Modeling and analysis of the properties of supercapacitors and working electrode systems containing polymer electrode materials

Accurate impedance modeling of pseudocapacitive supercapacitors is essential for understanding charge storage mechanisms. This paper investigates the electrochemical characteristics of conducting polymers—polypyrrole (PPy), poly(3-n-octylpyrrole), and poly(phenylpyrrole)—in LiClO 4 and NBu 4 ClO 4 electrolytes. Using Electrochemical Impedance Spectroscopy (EIS) across a 10 mHz–1 MHz range, impedance spectra were analyzed via three fractional-order models. A novel ladder model is proposed, utilizing parallel branches of fractional-order capacitances (CPEs) and resistances to represent the distributed capacitive and diffusive response of the electrode. Model parameters were identified using the Particle Swarm Optimization (PSO) algorithm. The proposed model outperforms the compared fractional-order approaches for the studied systems, achieving normalized fitting errors below 0.1. The optimized performance of the PPy/NBu 4 ClO 4 system, characterized by the highest capacitance and lowest resistance, is linked to favorable ion–polymer interactions that reduce transport barriers. These findings advance physically interpretable models for the diagnostics and performance prediction of polymer-electrode supercapacitors.