Thermodynamic Favorability Zones for the Selective Recovery of Critical Elements

Abstract Increased use of modern technologies has triggered a need to secure the supply chain of critical minerals. This can be potentially achieved through their separation and recovery from waste and industrial streams. To begin to address this need, we adapt Lackner’s thermodynamic calculations for carbon capture from air to define thermodynamic favorability zones consistent with mineral concentrations from various waste streams. These calculations are based on the use of an ideal sorbent, allowing for the determination of the minimum energy a sorbent would need to drive the concentration of ions in solution from an initial concentration (C1) to a final equilibrium concentration (C2). Our analysis focuses on dilute solutions in which full dissociation of ionic species can be assumed. We find that when the initial concentration of the ion in solution is sufficiently low (C1 ≤ 1 × 10–6 mol kg–1) solutions approach ideal behavior, and the free energy of sorption becomes independent of ion identity establishing a free energy limit of approximately −13.64 kcal mol–1 for near-quantitative capture. Conversely, in concentrated solutions, nonideal activities manifest differences in the required sorption free energy based on ion size and charge. We observed that as concentration increases, the necessary free energy of sorption becomes less negative, and an inherent selectivity for monovalent over multivalent ions emerges. This selectivity collapses at both the infinitely dilute limit and near-quantitative capture. These results suggest that solution concentration is not just a boundary condition for ion separation processes, but a potentially tunable design parameter that governs both energetic cost and intrinsic electrostatic selectivity.