A ladder network modelling the electrochemical impedance of the diffusion and reaction processes in semi-infinite space.

The Gerischer impedance, i.e., the diffusion-reaction impedance of an ionic species in semi-infinite space, has been modelled by means of a novel simple equivalent ladder electric circuit constituted by a finite number of resistors and capacitors, which corresponds to the Cauer structure obtained from development into continued fractions. The Nyquist plots of the impedance of the ladder network or Cauer circuit and the deviation with respect to the Gerischer impedance have been originally analysed as a function of the number of circuit elements. From the Cauer equivalent circuit, a new and simple expression modelling the Gerischer impedance at the limit of the lowest frequencies has been derived.