Regular Article
The Impedance of the Planar Diffuse Double Layer: An Exact Low-Frequency Theory

https://doi.org/10.1006/jcis.1995.1131Get rights and content

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 Hz), and provides high-frequency corrections (>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 1Zel = 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 by δ2 = ωΛ̄κ2kT′ (2)Λ̄ being a typical ion drag coefficient and κ-1 the Debye screening length. The resulting series is expected to be valid from DC to at least 10 kHz. Exact analytic expressions for A2, A3, and A4 as functions of the zeta potential ζ of the unperturbed electrode and the electrolyte compositional properties are derived. Thus, the diffuse double-layer contribution to the electrode conductance and capacitance can be explicitly exhibited to leading order in frequency for all values of ζ and electrolyte composition.

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