Nonequilibrium ion transport in a hybrid battery material

Hybrid materials, which combine inorganic and molecular components, often exhibit structural flexibility that enables unusual functional responses. Among them, Prussian blue analogs (PBAs) are a promising class for post-lithium battery technologies. Here, we show that nonequilibrium transformation processes govern the charge-storage mechanism of a PBA electrode, K₂Mn[Fe(CN)₆]. Ostensibly, this behavior mirrors that observed in high-rate cycling of conventional cathodes such as LiFePO₄ yet arises here for fundamentally different reasons-namely, low elastic moduli and cooperative distortions inherent to the hybrid framework. Using operando x-ray absorption spectroscopy with Metropolis matrix factorization and x-ray diffraction, we show that framework flexibility limits transport kinetics and promotes collective, metastable pathways. Our results not only highlight various directions for PBA cathode optimization but also suggest a broader relevance of nonequilibrium mechanisms for mass transport in hybrid materials beyond PBAs alone.