Evaluation of extraction efficiency, thermodynamics, and kinetics of selective rare earth elements using TOPO-stearic acid deep eutectic solvent

The growing demand for rare earth elements (REEs) in advanced technologies has intensified the need for sustainable and efficient recovery methods. In this study, hydrophobic deep eutectic solvent (HDES) composed of trioctylphosphine oxide (TOPO) and stearic acid were investigated for the liquid–liquid extraction of five REEs—praseodymium (Pr), neodymium (Nd), samarium (Sm), dysprosium (Dy), and erbium (Er)—from aqueous solutions. The effects of key parameters including phase ratio, contact time, REE concentration, temperature, and solution pH were systematically examined. Maximum extraction efficiencies reached 98.4% for Dy(III), 98.1% for Er(III), 97.2% for Sm(III), 96.4% for Nd(III), and 95.9% for Pr(III) under optimal conditions of 0.75 mL HDES volume, 30-minute contact time, and pH 4.37. Thermodynamic analysis indicated endothermic and spontaneous extraction, with ΔH ranging from 17.86 to 82.39 J/mol and ΔG values below -32.5 kJ/mol, supporting the role of metal–ligand complexation and HDES structural rearrangement. Kinetic studies confirmed that the extraction follows a pseudo-second-order model (with R 2 ∼ 1 ), with reaction rates governed by interfacial complexation rather than bulk diffusion. Additionally, increased stirring rate and interfacial area enhanced extraction efficiency from ∼ 96% to a plateau at 100% removal for both parameters, indicating that film diffusion at the interface is a key rate-limiting factor. These findings demonstrate the promising application of TOPO-based HDES for selective, efficient, and greener REE recovery from aqueous systems.