Ultrasound-Assisted Persulfate Activation for Degradation of Carbamazepine Using Fe ₃ O ₄ Catalyst: ANN–GA and RSM Modeling with Mechanistic Insights

Carbamazepine (CBZ), a persistent pharmaceutical contaminant in aquatic environments, poses ecological and human health risks due to its low biodegradability. This study investigates an effective strategy for CBZ removal via a heterogeneous Fenton system (Fe3O4 + H2O2) combined with peroxydisulfate (Na2S2O8, PDS) under ultrasound (US) irradiation. Fe3O4 particles synthesized by reverse coprecipitation exhibited higher surface area and porosity, enhancing catalytic activity compared to coprecipitation. Process optimization was performed using response surface methodology (RSM) and artificial neural network–genetic algorithm (ANN–GA) models. Under optimized conditions, RSM predicted 99.67% of degradation with an experimental value of 96.23 ± 1.27%, while ANN–GA predicted 98.79% with an experimental value of 94.61 ± 1.14%. Radical scavenging experiments revealed that SO4•– was the dominant reactive species, while •OH contributed secondarily. Energy efficiency analysis indicated that the US + Fe3O4 + H2O2 + PDS system exhibited the lowest electrical energy per order (EEO = 2662 kWh m–3 order–1) highlighting system efficiency. Fukui function analysis revealed four reactive carbon atoms (C1, C2, C9, and C13) on CBZ as highly susceptible to radical attack, validating their involvement in degradation pathways.