Moving front phenomena in the switching of conductive polymers

Abstract

Abstract A theoretical analysis of mass transport phenomena in conductive polymer-modified electrodes is presented. In the first part, the electronic transport properties of such polymers are described by two different diffusion coefficients: one relates to the electron mobility in the conductive state, the other describes electronic transport in the non-conductive state. Thus, this approach postulates a discontinuity for the electron diffusion coefficient with the local concentration of oxidized states within the film. It is shown that this hypothesis leads to the concept of a moving front which separates an area where the film is in its conductive state from one where it is in its insulating state. The same conclusions are drawn when D increases steeply with the concentration of oxidized sites, i.e. the doping level of the polymer. Thus, moving front phenomena appear to be intrinsically linked to the specificity of conductive polymers, i.e. the dramatic change in electronic conductivity upon switching. Assuming that the electrochemical process, for a chronoamperometric experiment, is controlled by electron diffusion leads to a front velocity proportional to t −1/2 and to the diffusion coefficient of the electron in the conductive zone. When this coefficient tends towards infinity a contradiction to the assumption of a process controlled by electron movements occurs. In this case, the electrochemical process can be controlled either by counter-ion movements or by the rate of the electrochemical reaction that takes place at the moving boundary; the velocity of the front is not proportional to t −1/2 and the chronoamperometric response can deviate from the usual Cottrell behaviour. In the second part of this work, the counter-ion movement is analysed. It is proposed that the conducting properties of the material might lead to a marked enhancement of the migrational aspect of ion transport within the internal structure of the film. It is then shown that describing ion transport as a migration phenomenon instead of a diffusion phenomenon leads again to the concept of a moving front. Several propagation equations are demonstrated: the first describes the concentration profile of counter-ions and the second describes the potential profile within the film. These two equations indicate that both concentration and electric potential propagate in the material at the same velocity. This velocity is proportional to the driving electric field, i.e. the potential drop that develops at the conductive|insulating interface or within the insulating zone of the material and varies with anion mobility.