Electron conduction in nanoparticle agglomerates limits apparent Na⁺ diffusion in prussian blue analogue porous electrodes

Prussian Blue and its analogues (PBAs) are promising cation intercalation materials for energy storage and environmental applications. Here, we investigate Na⁺ diffusion in porous electrodes comprised of nickel hexacyanoferrate (NiHCF) PBA nanoparticles (NPs), conductive carbon additive, and polymer binder. We combine experimental characterization, an electronically limited version of porous electrode theory, and simulation to link rate limitations in galvanostatic cycling to electron conduction through NP agglomerates. Using potentiostatic intermittent titration (PITT), we find that the apparent diffusion coefficient of Na⁺ within NiHCF electrodes varies non-monotonically between 10−¹¹ cm²/sec (at 50% degree of intercalation, DOI) and 10−¹⁰ cm²/sec (at DOIs of 0% and 100%). Galvanostatic cycling of electrodes with different average NP-agglomerate sizes reveals that two-fold higher rate capability is achievable when agglomerate radius reduces two-fold, despite having the same NP size distribution. We subsequently introduce and validate theory that explains the variation of diffusion coefficient with DOI, yielding a simple expression for the apparent diffusion coefficient that is proportional to the effective electronic conductivity through NP agglomerates. Finally, using DOI-dependent PITT data we model galvanostatic (dis)charge through electroactive spheres and show agreement with experimental results, confirming that electron conduction through NP agglomerates limits the rate capability of NiHCF electrodes.