Statistical modelling of electrochemical deposition of nanostructured hybrid films with ZnO–Eosin Y as a case example

We study models of electrodeposition of hybrid organic–inorganic films with a special focus on the growth of ZnO with Eosin Y. First we propose a rate equation model which assumes that the organic additives form branches with an exposed part above the ZnO deposit, growing with larger rate than the pure film and producing ZnO at the exposed length. This accounts for the generation of OH− ions from reduction of dissolved oxygen near the branches and reactions with Zn2+ ions to form ZnO molecules. The film grows with the same rate of the branches, which qualitatively explains their catalytic effect, and we discuss the role of the additive concentration. Subsequently, we propose a statistical model which represents the diffusion of the hydroxide precursor and of eosin in solution and adopt simple probabilistic rules for the reactions, similarly to diffusion-limited aggregation models. The catalytic effect is represented by the preferential production of OH− ions near eosin. The model is simulated with relative concentrations in solution near the experimental values. An improvement of the growth rate is possible only with a rather large apparent diffusion coefficient of eosin in solution compared to that of hydroxide precursors. When neighboring eosin clusters competitively grow, the increase in the growth rate and a high eosin loading are observed in the simulated deposits. Those features are in qualitative agreement with experimental results.