(389f) Moving Front Dynamics of Ions in Conjugated Polymer Films

Recent experiments on ion injection into a conjugated polymer film have shown that the location of the advancing ion front increases as the square root of time [Stavrinidou et al., Adv. Mater. 25, 4488-4493 (2013)], a scaling typically associated with diffusive transport. However, the potential difference across the film is on the order of volts; hence, one would expect that ion transport is dominated by electro-migration as opposed to diffusion. In this work, we analyzed the moving front dynamics of ions in a planar mixed ionic-electronic conducting polymer film. The film contains a fixed negative charge density supplied by the polymer backbone, which is initially compensated by a uniform density of holes (electron vacancies). As the cations invade the film the holes evacuate across a working electrode to maintain overall electroneutrality; thus, an ionic current is converted to an electronic signal. We modeled the charge carrier transport via the Poisson-Nernst-Planck (PNP) equations. Under the (reasonable) assumption that holes are infinitely more mobile than cations, and for a strong driving voltage, a similarity transformation reduces the PNP equations to coupled nonlinear ordinary differential equations that can be readily solved numerically. Moreover, the similarity transformation clearly elucidates the square-root-of-time front scaling, with an effective voltage-dependent diffusivity. We compare the similarity solution to numerical solution of the full PNP equations, finding excellent agreement.  We also compare our modeling results to experimental data: although our model captures the variation of the front location, qualitative differences between the spatial cation profiles are seen, for which we offer plausible explanations.