Prussian blue analogues (PBAs) containing metal centers bridged by cyanide ligands exhibit one of the simplest structures among metal organic frameworks, which lends them to facile and reversible insertion of monovalent cations. Such a property has motivated their use in aqueous electrochemical separations, including our most recent demonstration of brackish water desalination with only 25% more energy consumption than thermodynamic minimum.¹ Despite their selectivity bias toward cations of small hydrated radius being known for 36 years,² the microscopic mechanisms responsible for such bias that could be used to inform the rational design of future materials are not well understood.

Accordingly, we report on our recent efforts^3,4 to uncover the interactions between inserted cations, interstitial water, and PBA lattices that produce selectivity bias. To understand the interplay between structural distortion, bonding, and water uptake from contacting electrolyte we use a first-principles approach that combines machine learning with density functional theory and grand potential analysis to explore the potential energy landscapes of disordered arrangements of interstitial species in nickel hexacyanoferrate PBA. Here, a competition for dative bonds of acidic interstitial cations between basic oxygen in interstitial water and basic cyanide ligands is shown to result in complexation between cations and water that deviate fundamentally from bulk hydration in pure water, despite the common attribution of PBA selectivity to purely steric effects of cation hydration. Van der Waals interactions are further shown to enhance the formation of water clusters and extended hydrogen-bonded networks within the PBA host, depending on the bare ionic radius of inserted cations. Grand potential analysis is performed to ultimately produce previously observed selectivity bias (Cs⁺ > K⁺ > Na⁺) and to determine the equilibrium hydration degree of the PBA in both reduced and oxidized forms. This analysis shows that small (Na⁺) and moderately sized (K⁺) cations require two to four water molecules per formula unit in both reduced and oxidized forms of the PBA, while large cations (Cs⁺) exhibit much smaller hydration levels in oxidized form and exhibit no hydration in reduced form.

References

1. Reale, E. R., Regenwetter, L., Agrawal, A., Dardón, B., Dicola, N., Sanagala, S. & Smith, K. C. Low porosity, high areal-capacity Prussian blue analogue electrodes enhance salt removal and thermodynamic efficiency in symmetric Faradaic deionization with automated fluid control. Water Res. X 13, 100116 (2021).
2. Ikeshoji, T. Separation of Alkali Metal Ions by Intercalation into a Prussian Blue Electrode. J. Electrochem. Soc. 133, 2108 (1986).
3. Liu, S. & Smith, K. C. Linking the polyatomic structure of interstitial H2O and cations to bonding within Prussian blue analogues ab initio using gradient-boosted machine learning. Phys. Rev. Mater. 5, 035003 (2021).
4. Liu, S. & Smith, K. C. Effects of interstitial water and alkali cations on the expansion, intercalation potential, and orbital coupling of nickel hexacyanoferrate from first principles. J. Appl. Phys. 131, 105101 (2022).