Rare-earth elements (REEs) are indispensable for modern technology; consequently, effective materials for REE extraction and separation are in demand. Polymeric chelators polymers with metal binding functional groupsare often used in these applications due to their low cost and high selectivity for target ions, with phosphonate-containing polymers often proving particularly effective. We synthesized linear poly(ethylenimine methylenephosphonate), a material previously made only with a branched architecture, and studied its rare-earth-element chelation properties as a function of molecular weight (7−680 kDa) and degree of phosphonation (0−85%) using isothermal titration calorimetry (ITC). ITC enabled the determination of the full thermodynamic profile (ΔG, ΔH, ΔS, K a , and stoichiometry) for each polymer−REE interaction in aqueous solution. We observed entropically driven metal−polymer binding with five REEs, independent of polymer molecular weight and degree of functionalization. Finally, we characterized the metal-ion-induced aggregation behavior of these polymers using dynamic light scattering.