The impedance of a tubular electrode - A model for a porous electrode
A cylindrical tube is used as the basis for a two-dimensional mathematical model to calculate the impedance of a flooded porous electrode. The model incorporates charge-transfer, mass-transfer, and ohmic resistances to obtain the axial and radial dependencies of the concentration and potential profiles. A linearized Butler-Volmer kinetic expression for a simple redox reaction O + e yielding R is used, in conjuction with analytical expressions for the surface concentration and overpotential, to compute the open-circuit impedance. The results of the two-dimensional model, which omits double-layer charging, are compared with the results of a more standardly applied one-dimensional model in which radial variations are neglected, with and without double-layer charging. The simpler-to-apply one-dimensional model is found to be satisfactory when mass-transfer and ohmic resistances are small with respect to charge-transfer resistance. The omission of double-layer charging does not introduce error into the two-dimensional model in the frequency range in which capacitive-like effects are caused by mass-transfer limitations.