Investigation into the influence of interdigital parameters on electrochemical performance for in-plane supercapacitors via mathematical modeling and conformal mapping techniques

Herein, we propose a mathematical model and corresponding analytical transformation approach based on the conformal mapping technique and equivalent circuit conversion method to investigate the influence of interdigital parameters such as electrode length (Le), width (We), and spacing (De) on the electrochemical performance of in-plane supercapacitors (SCs) fabricated via CO2 laser processing on polyimide film and encapsulation with PVA/H3PO4 gel electrolyte. We conclude from the experiments that the small gap ensures a compact structure, a high electrode utilization rate, and a short anion/cation transport channel, while the large electrode area generates a sufficient electrostatic double-layer effect to improve areal capacitance. Furthermore, interdigital length and width are particularly sensitive to capacitve performance, implying that electrode area plays a critical role. Eventually, the optimal electrode parameters are 10 mm (Le), 1.5 mm (We), and 0.35 mm (De), delivering high areal capacitance (2.43 mF/cm2), relatively low resistance (≈46 Ω) and excellent areal energy density (225 μWh/cm2) and power density (3.65 mW/cm2). Because the experimental values are compatible with the simulation curves and the different percentages between them are controlled within 13 %, the mathematical model has theoretical significance for the design of interdigital electrodes. •Capacitive performance of interdigital SCs is investigated by mathematical modeling and conformal mapping techniques;•An equivalent circuit conversion method is proposed to analyze the resistance of interdigital graphene electrodes;•The difference percentages between experimental and simulation values are controlled within 13 %.