Multi-reactional kinetic modeling of phosphate sorption on goethite using artificial neural networks
Authors:   , Pogorzelski Denison Queiroz 
Published: August 2022

Phosphorus (P) is a limiting nutrient for plant biomass production in terrestrial ecosystems, and the nutrient raising the most concern regarding its use and availability. Most of this limitation occurs in the highly weathered soils of the tropics, where the low bioavailability and overall geochemical cycling of P are controlled by sorption reactions on soil minerals, especially oxides. Goethite is one of the most important Fe oxides present in these soils, with sorption reactions occurring at the goethite-water interface defining P fate in such environment. As such, understanding the mechanisms controlling P sorption on these materials is of uttermost importance to improve our overall understanding of the P biogeochemical cycling to improve P use efficiency. Herein, we are bringing an approach which consists in assessing P sorption and desorption capacity of goethite at different temperatures and then investigating the kinetic mechanisms by applying multi-reactional modeling through Hopfield artificial neural network (HANN). Two mechanisms were investigated, a sequential reactions type (P in solution ⇌ B⇌ C) and another with independent reactions (B ⇌ P in solution ⇌ C). The mechanism that better fit the experimental data was used to provide the thermodynamic parameters. Furthermore, these mechanisms were also tested in a second sorption experiment on phosphate-preloaded goethite. The results showed that goethite adsorbed 13.34, 18.11 and 24.23 μmol g -1 of P and desorbed 48, 28 and 23 % of the sorbed P in water at 278, 298 and 323 K, respectively. After 20 days of incubation, phosphate-preloaded goethite sorbed 6.24 μmol g -1 more P and desorbed 54 % of that P at 298 K, demonstrating a lower adsorption capacity and a greater capacity for desorption facing a new P application. The mechanism with sequential steps better fit the experimental data, indicating that the step 1 (P in solution ⇌ B) is the trigger for the step 2 (B ⇌ C). Step 1 was faster than step 2, meaning that, kinetically, step 2 is the limiting step on P sorption mechanism onto goethite. Both steps were spontaneous (ΔG°<0), but the step 1 was exothermic (ΔH°<0) and an enthalpy driven reaction (ΔH°>TΔS°), indicating that specie B is related to a high intermolecular interaction force with the goethite surface; while step 2 was endothermic (ΔH°>0) and entropy driven (ΔH°<TΔS°), indicating that specie C is related to surface or bulk precipitated Fe-P (e.g., strengite or an analogue). Both tested mechanisms failed to fit the model on the P sorption data from second sorption experiment, indicating that the P sorption mechanism in phosphate-preloaded goethite has different key steps. This approach brings important information regarding P sorption on Fe oxides, one of the most important phenomena controlling P cycling and availability in highly weathered soils. Multi-reactional modeling by HANN were able to provide insights on the P sorption mechanism and their specific steps. Defining these steps and the thermodynamics controlling it help us clarifying and focusing our future research on our quest to elucidate such important environmental reactions. Keywords: Stirred-flow system. P adsorption. P desorption. Rate constants. Hopfield artificial neural network.