In this paper, we analyze the effect of electrode surface roughness on ionic polymer metal composite (IPMC) capacitance. We use the linearized Poisson–Nernst–Planck model to describe the charge and electric potential distribution in response to a small voltage applied across the IPMC electrodes. We use perturbation methods to develop a comprehensive understanding of the interplay among the scale of the electrode roughness, the Debye screening length, and the IPMC nominal dimensions on the electrical behavior of IPMCs. We derive a closed-form expression of the IPMC capacitance per unit nominal surface area in terms of the Debye screening length, the IPMC nominal thickness, and physically relevant statistical properties of the rough landscape. We find that IPMC capacitance is largely dictated by the effective electrode surface area when the Debye screening length is considerably smaller than the polymer thickness. In this case, the diffuse charge layers that form at the polymer-electrode interface closely follow the rough electrodes profile. As the Debye screening length increases, diffuse layers do not completely adhere to the electrode profile, and local curvature changes and additional geometric factors contribute to the overall IPMC capacitance. We specialize our findings to different electrode models, including fractal electrodes that have been recently observed in IPMC morphological studies. We corroborate our theoretical findings with experimental data on the capacitance of in-house fabricated IPMCs.

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