Impedance Response of Electrochemical Interfaces: Part I. Exact Analytical Expressions for Ideally Polarizable Electrodes

In this work, we revisit the impedance response of the electrical double layer (EDL) at an ideally polarizable electrode which is immersed in a dilute, symmetric, and monovalent electrolyte solution. Analytical impedance expressions are derived from the standard Poisson-Nernst-Planck (PNP) theory. These expressions are formally exact under the linear polarization approximation. Frequency dispersion of the double- layer capacitance (C-dl), ascribed to finite-rate ion transport in the electrolyte phase, is revealed. At the potential of zero charge (pzc), we compare the new impedance expression with that derived from the orthodox Gouy-Chapman-Stern (GCS) model. We reveal that the series connection of a compact layer and a diffuse layer in the GCS model tacitly prescribes a zero potential gradient at the solution-side boundary, which is, rigorously speaking, problematic. The bearing of this problematic assumption becomes more significant when the double layer is confined in narrower space. The analytical results derived at the pzc are good approximations (with a relative error in terms of C-dl less than 14% for reasonably-valued parameters) when the electrode potential is away from the pzc less than 0.2 V.