Advanced Chromatographic Modeling for Sustainable Rare-Earth Separation in Nitric Acid Using Impregnated Silica Adsorbents

Chromatographic extraction is a promising complementary approach to solvent extraction for rare-earth elements (REEs) separation, offering reduced chemical consumption, simplified solvent management and lower environmental impact. However, its broader application in hydrometallurgy requires predictive models capable of describing the coupled adsorption, ion-exchange and mixed-mode mechanisms governing metal retention. This work presents a chromatographic equilibrium model based on mass-action laws that simultaneously accounts for liquid-phase speciation, protonation equilibria and the pH-dependent capacity of the stationary phase. The model is evaluated using experimental data for the impregnation of C18-grafted silica with bis(2-ethylhexyl)phosphoric acid (D2EHPA) and its subsequent application to the separation of fifteen REEs in nitric acid media. D2EHPA impregnation is successfully reproduced assuming a Langmuir-type adsorption mechanism, allowing estimation of both the adsorption constant and the D2EHPA pKa in the organo-aqueous impregnation solvent. REE retention is then modelled through ion exchange between nitrated REE complexes and the impregnated D2EHPA using only two manually adjusted parameters per element: the complex charge and the exchange equilibrium constant. The model accurately predicts retention times under isocratic elution with 0.15 and 0.30 mol·L⁻¹ HNO₃ as well as under linear-gradient conditions. Deviations observed at 0.60 mol·L⁻¹ HNO₃ suggest the existence of an additional low-pH retention mechanism not captured by the present ion-exchange formalism. The proposed framework provides a flexible basis for modelling adsorption, ion-exchange and mixed-mode chromatographic systems relevant to hydrometallurgical separations.