qualitatively agrees with experimental findings. In the cases where a series of neighboring eosin clusters competitively grow,the increase in the growth rate and the high eosin loading observed in the simulated deposits also agree qualitatively with electrodeposition experiments. Preprint submitted to Elsevier Science 25 February 2008