THE IMPEDANCE OF THE PLANAR DIFFUSE DOUBLE-LAYER - AN EXACT LOW-FREQUENCY THEORY

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 Z(el) of the form [1] 1/Z(el) = kappa K(omega)[delta(2)A(2) + delta(3)A(3) + delta(4)A(4) + ...], where K(omega) is the complex conductance of the electrolyte solution and delta is a (small) frequency parameter given by [2] delta(2) = omega ($) over bar lambda/kappa(2)kT' ($) over bar lambda being a typical ion drag coefficient and kappa(-1) the Debye screening length. The resulting series is expected to be valid from DC to at least 10 kHz. Exact analytic expressions for A(2), A(3), and A(4) as functions of the zeta potential zeta 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 zeta and electrolyte composition. (C) 1995 Academic Press, Inc.