ONE-DIMENSIONAL GROWTH-MODEL FOR COMPETITION BETWEEN INTERMOLECULAR AND INTRAMOLECULAR PROPAGATION OF THE CONDUCTING ZONE AT CONDUCTING POLYMERS-COATED ELECTRODES

The conducting zone of an electronic conducting polymer propagates by intermolecular and intramolecular charge transport in response to electrochemical switching. The sluggish intermolecular propagation is predicted to disperse the conducting zone. In order to discuss the influence of the types of propagation, a one-dimensional growth model is presented. The model film is an assembly of randomly connected linear polymers whose molecular length obeys a given distribution function. When the conducting polymer reaches length l at time t passing over k molecular boundaries, the length is given by l = u(t - kr), where u is the intramolecular propagation speed and tau is the time of intermolecular conversion. Then the probability of making the length be l is expressed in general form by a distribution function. In order to evaluate the length explicitly, a uniform distribution function is used for the computation. The conducting zone thus computed grows linearly with time, but the conducting front becomes indistinct. The dispersion of the conducting zone obeys Fick's second law. The computation is extended to a normal distribution function. The degree of dispersion is not diffusional but shows a linear time dependence.