Dual transmission line with charge-transfer resistance for conducting polymers

To describe charge conduction in conducting polymers a dual transmission line with one resistance describing electronic motion in the polymer and a second resistance describing ionic motion in the pores has proved applicable to a number of systems. A further feature of ac impedance plots for these polymers is a high-frequency semicircle. This may be attributed to a charge-transfer resistance and double-layer capacitance at either the electrode/polymer or the polymer/electrolyte interface. A general expression for such a charge-transfer resistance is derived and it is shown that the current will be proportional to the difference in Nernst potential across such a resistance. This circuit element together with a double-layer capacity is then combined with the dual transmission line. A general expression for the ac impedance for the combined circuit is obtained. Care has to be taken to use the right potentials, Nernst, Donnan or the actual potential. Depending on the relative resistances in the transmission line different types of behaviour can be found. In particular the variation of the real part of the impedance at high frequency can be used to determine whether the charge-transfer resistance is at the electrode or at the electrolyte interface. The procedure is exemplified with results from polypyrrole.