Relation Between Particle Coordination Number and Porosity in Nanoparticle Films: Implications to Dye-Sensitized Solar Cells

The morphology and local three-dimensional structure of mesoporous nanoparticle TiO₂ films are simulated by using a simple method based on the random packing of spheres. The pore size distribution in the film that is predicted by the simulations is in excellent concurrence with experimental data. The spatial distribution of particles appears essentially random outside of the first shell of nearest neighbors. The average coordination number of particles depends strongly on film porosity. For compact films (40% porosity), the average coordination number is about 6.6, whereas for open-structured films (80% porosity), the average number of particle interconnections is as low as 2.8. At porosities (50-65%) typically present in nanocrystalline TiO₂ films employed in dye-sensitized solar cells, the simulations indicate that each particle is, on average, in contact with 4 or 5 others. However, the distribution of coordination numbers is broad. The implication of such highly branched particle structures on electron transport is discussed.