Self-Similar Response of Electrode Polarization for Binary Electrolytes in Parallel Plate Capacitor Systems.

Classical electrochemistry problem of polarization of an electrode immersed in a symmetric binary electrolyte and subjected to a small external ac voltage is revisited. The Nernst-Planck equations are simplified to the Debye-Falkenhagen equation, which is solved together with the Poisson equation, leading to analytical formulas for the space charge density and impedance of the system for two parallel plate electrodes. We then define a limit of thin electrical double layer and illustrate the emergence of the characteristic time scale, τ