Modeling and experimental verification of operation of supercapacitors with carbon electrodes in non-aqueous electrolytes. The energy efficiency

Charge-discharge processes of supercapacitor with carbon black KJEC 600/Li in non-aqueous electrolyte: 1 M LiPF6 in a mixture of ethylene carbonate (1/3), diethyl carbonate (1/3), dimethyl carbonate (1/3) are investigated. Galvanostatic cycling was carried out in the range from 1 to 4 V with currents from 100 to 5000 mA/g of carbon black. The maximum discharge capacity of 196 F/g has been reached. The porous structure and hydrophilic-hydrophobic properties of carbon black KJEC 600 were investigated by the standard contact porosimetry method (MSCP). The following values were obtained: total specific surface area of 2500 m²/g, total porosity of 7.8 cm³/g, hydrophilic porosity of 4.9 cm³/g, hydrophobic porosity of 2.9 cm³/g. The obtained experimental dependence of the energy efficiency has a maximum (80%) at a current of 250 mA/g. Mathematical modeling of charge-discharge processes of the supercapacitor is developed with taking into account the charging of the double electric layer (EDL) and adsorption of lithium ions according to the Butler-Volmer equation and the Frumkin isotherm for the carbon electrode are taken into account. From the comparison of the calculated and measured charge-discharge curves it follows that these curves are satisfactorily consistent with each other, which indicates the correctness of the model. The density of the exchange current and the specific capacitance of the EDL refereed to the true surface found by the fitting are equal to i_0,ad = 2.8 × 10⁻²⁹A/сm² and C_dl = 3.5 μF/сm² respectively. On the basis of the developed model for different specific currents the energy efficiency dependences on the exchange current density of the adsorption reaction were calculated. Interestingly, these dependencies have a minimum. Based on the model, the profiles of the potential the surface coverage of lithium ions were also calculated.