β Scribed by J.R. Macdonald
No coin nor oath required. For personal study only.
The question of the most appropriate equivalent circuit to use in analyzing impedance measurements for a given electrolytic cell situation is an important one which is currently attracting renewed interest l-s. An incorrect choice can lead to misleading conclusions about the processes occurring in the cell. In this note, I shall consider only a cell containing a binary electrolyte; thus no supporting indifferent electrolyte is added, and only two mobile charge types of opposite sign are present. The results should apply not only to dissociated charge in liquid solvents but also to many fused salt and solid material situations.
In a recently published paper 6 , a quite general exact microscopic theory of the impedance of a binary-charge system is presented which allows the charges to have arbitrary mobilities,/.t n and/ap, and arbitrary valence numbers, Zn and Zp. The situation analyzed includes extrinsic as well as intrinsic conduction; here, however, only intrinsic will be considered. This treatment involves the usual boundary condition dimensionless param. eters rp and r n. When one of these is zero, the electrode is blocking (ideally polarized) for the charge type involved; alternatively, when r n = 0% say, negative charges discharge and/or appear at the electrode (first-order reaction) without perturbing the steady-state concentration there, equivalent to an infinite reaction rate for the charges involved. Although rp and rn do not allow the possibility of rectification, they do cover the entire range of conditions from complete blocking to infinite reaction rates and are thus relatively general.
Because of the complexity of the closed-form analytical results of the above theory, only the zero-frequency limiting values of the frequency-dependent capacitance, Ci, and resistance,:Ri, were examined in detail in ref. 6. A further paper is in preparation which discusses the freqiaency response of the overall cell impedance and admittance components in detail for all frequency regions of interest for the intrinsic conduction situation 7. The analysis of the Warburg response region, one of the main regions of usual electrolytic interest, has yielded several unexpected results which seem likely to explain a considerable body of experimental measurements and thus warrant this preliminary discussion. It is
π SIMILAR VOLUMES
The derivation of equivalent electrical circuits for cells is a matter of considerable difficulty when the cell impedance is affected by several factors such as distributed space charges in the solution near the electrodes, reactions at one or both electrodes, the finite dielectric constant of the s