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 solution and mass transfer of some chemical components by electro-migration as well as by diffusion. Macdonald 1-3 has made notable contributions to the theory of such cells and has given relatively simple equivalent circuits for special situations. However, recent contributions from Armstrong 4 and Macdonald s indicate clearly the uncertainty which sometimes exists as to the exact form of the equivalent circuit and the difficulties encountered when a circuit is derived by a conventional analytical method.
In the present note it is shown that it may sometimes be advantageous to employ an approach that is the reverse of the one usually employed. Instead of first deriving an explicit expression for, or computing, the cell impedance and later attempting to find a circuit compatible with the expression or computations, one first derives very rapidly an aperiodic circuit for the cell that, apart from inexactness attributable to errors in the model for the electrochemical system that is adopted at the outset, describes exactly in electrical terms the real system. Then one attempts to transform this circuit into a simpler but less accurate equivalent circuit of greater practical value than the initial aperiodic circuit which usually is a 2-dimensional electrical matrix. This procedure is not especially novel but previously it has never been applied to a faradaic-nonfaradaic system of the type here considered. The present note is but a logical extension of reasoning (superficially of high intuitive content but based on thermodynamic and physical principles) used earlier when considering the structure of aperiodic circuits for the faradaic impedance 6. and for an electrode in contact wit.h an electrolyte solution 7 . More explicitly the method * An English digest of this paper is available on application to the author.