Sodium to cesium ions: a general ladder mechanism of ion diffusion in prussian blue analogs

Prussian blue analogs (PBAs) form crystals with large lattice voids that are suitable for the capture, transport and storage of various interstitial ions. Recently, we introduced the concept of a ladder mechanism to describe how sodium ions inside a PBA crystal structure diffuse by climbing the frames formed by aligned cyanide groups in the host structure. The current work uses semi-empirical tight-binding density functional theory (DFTB) in a multiscale approach to investigate how differences in the size of the monovalent cation affect the qualitative and quantitative aspects of the diffusion process. The results show that the ladder mechanism represents a unified framework, from which both similarities and differences between cation types can be understood. Fundamental Coulombic interactions make all positive cations avoid the open vacant areas in the structure, while cavities surrounded by partially negatively charged cyanide groups form diffusion bottlenecks and traps for larger cations. These results provide a new and quantitative way of understanding the suppression of cesium adsorption that has previously been reported for PBAs characterized by a low vacancy density. In conclusion, this work provides a unified picture of the cation adsorption in PBAs based on the newly formulated ladder mechanism.