Prussian blue (PB) and its analogues (PBAs) are drawing attention as promising materials for sodium-ion batteries and other applications, such as desalination of water. Because of the possibilities to explore many analogous materials with engineered, defect-rich environments, computational optimization of ion-transport mechanisms that are key to the device performance could facilitate real-world applications. In this work, we have applied a multiscale approach involving quantum chemistry, self-consistent mean-field theory, and finite-element modeling to investigate ion transport in PBAs. We identify a cyanide-mediated ladder mechanism as the primary process of ion transport. Defects are found to be impermissible to diffusion, and a random distribution model accurately predicts the impact of defect concentrations. Notably, the inclusion of intermediary local minima in the models is key for predicting a realistic diffusion constant. Furthermore, the intermediary landscape is found to be an essential difference between both the intercalating species and the type of cation doping in PBAs. We also show that the ladder mechanism, when employed in multiscale computations, properly predicts the macroscopic charging performance based on atomistic results. In conclusion, the findings in this work may suggest the guiding principles for the design of new and effective PBAs for different applications.
Keywords: Prussian blue analogues; capacitive deionization; finite element; multiscale modeling; quantum chemistry; self-consistent mean-field theory.