Kavuran, G., Gurgenç, T. & Özkaynak, F. On the modeling of the multi-segment capacitance: a fractional-order model and Ag-doped SnO2 electrode fabrication. J Mater Sci 57, 2775–2793 (2022). https://doi.org/10.1007/s10853-021-06670-y
This study proposes a methodology of electrochemical capacitor modeling via fractional-order impedance equation for porous electrodes fabricated with pure and Ag-doped SnO2 nanoparticles. It was carried out to prove the assumption that fractional-order integrodifferential expressions better model the various real systems. Firstly, the pure and different amounts of silver (Ag)-doped tin oxide (SnO2) nanoparticles were produced using the hydrothermal method. Tin (II) chloride dihydrate (SnCl2·2H2O) was used as an Sn source and (AgNO3) as an Ag source. Hydrothermal synthesis was completed at 200 °C for 24 h. The synthesized particles were calcined at 600 °C for 2 h. All of the structural and morphological properties were investigated by FT-IR, XRD, FE-SEM, and EDX. It has been observed that the hydrothermal method successfully produced nano-SnO2 particles without and with Ag dopant. As a result of the applied procedure, the structural properties of SnO2 nanoparticles, such as physical shape, were changed from spherical-like to nano-sheet with the Ag doping. Next, the nanopowders were coated on AZ31 magnesium sheets. Electrochemical impedance spectroscopy measurements were examined to determine the capacitance of EC materials with Ag-doped SnO2 nanoparticles. Finally, using the multi-objective cost function, the experimentally measured real and imaginary impedance parts are fitted to the proposed fractional-order model by the particle swarm optimization algorithm. It has been proven that fractional-order modeling enables finding the electrical parameters and properties of EC with higher accuracy. Furthermore, the Ag-doped SnO2 electrode can significantly improve electrical performance because of the increase in conductivity. The total capacitance gets increased by 10.788% for 7% Ag-doped SnO2 against pure SnO2.