The impedance of the planar diffuse double layer: An exact low-frequency theory

Abstract

The classical Gouy-Chapman-Grahame theory for the impedance of the diffuse double layer extending out from a planar electrode is extended to incorporate the effects of ionic diffusion normal to the plane. The resulting theory accounts quantitatively for the divergence of the double-layer resistance at low frequencies (10 kHz) to the capacitance due to diffusion effects. The transport equations are solved by a perturbation theory approach, which produces a low-frequency expansion for the diffuse layer small-signal impedance Zel of the form 1 Zel = κK(ω)[δ2A2 + δ3A3 + δ4A4 + …], (1) where K (ω) is the complex conductance of the electrolyte solution and δ is a (small) frequency parameter given ..