A kinetic framework based on effective reactive centers for optimizing Fe3⁺-doped TiO₂ photocatalysts: mechanistic insights into Acid Orange 7 degradation and implications for wastewater treatment.

Optimizing doped photocatalysts for advanced oxidation processes requires kinetic models that connect macroscopic removal rates with the surface processes governing charge carrier dynamics. Here, a deterministic kinetic framework employing two operational concepts-the effective photon concentration (Ieff) and effective reactive center concentrations-is developed to describe the photodegradation of the model pollutant Acid Orange 7 over Fe3⁺-doped TiO₂ under UV-A irradiation. An 18-step elementary reaction network incorporating seven chemically distinct reactive centers (Ti-OH, Fe-OH, Ti-O₂, Fe-O₂, semi-effective traps, and a collective •OH sink) is constructed and validated against 15 experimental datasets covering systematic variations in pH, Fe3⁺ loading, TiO₂ dosage, H₂O₂ concentration, and dissolved oxygen. The Fe3⁺/Fe2⁺ redox shuttle is kinetically embedded within Fe-specific steps. Rate constants (16 global parameters) were estimated together with condition-dependent Ieff and reactive center concentrations using a hybrid manual-automatic fitting procedure in MATLAB; the model reproduces all measured concentration-time profiles with R2 > 0.99. The complexity of the mechanism is justified by its ability to capture non-monotonic degradation trends and pH-dependent surface charging with a single set of rate constants, while the effective variables follow physically reasonable trends across all conditions. The model indicates that under optimal conditions (3 wt% Fe, pH 3, air-sparged), the superoxide generation flux at Fe3⁺-O₂ centers is estimated to be approximately 1.8-fold higher than that at Ti4⁺-O₂ centers-a model-derived inference awaiting independent experimental verification. The framework quantitatively captures the dual promoter/scavenger role of H₂O₂ and identifies maximization of Ieff and hole-trapping centers at pH 3 with 3 wt% Fe as clear optimization criteria. This kinetic tool can assist in the rational selection of operating conditions for Fe-doped TiO₂ in photocatalytic wastewater treatment and provides a transferable methodology for the mechanistic diagnosis of other doped catalyst systems.