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 groups-are 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 methyl-enephosphonate), 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 (Delta G, Delta N, Delta S, 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.