Critical materials such as rare earth and battery elements are essential to clean energy, electric mobility, and modern technologies, yet their production remains dominated by solvent
extraction, an inefficient, costly, and environmentally cumbersome process. We developed advanced displacement and ligand-assisted displacement (LAD) chromatography methods that enable scalable, high-purity recovery of these materials from both mineral ores and waste streams. Our design framework, which is based on constant-pattern wave theory, dimensionless group analysis, and intrinsic (scale-independent) parameters, allows predictive optimization of operating conditions, including displacer concentration, loading fraction, and flow rate, for desired purity, yield, and pressure drop targets. This approach was used to develop multizone chromatographic cascades, capable of producing >99.5% pure Nd, Pr, and Dy from waste magnets and Nd, Pr, Ce, and La from bastnäsite or monazite concentrates. A three-zone LAD cascade with recycle achieved up to a 700-fold increase in sorbent productivity relative to a single-zone LAD system. A parallel process for lithium, nickel, cobalt, and manganese salts attained 99.5% purity and 99% yield. The rare earth process was scaled up 1,500-fold and the battery element process 500-fold, both successfully demonstrated at the ReElement Technologies pilot facility (Noblesville, Indiana). All experimental chromatograms were in close agreement with process model predictions across various scales and feed compositions. These results establish chromatographic separation as a viable, efficient, and environmentally sustainable alternative to solvent extraction and indicate its potential for contributing to a resilient circular economy of critical materials.