Effect of electrode surface roughness on the electrical impedance of ionic polymer-metal composites

In this paper, we study the effect of electrode surface roughness on the electrochemical response of ionic polymer-metal composites (IPMCs) subjected to a time-varying voltage input. We use the linearized Poisson-Nernst-Planck model to describe the dynamics of the electric potential and mobile counterions' concentration within the polymer. We derive a closed form solution of the three-dimensional boundary value problem by employing the method of matched asymptotic expansions. Specifically, the polymer region is decomposed into a bulk region, where mainly diffusive phenomena take place, and boundary layers in proximity of the polymer-electrode interfaces, where charge storage develops as a function of the electrode surface roughness. Leading order solutions are derived and matched on account of electric potential, counterions' concentration, and counterions' flux continuity. We find that IPMC charge storage is greatly enhanced by the increase in effective electrode surface area. On the other hand, bulk diffusion phenomena remain largely independent of the microscopic topography of the electrode. Thus, the hypothesis of rough electrodes is found to be very well suited in interpreting the anomalous values of IPMC capacitance which scales linearly with the electrode's actual surface area.