Interplay of Hydration and Framework Dynamics for Na ⁺ Diffusion in Defect-Free Mn-Based Prussian Blue Analogues: First-Principles Calculations

Mn-based Prussian blue analogues (Mn-PBAs, Mn[M(CN)6]; M = transition metal), three-dimensional metal–organic frameworks (MOFs), are promising cathode materials for next-generation Na-ion batteries (NIBs). However, the Na+ diffusion mechanism remains unclear due to the uncertainty of Na+ occupation within the unit cell and the inevitable presence of defects and water in the bulk. Here, we comparatively investigate Na+-ion self-diffusion in defect-free Mn[M’(CN)6], where M’ is Fe and Mn, using density functional theory and molecular dynamics simulations. We focus on the influence of interstitial water and the framework cage size on Na+ diffusivity. For hydrous Mn[M’(CN)6], Na+ ions exhibit negligible self-diffusivity because of strong coordination by interstitial H2O molecules, forming slowly diffusing Na+–H2O complexes. This behavior implies that the classical Stokes picture frequently discussed, in which diffusivity is governed by the size of the solvation shell, does not hold in these systems. Accordingly, the removal of interstitial water is expected to improve the rate capability of PBA cathodes in NIBs. Regarding anhydrous Mn[M’(CN)6], the Na+-ion self-diffusion coefficients in NaMn[Fe(CN)6] and NaMn[Mn(CN)6] are comparable at low temperatures. At higher temperatures, however, NaMn[Mn(CN)6] exhibits higher diffusivity despite having lattice parameters similar to those of NaMn[Fe(CN)6]. This difference is found to arise from enhanced octahedral tilting fluctuations in NaMn[Mn(CN)6], leading to higher activation energies, and demonstrates that dynamical framework distortions, rather than static lattice parameters, provide a more suitable descriptor of Na+ self-diffusivity. Overall, this study clarifies the atomistic picture of the detrimental effect of hydration on Na+ transport and offers a new perspective for the design of high-performance PBA cathodes.