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 ( L e ), width ( W e ), and spacing ( D e ) on the electrochemical performance of in-plane supercapacitors (SCs) fabricated via CO 2 laser processing on polyimide film and encapsulation with PVA/H 3 PO 4 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 ( L e ), 1.5 mm ( W e ), and 0.35 mm ( D e ), delivering high areal capacitance (2.43 mF/cm 2 ), relatively low resistance (≈46 Ω) and excellent areal energy density (225 μWh/cm 2 ) and power density (3.65 mW/cm 2 ). 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.