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A finite element model for charge transport in conjugated polymers is developed based on transport equations for ionic and electronic charge coupled with the Poisson equation. The model behavior is fully explored, and its complexity is gradually increased to realize a full model that treats non-Fickian diffusion through nonconstant coefficients and that includes ion transport in the electrolyte. The simulation results are compared qualitatively with the experimental results for an ion-barrier-covered PPy(DBS) film during electrochemical reduction, and the model is found to successfully account for the dominant behaviors, including the emergence of a front. One of the key findings of the simulations is that migration must be taken into account to correctly describe ion ingress: none of the various simulations in which ion transport was only by diffusion predicted the experimental results. Another is that the front velocity is proportional to the applied voltage, as found experimentally, and that the cation front can move into the polymer with a velocity v ∼ √t even when the ions move by migration alone.
Wang et al. (Thu,) studied this question.