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Four new and one previously reported silver 4,4′-vinylenedipyridine (Vpe) coordination polymers were tested as anion exchange materials to assess their potential for pollutant sequestration and compared to analogous silver 4,4′-bipyridine (bipy) coordination polymers. The materials were synthesized using nitrate, tetrafluoroborate, perchlorate, perrhenate, or chromate as the anion to produce cationic coordination polymers with solubilities ranging from 0.0137(7) to 0.21(5) mM. These values are much lower than silver bipy coordination polymers [0.045(3) to 5.5(5) mM] and agree with thermochemical calculations. [Ag(Vpe)+][BF4–], [Ag2(Vpe)2.52+][CrO42–]·5H2O, and [Ag(Vpe)+][ReO4–]·2H2O structures are reported. Perrhenate and chromate ions in an equimolar solution were fully adsorbed by [Ag(Vpe)+][NO3–]·3H2O [620(2) and 137.1(6) mg/g, respectively] as well as by [Ag(Vpe)+][BF4–] [661.8(3) and 190(3) mg/g, respectively] via anion exchange. DFT calculations show that torsional energetics play a significant role in the formation thermodynamics by reducing the energy cost by as much as 4.8 kJ/mol when bipy is replaced with Vpe in silver-based coordination polymers. The results obtained with the flat Vpe ligand highlight the potential role of coordination polymers in practical anion exchange.