Understanding intra-pore electrolyte resistances and distributed capacitances in carbon electrodes used in supercapacitors using a robust modeling process to separate the charge-storage occurring into macro-, meso-, and micro-pore structures

Abstract

In this study, a Modified Generic Electrochemical (MGE) model is introduced for studying rough/porous carbon-based electrode materials employed in electrical double-layer capacitors (EDLC) which contain different types of surface defects. Instead of adopting the common theoretical approach involving the use of transmission line models or ad hoc equivalent circuits, a rational equivalent circuit model has been devised, which permitted us to derive the different equations for each electrochemical technique. The MGE representing the overall electrochemical behavior of EDLCs obtained using the different techniques (e.g., cyclic voltammetry, chronoamperometry, chronopotentiometry, and impedance) is formally derived based on a simple premise considering that the different inhomogeneous surface defects, which are geometrically arranged under equipotential conditions, are not electrochemically equivalent. In this sense, the presence of hierarchically distributed charge-storage processes with different time constants, accounting for the ionic accumulation at the electrode/solution interface, can be ascertained. We verified that is imperative to avoid the determination of the specific capacitances and resistances in EDLCs using a single electrochemical technique or several techniques whose model equations are based on different theoretical premises. The use of the MGE model unequivocally revealed that isolated measurements of the specific capacitance in the absence of the associated intra-pore resistances are not sufficient to ensure the presence of rapid charge storage allied with high-power characteristics. With the appropriate choice of carbon-based materials with very low intra-pore resistances, substantial progress can be made in ushering in the next generation of EDCLs with very high-power characteristics.