Theory for Reversible Electron Transfer Admittance with Diffusion and Electric Double Layer Coupling at Rough Fractal Electrodes

Abstract The theory for DC bias admittance of rough electrode is developed for reversible electron transfer kinetics; coupled to migration in electric double layer and solution resistance. The electronic screening in metal jellium and non‐uniform interfacial dielectric in electric double‐layer (EDL) is accounted in modeling the electric field ( responsible for migration. The piece‐wise solutions in different dielectric regions (with size‐corrected ionic screening length) are obtained to estimate . This approach accounts for the under‐screening phenomenon in diffuse‐EDL for concentrated electrolytes, which accounts for the non‐monotonic ionic strength‐dependent screening length and . The effective interfacial diffusion coefficient is modeled, accounting for the loss of configurational entropy in EDL and electrostatic interactions, used for migration flux. Entropy governed interfacial diffusion coefficient is lower by a factor of as compared to bulk. The finite fractal roughness is accounted for using a power‐law power spectrum. Impedance response is analyzed for three roughness parameters: fractal dimension, lower cut‐off length, and topothesy length. Theory shows impedance is enhanced while qualitative frequency shifted to lower values significantly with the inclusion of migration while roughness suppresses it. This approach circumvents the non‐linearities of the Nernst–Planck approach for dilute solutions while quantitatively explaining experimental data.