Combined supramolecular and mesoscale modelling of liquid–liquid extraction of rare earth salts

International audience; We develop a minimal model of weak aggregation in water in the case of neutral extractant in a Winsor II regime, i.e. dispersed microemulsions in thermodynamic equilibrium with concentrated brine. All the terms involved in the free energy associated with the transfer of ions from a concentrated aqueous to an organised organic phase have been estimated: supramolecular effects, bulk terms, extractant film bending and electric polarisation terms. This allows the rationalization of the paradoxical observation of apparent stoichiometry: “constant” associated with the phase transfer that varies with the nature of the solvent and the bending properties of the surfactant. The extractant film is characterized by its spontaneous packing parameter (of the order of 4) and its intrinsic rigidity of the order of 6.25 kJ mol$^{−1}$ (2.5 $k_BT$). This multi-scale study combining supramolecular chemistry and mesoscale modelling approach allows a large reduction of the number of parallel apparent equilibria currently used for dimensioning extraction devices. Prediction power versus variations of water activity and temperature is in reasonable agreement with observations made in typical pilot cascade