Aperiodic equivalent circuit for charge permeable thin-layer cells of symmetric, asymmetric types

Abstract

In this paper, some of the various predictions of the original BBB (Barker–Brumleve–Buck) circuit, primarily the high frequency migration (geometric), and the low frequency diffusion–migration sub-circuit units, are illustrated using a newer procedure that was not available in our laboratory in 1980: SPICE circuit simulation. The aperiodic Rs and Cs generate the low-frequency Warburg characteristics. The Poisson string generates the high frequency geometric cell capacitor in parallel with the unperturbed-concentration ac resistance. The well known two feature impedance plane plot arises, for reversible interfacial ion and electron transport, from this simple circuit. The usual three feature impedance plane plots can follow for slow, potential-dependent ion and/or electron transfers with the usual linearized activation kinetics, by addition of parallel activation resistance and double layer capacitance networks for each ion requiring activation to cross the interfaces. Likewise the uncompensated solution resistance gives a fourth feature that is not often observed experimentally except as a non-zero real intercept at highest frequencies. The theory and the basic two-feature circuit of nearly 20 years contains most of Albery's recent contributions, as well as much more advanced analysis. The new analysis using SPICE shows the scope and limits of classical transmission lines compared with the more general BBB circuits.