Modelling competitive coadsorption in electrochemical growth processes
  We present models of electrodeposition of ZnO films with organic additives, with 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, growing with larger rate than the pure film, and that the rate of production of ZnO near those branches is proportional to the height exposed to the solution. This accounts for the production of OH- ions near the branches and the reactions with Zn++ ions. The steady state solution shows both species growing with the rate of the branches, and qualitatively explains their catalytic effect. Subsequently, we propose a more realistic statistical model for the formation of the hybrid deposits from Zn++ ions, a hydroxide precursor and eosin in solution. Simple probabilistic rules are used for reactions of eosin and oxygen, taking 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. 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, in agreement 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. 
Fabio D. A. Aarao Reis, J. P. Badiali, Thierry Pauporte, Daniel Lincot