Probing the Role of Electronic Conduction during the Apparent Diffusion of Cations in Nickel Hexacyanoferrate
Authors: Smith Kyle Christopher , Shrivastava Aniruddh 
Published: February 2020

Nickel hexacyanoferrate (NiHCF) is an attractive candidate intercalation host compound for grid scale sodium-ion batteries1,2 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
=R
2/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, Dapp
varied with a concave-up profile with respect to the degree of intercalation (x in Na1+

x
NiFe(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 Dapp
varies (1) in inverse proportion with the volumetric differential capacitance Cdiff
of NiHCF and (2) in proportion to the effective electronic conductivity of NiHCF nanoparticle agglomerates: D

app

=
σ/
Cdiff
. Here, Cdiff
varies inversely with the slope of intercalation potential with respect to x and thus, is responsible for the concave-up variation of Dapp
with x. Furthermore, electronic conductivity of dry porous NiHCF compacts was measured, based upon predicted values of Dapp

, 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

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