Influence of electrode surface roughness and steric effects on the nonlinear electromechanical behavior of ionic polymer metal composites

In this paper, we analyze the influence of electrode surface roughness and steric effects on the nonlinear electromechanical behavior of ionic polymer metal composites (IPMCs). We use the modified Poisson-Nernst-Planck equations to describe the electric potential and mobile counterion distributions within the IPMC for a steady voltage applied across the IPMC rough electrodes. We present an analytical solution of the nonlinear three-dimensional boundary value problem based on the method of matched asymptotic expansions. The distribution of mobile counterions within the polymer region is characterized by thin boundary layers in the proximity to the polymer-electrode interfaces, where enrichment and depletion of mobile charges take place. The presence of rough landscapes drastically increases the polymer-electrode surfaces and thereby significantly improves the overall charge storage. We determine closed-form expressions for the average bending moment produced by the IPMC and for its average stored charge and capacitance. We show that the bending moment produced by an IPMC is linearly proportional to the stored charge, which in turn increases nonlinearly as the voltage applied across the electrodes increases. The average charge stored in the IPMC increases as the electrode surface roughness increases and decreases as steric effects become prominent.