Electrochemical characterization of electroactive films at electrodes requires models for interpretation of experimental results. Such films at electrodes may range in complexity from dense films for which uniform one-dimensional diffusion of intercalants provides an adequate description to porous systems with conductivity varying with state of charge and where more than one species may contribute to film conductivity. We describe here on-going attempts at extending models to these more complex situations within an analytical framework, and focus on interpretation of experimental results in view of the models. We thus review previous models suggested for describing the impedance of porous electroactive films of mixed conductivity, and extensions of the theory to include the effect of space charges within the porous matrix on the electrode capacitance. The Poisson-Boltzmann equation was thus solved for spherical geometry by use of Green’s functions, resulting in an analytical (closed form) integral expression that could be solved iteratively using a solution to the linearized Poisson-Boltzmann equation as the first order approximation for the potential. Practically identical results were produced when solving the governing equation by finite differences. Calculated concentration and potential profiles can be used to determine at which combination of carrier concentration and radius a particle is too small to sustain an extended space charge layer. Also, the surface capacitance-potential behavior has been obtained for extrinsically and intrinsically semiconducting particles. For the intrinsic case the behavior had a minimum value at the flatband potential. Extrinsic particles approached Mott-Schottky behavior at high dopant levels or large radii. These results will be discussed in the context of intercalation in porous electrodes, as well as extensions to other measurement methods than impedance.

References

[1] S. Sunde. I. A. Lervik, L.-E. Owe, and M. Tsypkin, “An impedance model for a Porous Intercalation Electrode with Mixed Conductivity”, J. Electrochem. Soc., 156 (2009) B927

[2] Sunde, S. , Lervik, I.A., Tsypkin, M., Owe, L.-E. , “Impedance analysis of nanostructured iridium oxide electrocatalysts”, Electrochimica Acta, 55 (2010) 7751 – 7760

[3] M. Tjelta and S. Sunde, “Current-distribution effects on the impedance of porous electrodes and electrodes covered with films”, J. Electroanal. Chem. 737 (2015) 65 -- 77