Self-assembly drives rare-earth separations in a family of M₄L₄ cages

Rare-earth elements are indispensable to high-tech applications, making efficient rare-earth separations increasingly essential. An emerging approach to these challenging separations is the self-assembly of lanthanide-based supramolecular cages. In this study, we establish design principles for self-assembly-driven rare-earth separations by investigating four ligands with distinct substituents (termed L-Cbz, L-alkene, L-propyl, and L-benzyl). We found that these ligands react with rare-earth metals to yield M₄L₄ cages, M₂L₂ complexes, or no self-assembly products, depending on the identity of the metal. Single crystal X-ray diffraction shows that Dy₄(L-benzyl)₄ cages adopt a tetrahedral geometry, while pure L-Cbz precipitates from La₂(L-Cbz)₂ solution, suggesting that M₂L₂ is an unstable intermediate. Our results indicate that the bulk and flexibility of the ligand substituents modulates these cage-formation thresholds, providing design rules for L-based rare-earth separations. In a simple separation procedure, we found that L-Cbz exhibits outstanding separation factors (SF) for mixtures involving early lanthanides, achieving SF values of 639 for an La/Dy mixture, 835 for a Nd/Lu mixture, and 1767 for an La/Lu mixture. Density functional theory (DFT) calculations and extended X-ray absorption fine structure (EXAFS) measurements reveal that inter-ligand interaction, ligand-arm flexibility, and M-N bond lengths collectively govern M₄L₄ cage formation, providing practical guidelines for designing ligands for self-assembly-based rare-earth separations.