Correlating electrochemical impedance with hierarchical structure for porous carbon-based supercapacitors using a truncated transmission line model

This work considers the relationship between the morphology of porous carbon materials used for supercapacitors and the electrochemical impedance spectroscopy (EIS) response. EIS is a powerful tool that can be used to study the porous 3-dimensional electrode behavior in different electrochemical systems. Porous carbons prepared by treatment of cellulose with different compositions of potassium hydroxide (KOH) were used as model systems to investigate the form vs. electrochemical function relationship. A simple equivalent circuit that represents the electrochemical impedance behavior over a wide range of frequencies was designed. The associated impedances with the bulk electrolyte, Faradaic electrode processes and different pore size ranges were investigated using a truncated version of the standard transmission line model. The analysis considers the requirements of porous materials as electrodes in supercapacitor applications, reasons for their non-ideal performance and the concept of ‘best capacitance’ behavior in different frequency ranges. Graphical Abstract: The electrolyte ions penetrate the macropores, into the mesopores and finally reach the micropores. The capacitance measured by impedance spectroscopy is a function of frequency and porous structure.