Theory of Anomalous Dynamics of Electric Double Layer at Heterogeneous and Rough Electrodes

A generalized model for dynamics of the electric double layer (EDL) at a heterogeneous and rough electrode is developed using the Debye–Falkenhagen equation for the potential. The influence of surface heterogeneities which causes the distribution in relaxation time in the compact layer is included through the current balance boundary constraint at the outer Helmholtz layer. The results for the admittance response are obtained for deterministic and stochastic roughness. The response for the deterministic surface is expressed as a functional of an arbitrary surface profile and the stochastic roughness as a functional of an arbitrary power spectrum of roughness. The dynamics is understood in terms of phenomenological (viz., dynamic diffuse layer and polarization) lengths and various relaxation (viz., compact layer, diffuse layer, and mixed) frequencies resulting from the interaction of compact and diffuse double layer. A strong influence of heterogeneity, finite fractal roughness, electrolyte concentration, and their diffusion coefficient is found. Our model unravels anomalous roughness-dependent pseudo-Gerischer behavior at high frequency, classical Helmholtz behavior at intermediate frequencies, and emergence of CPE at low frequency due to heterogeneity of the surface. Comparison of the theory with experimental data shows good agreement.