Adsorption isotherms of N3 dye on TiO2 mesoporous for dye sensitized solar cells: Their realization, their modeling and consequent interpretations using a statistical physics treatment

Highlights: • A statistical physics model has been developed for the considered N3 adsorption. • Three adsorption isotherms of N3 dye on TiO₂ were fitted and interpreted. • Using the energetic parameters to calculate the adsorptions energies. • New method based on Kelvin equation is used to determine the (PSD) and the (AED). In this paper, we have realized three adsorption isotherms of the ruthenium-based dye molecules, cisdi (thiocyanato)bis (2,2′bipyridyl-4,4′-dicarboxylate)ruthenium (II) (N3) into the mesoporous TiO₂ (anatase) at three different temperatures:298.15, 313.15 K and 333.15 K using the UV–vis spectroscopy method. These adsorption isotherms have been simulated using several models established through a statistical physics formalism in order to involve in model expressions some parameters which have physicochemical meaning and to better interpret information about the adsorption process at the molecular level. A multilayer model was determined to best reproduce and simulate the experimental data. In this model, five parameters affecting the adsorption process have been adjusted, namely the number of molecules per adsorption site n, the density of receptor sites N_m, the two energetic parameters: the concentrations at half saturation C₁ and C₂ and the number of layers N_L. These parameters have been deduced from the fitting of the experimental adsorption isotherms by numerical simulation. Thanks to the grand canonical ensemble in statistical physics, the energetic parameters suggest physical bonding of the N3 dye to the TiO₂ surface in the case of low concentrations through monodentate and bidentate with hydrogen bond configurations. Finally, a new method based on Kelvin equation in the liquid phase is used to determine the pore size distribution (PSD) and the adsorption energy distribution (AED) of the mesoporous TiO₂.