Nickel hexacyanoferrate (NiHCF) is an attractive candidate intercalation host compound for grid scale sodium-ion batteries^1,2 and for efficient electrochemical desalination of sea and brackish water resources.^3,4 Its open-framework crystal structure and facile intercalation kinetics produce long life with high capacity retention, while achieving charge capacities between 60 to 70 mAh/g.¹ However, to improve the in operando rate capability and selectivity of cation intercalation within NiHCF, and similar Prussian Blue analogues (PBAs), transport and kinetic processes must be characterized to identify rate-limiting mechanisms. In particular, a lack of clarity exists with respect to apparent diffusion that takes place during (de)-intercalation of cations. In the present work we explore this phenomenon through a combination of experimental characterization and particle-scale transport modelling. Most significantly, our preliminary results reveal that slow electronic conduction in NiHCF nanoparticle agglomerates limits apparent diffusion, rather than crystal-scale diffusion of cations themselves.We also show that experimental measurement of the apparent diffusion time scale (τ_D=R²/D_app where R and D_app are particle radius and the apparent diffusion coefficient) is more insightful and reliable, compared to measurements of diffusion coefficients alone.

Previous research has focused on the measurement of PBA electronic conductivity σ and bulk Diffusivity D for fully dense thin films, while electron and cation transport within PBAs in the nanoparticulate formats needed for economically constrained applications (which require simultaneously high charge capacity and current density) have not been explored in detail. Prussian Blue thin films are known to have slow electronic conduction with σ≅5x10^-5S/m.⁵ Diffusion coefficients of Na⁺ and Rb⁺ in NiHCF⁶ and of K⁺ in copper hexacyanoferrate (CuHCF)⁷ thin films were approximately 10^-9 cm²/s using chronoamperometry,⁶ cyclic voltammetry,⁷ and impedance spectroscopy.⁷ Further, the coupling of cation diffusion and electron hopping inhibits isolation of these two effects using electrochemical characterization techniques.⁷

Presently we characterize cation diffusion rates within slurry-cast porous electrodes that contain NiHCF nanoparticles, electronically conductive carbon, and polymer binder. We use the potentiostatic intermittent titration technique (PITT) to determine the apparent diffusion time scales by fitting current/time response to closed-form expressions⁸ derived for porous electrodes having kinetic and diffusive transport limitations. We probed the effect of agglomeration of NiHCF nanoparticles by fabricating two types of electrodes. In particular, NiHCF powder was mixed with conductive carbon using either (1) a mortar/pestle or (2) a vortex mill with 5mm steel beads. Microscopy of cast electrodes revealed a larger agglomerate size and higher size dispersity for milled electrodes than for unmilled ones. Consequently, the milled electrode showed a significantly poorer galvanostatic rate capability and longer diffusion time scales. For both electrodes, D_app varied with a concave-up profile with respect to the degree of intercalation (x in Na_1+xNiFe(CN)₆). Transport modelling of these diffusion processes during galvanostatic (dis)charge, which predicts the spatiotemporal variation of of x within NiHCF nanoparticles, showed consistent scaling of charge utilization with C-rate.

To explain the variation of diffusion coefficients with intercalant fraction, a new theoretical model is presented. Assuming facile crystal scale diffusion and interfacial kinetics, we find that D_app varies (1) in inverse proportion with the volumetric differential capacitance C_diff of NiHCF and (2) in proportion to the effective electronic conductivity of NiHCF nanoparticle agglomerates: D_app=σ/C_diff. Here, C_diff varies inversely with the slope of intercalation potential with respect to x and thus, is responsible for the concave-up variation of D_app with x. Furthermore, electronic conductivity of dry porous NiHCF compacts was measured, based upon predicted values of D_app, based on our theory, were consistent with measured values from PITT. These findings confirm that apparent diffusion in NiHCF is indeed limited by slow electronic conduction and motivate further studies to enhance diffusion rates and to explore selectivity.

Acknowledgements: We are grateful for funding and support by the College of Engineering, UIUC and Mechanical Science and Engineering Department at UIUC

References

1. S. V. . Wessells, C. D.; Peddada and Y. Huggins, R. A.; Cui, Nano Lett., 11, 5421–5425 (2011).
2. M. Pasta, C. D. Wessells, R. A. Huggins, and Y. Cui, Nat. Commun., 3, 1149 (2012)
3. K. C. Smith, Electrochim. Acta, 230, 333–341 (2017)
4. S. Porada, A. Shrivastava, P. Bukowska, P. M. Biesheuvel, and K. C. Smith, Electrochim. Acta, 255, 369–378 (2017)
5. A. Xidis and V. D. Neff, 138 (1991).
6. T. Shibata and Y. Moritomo, Chem. Commun. (Camb)., 50, 12941–3 (2014)
7. H. Kahlert, U. Retter, H. Lohse, K. Siegler, and F. Scholz, J. Phys. Chem. B, 102, 8757--8765 (1998).
8. J. Li, F. Yang, X. Xiao, M. W. Verbrugge, and Y. T. Cheng, Electrochim. Acta, 75, 56–61 (2012).