A physically consistent electric circuit to interpret the galvanostatic charge-discharge curves of electric double layer capacitors

The galvanostatic charge-discharge (GCD) curves of electric double layer capacitors (EDLCs) are interpreted by means of a physically consistent electric circuit which includes elements to separately model the diffusion and electrostatic processes. Three commercial EDLCs with nominal capacitances in the range from 0.1 to 1 F and maximum voltage 5 V, are selected. The time evolution of the electric voltages of the EDLCs obtained during a GCD cycle, is gathered for different values of the current amplitude. The results are interpreted by means of an electric circuit constituted by the series combination of the high-frequency resistance, the capacitance, and a branch with the parallel combination of the internal or diffusion resistance and capacitance. This dynamic circuit is based on the low-frequency developments of the restricted Warburg diffusion impedance. A simple mathematical procedure is novelty proposed to determine the elements of this electric circuit. The observed asymmetry in the charge and discharge curves during the galvanostatic cycling, the energy balance in the EDCLs, as well as the maximum charge time and the coulombic efficiency, are analysed and discussed. • A physically consistent circuit is proposed to interpret GCD curves of EDLCs. • Diffusion capacitance describes asymmetrical GCD curves at short times. • Energy balance for the GCD of EDLCs including diffusion processes, is presented. • Diffusion capacitance can be estimated as two sevenths of the EDLC capacitance.